Legal Theory Lexicon

Legal Theory Lexicon 062: Path Dependency

Introduction  The phrase "path dependency" is used to express the idea that history matters--choices made in the past can affect the feasibility (possibility or cost) of choices made in the future.  This entry in the Legal Theory Lexicon introduces this idea to law students, especially first-year law students, with an interest in legal theory.

The General Idea of "Path Dependency"  The general idea of path dependency is that prior decisions constrain (or expand) the subsequent range of possible or feasible choices.  That is, a decision, d, made at t₁ may affect the choice set, S = (c₁, c₂, . . . c_n) at t₂.  We can define a choice set as a set of actions that a given agent could take.  Or to expand the path metaphor, if we imagine a network of paths through time, from past to future, decisions to branch at an earlier point on the chosen path may affect the destinations that one can reach from a later point on the path.  Sometimes, if we choose the left fork, we may be able to reach exactly the same destinations we could have reached via the right fork, but sometimes, our choices foreclose some possibilities altogether.  It isn’t always the case that in the long run, there’s still time to change the road you’re on.

The notion of path dependency is associated with the discipline of economics and also with political science.  In the context of economics, there is a tendency to associate "path dependency" with effects on the costs of various options.  But the phrase "path dependency" can be (and is) used in a more general sense--to encompass the ideas of feasibility and possibility.  The terminology doesn't matter for its own sake, but it is important to be clear about the meaning of the phrase when discussing path dependency.

Specifying Parth Dependency This general notion can be specified in various ways.

The Type of Effect First, we can specify the type of effect that d₁ has on the choice set.  One type of seffect is an effect on which actions are members of the choice set.  Thus, by making a decision d at t₁, the resulting choice set at t₂ would have members c₁, c₂, and c₃, but if the decision had been d′ (d prime), then the choice set at t₂ would have members c₁, c_3, and c₄.  In this illustrative case, making decision d rather than d′ both added and subtracted from the choice set at t₂.  Another type of effect is an effect on the costs associated with the actions that are members of the choice set.  That is, decision, d, might result in the price of a given choice P(c₁) being greater than that price would have been if an alternative decision, d′, had been made.  Notice, however, that if we include price in the specification (or description) that designates a choice, then the second type of effect (that is, cost effects) are reducible to the first type of effect (possibility effects).

What Causal Mechanisms?  A second way in which we can specify the general notion of path dependency is to describe the causal pathway by which decisions affect future choices.  On the one hand, one might use the phrase “path dependency” to refer to all causal mechanisms.  On the other hand, we could reserve the phrase for a specific type of causal mechanism.  For example, Paul Pierson has suggested that the notion of path dependency should be limited to what he calls “positive feedback.”  Positive feedback (or self-reinforcement) involves the idea that as time progresses, the relative benefit of maintaining some feature of the system (and hence the relatively costliness of modifying or eliminating that feature) increases.  Once a constitution has been adopted and gone into effect, it becomes more costly to adopt a different constitution.  Once a federal system has been created out of sovereign subunits, it becomes more costly to eliminate that the federal (or national) government.  Once a judicial precedent has been established and relied upon, the costs of reversal grow.

Remediable and Nonremediable Path Dependency  A third way in which we can specify the idea of path dependency is by differentiating between “remediable” and “nonremediable” path dependency.  Path dependency is remediable if there are some points on the path at which there is an alternative decision, d′, such that if the decision had been d′ rather than d, the outcome would have been better (relative to some goal or criteria for evaluation).  Path dependency is nonremediable if no alternative could have improved the outcome.  For the idea of nonremediable path dependency to be plausible, we must assume that we are talking about particular choices in relationship to particular consequences within some time frame.  Thus, the framers’ decision to create equal suffrage in the Senate might be nonremediable with respect to the goal of establishing majoritarian democracy if all of the alternatives (say, vetoes of national legislation by a single state governor) had been worse with respect to this goal.

Applications in Normative Legal Theory

Path dependency interacts with legal theory in a variety of ways.  One simple example--stare decisis--is described by Oona Hathaway:

Path dependence theory is relevant to the common law system for a simple reason: the doctrine of stare decisis. Under the doctrine of stare decisis et non quieta movere--"let the decision stand and do not disturb things which have been settled" [FN88]--decisions of higher courts are controlling in subsequent cases involving similar circumstances. [FN89] Courts also give their own prior decisions great weight, though they are not strictly bound to follow their own precedents. [FN90] Furthermore, even when decisions of other *623 courts are not explicitly binding, they can provide persuasive authority. [FN91] Judges who follow the doctrine thus generally apply decision rules that entail explicit reliance on earlier choices and thereby generate path dependence.

Another example is provided by a recent article by Lucian Arye Bebchuk and Mark J. Roe.  They argue that initial decisions made about the form of corporate organization create path dependencies--making changes in form more costly or infeasible.  And a final example is provided by Article V of the United States Constitution.  Article V makes amendment difficulty by subjecting amends to a supermajoritarian process of proposal and ratification.  Once the Constitution of 1789 had been adopted and gained legitimacy, "path dependency" made substantial changes without supermajority support infeasible.

Conclusion  The idea of path dependency is now a familiar one to many legal theorists, but its use in academic legal discourse is frequently vague or ambiguous.  I hope this brief introduction will give you a more precise sense of

Online Resources

Lawrence B. Solum, Constitutional Possibilities (forthcoming Indiana Law Journal).

Bibliography

Paul Pierson, Increasing Returns, Path Dependence, and the Study of Politics, 94 American Political Science Review 251 (2000)

Paul Pierson, Politics in Time: History, Institutions, and Social Analysis (Princeton University Press 2004)

William H. Sewell, Three Temporalities: Towards an Eventful Sociology, The Historic Turn in the Human Sciences 262-63 (Ann Arbor, University of Michigan Press 1996)

S.J. Liebowitz & Stephen E. Margolis, PATH DEPENDENCE, LOCK-IN, AND HISTORY, 11 J.L. Econ. & Org. 205 (1995)

Oona A. Hathaway, PATH DEPENDENCE IN THE LAW: THE COURSE AND PATTERN OF LEGAL CHANGE IN A COMMON LAW SYSTEM, 86 Iowa L. Rev. 601 (2001)

Lucian Arye Bebchuk & Mark J. Roe, A THEORY OF PATH DEPENDENCE IN CORPORATE OWNERSHIP AND GOVERNANCE, 52 Stan. L. Rev. 127 (1999)

(This entry was last revised on November 11, 2007.)

Legal Theory Lexicon 060: Efficiency, Pareto, and Kaldor-Hicks

Introduction  Almost every law student get's some introduction to normative law and economics in their first year of law school.  One of the basic ideas of normative law and economics is that the law should be "efficient."  But what does efficiency mean?  For economists, "efficiency" is a technical idea--with only a tangential connection to the use of "efficiency" in ordinary speech.  In order to understand economic efficiency, we will look at what are called the Pareto principles and a related idea that is sometimes called Kaldor-Hicks efficiency.

In addition to explicating the idea of efficiency, we will take a qucik look at some of the criticisms that might be made of this concept.  Although many economists operate on the assumption that "efficiency" is an uncontroversial good, that conclusion is controversial both inside and outside of the discipline of economics.

As always, the Legal Theory Lexicon is aimed at law students, especially first-year students, with an interest in legal theory.  This is very much a "quick and dirty" look at a topics upon which whole books can be written.

The Idea of Utility and the Problem of Measurement  There are several plausible formulations of normative economics, but almost all of normative economics begins with the fundamental idea of utility as a conception or measure of the good. Economists may disagree about the nature of utility, the relationship of utility to social welfare, and the role of welfare in public policy, but most (if not all) economists would assent to the abstract proposition that ceteris paribus more utility is a good thing.

Beyond such very general agreements, there are many disagreements within economic theory. One key divide is between cardinal and ordinal interpretations of utility. An ordinal utility function for an individual consists of a rank ordering of possible states of affairs for that individual. An ordinal function tells us that individual i prefers possible world X to possible world Y, but it doesn’t tell us whether X is much better than Y or only a little better.  A cardinal utility function yields a real-number value for each possible world. If we assume that utility functions yield values expressed in units of utility or utiles, then individual i’s utility function might score possible world (or "state of affairs") P at 80 utiles and possible world Q at 120 utiles.

The distinction between cardinal and ordinal utilities is potentially important for utilitarianism, at least on certain interpretations. As a theory of evaluation, utilitarianism is the view that an action is the best action if and only if the action maximizes utility when compared with all possible alternative actions. For technical reasons, utilitarianism requires both cardinality and full interpersonal comparability.  But both cardinality and interpersonal utility comparisons are problematic.  It is difficult to measure cardinal utilities for even a single individual. 

And it is even more difficult to compare utilities among different persons.  How can we compare the value that I assign to consuming a glass of fine wine with the value that you assign to imbibing a fine single-malt scotch?  And some things seem even more incommensurable: how do we compare the value that Ben derives from viewing a beautiful photograph by Ansel Adams to the joy that Alice takes in serving meals to the homeless on Thanksgiving Day?  Or Ben's satisfaction from solving difficult math problem with Alice's pleasure in a new pair of Jimmy Choo's?  These examples suggest that the problem of interpersonal comparison may be compounded by the problem of incommensurability--the idea that some preferences may not be comparable on the same scale.

This point about the difficulties faced by utilitarianism is closely related to the history of welfare economics, the explicitly normative branch of economic theory. Both cardinality and interpersonal comparability pose measurement problems for economists. The challenge for welfare economics was to develop a methodology that yields robust evaluations but does not require the cardinal interpersonally comparable utilities.

The Pareto Principles  This is the point at which the Pareto principles arrive on the scene. Suppose that all the information we have about individual utilities is ordinal and not interpersonally comparable. In other words, each individual can rank order states of affairs, but we (the analysts or policymakers) cannot compare the rank orderings across persons. The weak Pareto principle suggests that a state of affairs P is socially preferable to state of affairs Q, if everyone’s ordinal ranking of P is higher than their ranking of Q. Weak Pareto doesn’t get us very far, because such unanimity of preferences among all persons is rare.

The strong Pareto principle suggests that state of affairs P is socially preferable to state of affairs Q, if at least one person ranks P higher than Q and no one ranks Q higher than P.  Or to put it more colloquially: strong Pareto says that it is good to make one person better off if no one will be made worse off. Unlike weak Pareto, strong Pareto does permit some relatively robust conclusions. The so-called new welfare economics was based on the insight that market transactions without externalities satisfy strong Pareto. If the only difference between state P and state Q is that in P, individuals i1 and i2 engage in an exchange (money for widgets, chickens for shoes) where both prefer the result of the exchange, then the exchange is Pareto efficient—and hence satisfies the strong Pareto principle. A state of affairs where no further Pareto efficient moves (or trades) are possible is called Pareto optimal. The assumption about externalities is, of course, crucial. If there are negative externalities of any sort, then the trade is not Pareto efficient.

From Pareto to Kaldor Hicks  Because Pareto efficiency assumes no negative externalities, it has significant limits as a normative concept.  For example, there are many questions of legal policy in which externalities are particularly important--pollution is a class example.  If I operate a factory that pollutes the air or water, my action may cause harms to my neighbors.  If even one person would lose by the move from state P to state Q, then that move is not Pareto efficient.  So if Pareto efficiency were the only normative principle available to law and economics, the consequence would be that economics would have nothing to say about many of the most important legal questions, e.g. questions of environmental law.

Kaldor-Hicks is a technique for extending the normative implications of economic analysis.  Here is how it works.  We take a situation in which their are externalities, e.g. pollution that affects third parties. Let's assume that markets can't reach a Pareto-efficient outcome.  That assumption might be accurate because of high transactions costs, as in the case where the pollution impacts on so many individuals that bargaining is impractical or costly.  Counterfactually, however, we can imagine that there were zero transaction costs.  We can then ask what outcome would occur if those who were effected by the externality (the pollution) were compensated.  Outcomes that would be Pareto-efficient if there were zero transaction costs are Kaldor-Hicks efficient.

Kaldor-Hicks extends normative law and economics to a wide range of situations in which externalities and transaction costs prevent markets from reaching Pareto-efficient outcomes.

Criticisms of Efficiency  Does efficiency (either Pareto or Kaldor-Hicks) provide an attractive normative yardstick by which legal policies may be judged?  That's a complex question, but we can quickly explore a few critical ideas:

Wealth Effects  When Pareto is applied to market transactions, preferences (or utility) is interpreted as a function of willingness to engage in market transactions (or willingness to pay).  But willingness to pay is a function of wealth.  Thus, someone who is very poor may be willing to engage in degrading or dangerous work, because they have no real alterantive.  But this does not mean that the efficient transaction is better than the alternative, which might involve a redistribution of wealth that would obviate willingness to engage in degrading work.

Bad Preferences  Pareto and Kaldor-Hicks assume that state A is better than state B on the basis of individual preferences.  But preferences aren't fixed.  Preferences can change for a variety of reasons and some preferences may be better than others.  For example, the preference to sexually abuse children is considered evil--satisfying it is not a moral good.  Efficiency takes preferences as a given: it can't tell us whether the law should attempt to shape or alter preferences.

Kaldor-Hicks and Rights  Kaldor-Hicks characterizes a move from state P to state Q as efficient even if a third party is injured by the move.  That injury may involve unfairness or a violation of the third party's rights.  From a consequentialist perspective, rights violations may have no significance in themselves, deontological normative theories do afford moral signficance to rights.

Efficiency & Social Welfare Functions  Some economists move beyond Pareto and Kaldor-Hicks and embrace what are called "Bergson-Samuelson Social Welfare Functions."  There is a separate entry (Social Welfare Functions) in the Legal Theory Lexicon, but the general idea is to reintroduce interpersonal comparability for individual utilities.

Conclusion  Efficiency is one of the bedrock ideas for normative law and economics.  The point of this Lexicon entry is to give you the tools to understand what economists mean by efficiency.

(This entry was last revised on October 28, 2007.)

Legal Theory Lexicon 052: Property Rules and Liability Rules

Introduction One of the most famous distinctions in contemporary legal theory was made popular by Guido Calabresi & A. Douglas Melamed s famous article, Property Rules, Liability Rules, and Inalienability: One View of the Cathedral.  The core idea is simple.  Legal rules that create private causes of actions (or claims for relief) can be sorted into two kinds.  Kind one consists of rules that entitle the claimant to an injunction.  Kind two consists of rules that entitle the claimant to damages.  The first kind of rule is associated with property rights--hence, we can call the first kind "property rules."  The second kind of rule is associated with tort liability or contractual liability--hence, we can call the second kind "liability rules.  The distinction between property rules and liability rules is important, because injunctions and damages have different effects on future behavior and on negotiated settlements to claims.

This post in the Legal Theory Lexicon Series is aimed at law students--especially first-year law students--with an interest in legal theory.  As always, this is a very short introduction to a complex topic.  I've provided references for further reading and a deeper understanding.

Calabresi & Melamed's Famous Formulation "Another View of the Cathedral" is one of those articles that every law student should read.  But to get us started, let's quote the famous passages from near the start of the article where the distinction between property rules and liability rules is introduced:

An entitlement is protected by a property rule to the extent that someone who wishes to remove the entitlement from its holder must buy it from him in a voluntary transaction in which the value of the entitlement is agreed upon by the seller. It is the form of entitlement which gives rise to the least amount of state intervention: once the original entitlement is decided upon, the state does not try to decide its value.  It lets each of the parties say how much the entitlement is worth to him, and gives the seller a veto if the buyer does not offer enough. Property rules involve a collective decision as to who is to be given an initial entitlement but not as to the value of the entitlement.

Whenever someone may destroy the initial entitlement if he is willing to pay an objectively determined value for it, an entitlement is protected by a liability rule. This value may be what it is thought the original holder of the entitlement would have sold it for. But the holder's complaint that he would have demanded more will not avail him once the objectively determined value is set. Obviously, liability rules involve an additional stage of state intervention: not only are entitlements protected, but their transfer or destruction is allowed on the basis of a value determined by some organ of the state rather than by the parties themselves. An entitlement is inalienable to the extent that its transfer is not permitted between a willing buyer and a willing seller. The state intervenes not only to determine who is initially entitled and to determine the compensation that must be paid if the entitlement is taken or destroyed, but also to forbid its sale under some or all circumstances. Inalienability rules are thus quite different from property and liability rules. Unlike those rules, rules of inalienability not only "protect" the entitlement; they may also be viewed as limiting or regulating the grant of the entitlement itself.

There is a lot packed into this short package.  First, we get the basic distinction between enforcement by injunction and enforcement by liability for damages.  Second, we get the distinction between rights that are alienable and those which cannot be bought and sold and hence are "inalienable."  Third, we get an argument that alienable rights that can be enforced by injunctions require less state intervention than do inalienable rights that are only enforceable by damage awards.  These three ideas were the conceptual core of Calabresi and Melamed's distinction between property rules and liability rules.

Mixed Rules  Even if you have never encountered the distinction between property rules and liability rules before, you probably have already thought to yourself that the world is not quite as black and white as the distinction implies.  The same underlying "primary right"--such as the right to security of property--may be enforced by both injunction and damages and involve both alienable and inalienable aspects.  That is, there are "mixed rules" as Calabresi and Melamed themselves noted:

It should be clear that most entitlements to most goods are mixed. Taney's house may be protected by a property rule in situations where Marshall wishes to purchase it, by a liability rule where the government decides to take it by eminent domain, and by a rule of inalienability in situations where Taney is drunk or incompetent.

Choosing Between Property Rules and Liability Rules  Why should the law choose property rules for some situations and liability rules for others?  That's a very large and complex question.  Here are some of considerations that bear on an answer--recognizing that these are only starting points:

The Possibility of Bargaining--It might be argued that property rules are better suited to situations where the parties can bargain over the transfer of rights.  So the possessory interest in real estate or chattels might be protected by property rights, because the transfer of possession is something over which the parties can bargain.  An injunction against involuntary transfer forces the parties to agree on terms for a voluntary transfer.  On the other hand, it might be argued that liability rules are better suited to situations in which bargaining is impossible (or to be more precise, very costly).  For example, it would be difficult to bargain over an automobile accident--the parties may be strangers, the accident is unanticipated, and so forth.  In that situation, a damage award rather than an injunction seems like the only feasible mechanism for protecting the right.

Existence or Measurement of Damages--Sometimes it is very difficult to measure damages.  For example, in copyright law, it may be difficult to prove that my copying of portions of you book had the consequence of hurting your sales.  (It's possible my copying even helped your sales.)  When damages either don't exist or can't be measured, then liability rules may be ineffective.  But if the copyright holder--to continue the example--has the right to an injunction, this will force the infringer to pay for the right to continue the infringing activity.

Administrative Costs--Liability rules require the system to measure damages and that may be costly.  Evidence on the extent of damages must be gathered, processed, and evaluated by a finder of fact.  Property rules do not involve these costs.  This facto generally favors property rules over liability rules.

Of course, this is a partial and incomplete list.  But these examples illustrate the kinds of considerations that might favor a property rule or a liability rule as the solution to a particular legal problem.

Conclusion The distinction between property rules and liability rules is fundamental to private law.  As you study contracts, torts, and property, it is very useful to ask yourself whether a particular legal doctrine or cause of action involves a liability rule, a property rule, or a mixed rule.  Once you have the answer to that question, the next inquiry is "why?"  What justifications can be offered for the law's choice of a property rule over a liability rule, or vice versa.  If you ask these questions systematically in your study of private law, you will be well on your way to a deeper and more sophisticated understanding of these building block subjects.

References

Ian Ayres & J.M. Balkin, Legal Entitements as Auctions: Property Rules, Liability Rules, and Beyond, 106 Yale L.J. 703 (1996).

Guido Calabresi & A. Douglas Melamed, Property Rules, Liability Rules, and Inalienability: One View of the Cathedral, 85 Harv. L. Rev. 1089 (1972).

Louis Kaplow & Steven Shavell, Property Rules versus Liability Rules: An Economic Analysis, 109 Harv. L. Rev. 713 (1996).

(This entry was last revised on September 2, 2007.)

Legal Theory Lexicon 029: Public and Private Goods

Introduction One of the most powerful ideas that legal theory borrows from economics is the idea of a "public good." Sooner or later law students learn that within the framework of contemporary neoclassical economics, the standard line is that public goods (e.g. national security) should be provided by government whereas private goods (automobiles) ought to be provided by markets. For legal theorists, the line between public and private goods tracks one of the important fault lines in the law--between the private law fields of property, contract, tort, and so forth and public law fields such as environmental law, administrative law, and constitutional law. This post provides a basic introduction to the economic distinction between public and private goods for law students (especially first year law students) with an interest in legal theory.

It may be helpful to quickly preview the basic idea. So here goes:

• Public goods have two characteristics--nonrivalrousness and nonexcludability. For example, consumption of national defense is nonrivalrous (my being protected by the U.S. armed forces doesn't diminish your protection). National defense is a nonexcludable good: the Army cannot say to Mexico, "Solum hasn't paid his national defense bill, "Go ahead and attack him."
• Private goods are rivalrous and excludable. If I own a laptop computer, my use of it diminished your ability to use it; therefore, my consumption of the laptop rivals yours. Moreover, I can exclude you from the use of my laptop (by locking it up when I am not using it).

We use markets to provide goods like laptops (that excludable and rivalrous), but government provides goods like national defense (that are nonexcludable and nonrivalrous).

A Note on Terminology: "Public Goods" versus "Public Interest" versus "Public Resources." Before we go any further, let's make sure we agree about how we are using the phrase "public good." This is important because the same phrase is used for different purposes in different contexts. So let's stipulate to the following:

• The phrase "public good" or "public goods" shall be used to refer to the economists’ idea of good that meets the criteria of nonrivalrousness and nonexcludability.
• The phrases "public interest" or "common good" shall be used to refer to the idea of goods that benefit the public at large as distinguished from goods or interests that benefit a faction (or "special interest group").
• The phrase "public resource" shall be used to refer to private goods that are owned by the government or held in trust for the public. National parks are indisputably public resources, but it may not be the case that they are public goods in the economic sense.

We could use the phrase "public good" to refer to the public interest or to public resources, but for the purposes of this post, let's stipulate that "public good" shall be reserved for the economic sense of the phrase.

The Criteria for Public Goods There are two criteria by which public goods and distinguished from private goods. A good is public only if it is both nonrivalrous and nonexcludable. A good is private only if it is both rivalrous and excludable. (We will deal with the mixed cases in just a bit.)

"Rivalrousness" is a property of the consumption of a good. Consumption of a good is rivalrous if consumption by one individual X diminished the opportunity of other individuals, Y, Z, etc., to consume the good. Some goods are rivalrous because they are "used up." If I drink a glass of Heitz Martha's Vineyard, then you cannot drink that same glass of wine. If set off a firecracker, you cannot set off the same firecracker. Other goods are rivalrous because of crowding effects. If I am using the free internet terminal at the student lounge, then you cannot use the same time slice of the terminal--because only one person can sit in front of the screen at the same time.

"Excludability" is also a property of consumption of a good. It is helpful to distinguish two forms of excludability: (1) excludability through self help, and (2) excludability through law. If I want to exclude you from my land, I can build a fence--the exclusion results from self help. But if I want to exclude you from copying a novel that I've written and I want to make the novel generally available for sale, self help will not work. (It would be ridiculously expensive to hire a guard to monitor each copy or every photocopy machine.) Government, however, can make unauthorized copying a criminal offense or actionable civil wrong, thereby creating exclusion through law.

Markets and Government The conventional view is that markets should provide private goods and government should provide public goods. The case for market provision of private goods relies on the idea of Pareto efficiency. The weak Pareto Principle is the simple idea that if some action would make at least one person better off and no one worse off, then that action is good. If we have a private good, e.g. a widget, and a willing buyer and seller, then allowing the sale is Pareto efficient: the buyer prefers the widget to the money and the seller prefers the money to the widget. If we assume that the transaction has no external costs (harms to third parties), then allowing the transaction makes buyer and seller better off and hence is required by the weak Pareto principle.

But when we come to public goods, markets simply don't work. Why not? Most simply, because if a good is nonexcludable, then no one will pay for it. Suppose someone goes into the business of cleaning the air with a pollution removal machine. I won't voluntarily pay for this service, because I will be able to breathe the air even if I don't pay. If a private firm offered to defend me against foreign invaders, I won't voluntarily sign on. My individual payment would have a negligible effect on the size of the armed force. If others pay, I don't need to. If others don't pay, then my payment won't do any good. Of course, you will recognize that I am describing the free rider problem, a form of the Prisoner's Dilemma. Because markets cannot provide public goods, governments should.

As you might expect, the argument for government provision of public goods and market provision of private goods is controversial. Socialists argue that governments may do a better job of providing private goods, because government planning can create welfare benefits that cannot be realized by markets. Libertarian legal theorists argue that markets can provide most if not all private goods for various reasons, including arguments that nonexcludability can often be overcome by ingenious market solutions. I won't get into either the socialist or the libertarian critique of the argument for market provision of private goods and government provision of public goods, but you should know that these criticisms have been extensively developed.

The Expanded Typology: Public, Private, Toll, and Common Pool Goods So far, we have been assuming that excludability and rivalrousness go together and hence that there are only two categories, public goods and private goods. In fact, it is possible to have a good that is rivalrous but nonexcludable or one that is nonrivalrous but excludable. So there are four categories, not two:

1. Public goods are nonrivalrous and nonexcludable.
2. Private goods are rivalrous and excludable.
3. Toll goods are nonrivalrous and excludable.
4. Common pool goods are rivalrous and nonexcludable.

Table One shows the four categories as a two-by-two matrix:



We've covered the first two categories, but we need to consider categories three and four. So let's do that now.

Toll Goods and Intellectual Property A toll good is characterized by nonrivalrous consumption but excludability. Suppose we have a highway in a rural area, where the capacity of the highway would never be approached even if access were free. Nonetheless, use of the highway can be limited by the installation of toll booths. This means that we can charge for access to the highway. Economists call goods that are nonrivalrous but excludable "toll goods."

One of the most important applications of the concept of a toll good in legal theory arises in the context of intellectual property. A simplified version of the conventional story goes something like this. Without intellectual property rights created by law, the information (e.g. the invention or composition) would be a pure public good. In a world without intellectual property, for example, the first copy of a new book could be copied by the first purchasers. This copy could then be copied by others. Eventually, the "free" copies would dominate the market. And this would destroy the incentives of authors to write! (More on the question whether this is right towards the end of this post.)

Intellectual property law comes to the rescue. By enforcing patents and copyrights through legal sanctions, intellectual property law transforms information from a public good to a toll good. Intellectual property law creates excludability, but not rivalrousness. For more on this, see Water Wells and MP3 Files: The Economics of Intellectual Property.

Common Pool Goods and the "Tragedy of the Commons" Common pool goods are rivalrous but non excludable. An example might be the fish resource in those portions of the ocean that are outside national waters (the high seas). This resource is rivalrous, because over fishing can result in a reduction of the stock of fish. But excludability is difficult to establish. Self-help would work for a localized fishing area where the fish population does not range over a large area; in theory a patrol boat could establish a virtual fence. But this solution won't work if the fish population ranges over a wide area of the high seas. Unless some international treaty regime can establish enforceable quotas, the result may be a "tragedy of the commons." Each fisher has an incentive to take the most she can, but the result of all fishers doing this is a depletion in the stock of fish that harms everyone. (Once again, we have a version of the Prisoner's Dilemma.)

Club Goods We are almost done, but we have one or two more ideas to pick up. One is the idea of a "club good." A club good is a good where the utility of each individual's consumption of the good is a function of the number of others who consume the good. Take a golf course. If too many people try to use the course simultaneously, then the utility that each derives from the experience goes down. Golfers have to wait for tee times, the course is crowded, and so forth. In other words, there are "crowding" problems. One solution to such problems is to form a "club," which limits the number of persons with the right to use the golf course.

Private Goods and the "Tragedy of the Anticommons" And finally, we should note the flip side of the tragedy of the commons, dubbed by Frank Michelman, "the tragedy of the anticommons." This refers to the phenomenon where ownership in a resource has been divided among so many owners that transaction costs and holdout problems prevent Pareto efficient transactions from occurring. For example, when property was "privatized" in the former Soviet Union, a single apartment building might end up with many, many fractional owners, including ownership interests by various government entities and the residents of the building. In theory, every owner must agree before a transaction involving the building could take place. Given the large number of owners, the costs of completing the transaction and paying off the holdouts (those who withhold consent in order to increase their share of the profits) can make the transaction economically unattractive. This is a case where the market is incapable of efficiently allocating a pure private good.

Conclusions The public/private goods distinction is basic to a variety of topics in legal theory. Whenever you encounter a resource allocation problem, ask yourself, "Is this resource a public, private, toll, or common pool good?" And then ask, "Could a change in the legal rules governing this resource change its status?" Although the terminology may be daunting at first, they are really very simple and straightforward.

Legal Theory Lexicon 025: Social Welfare Functions

Introduction One of the key ideas in contemporary economic theory in general and law and economics in particular is the social welfare function. Law students without a background in economics might be put off by the fact that social welfare functions are expressed in mathematical notation, but there is no reason to be intimidated. The basic ideas are easily grasped and the mathematical notation can be mastered in just a few minutes. This post provided an introduction to the idea of the social welfare function for law students, especially first year law students, with an interest in legal theory. Here we go!

Background

Normative Economics The idea of a social welfare function is part of normative economics. There are several plausible formulations of normative economics, but almost all of normative economics begins with the fundamental idea of utility as a conception or measure of the good. Economists may disagree about the nature of utility, the relationship of utility to social welfare, and the role of welfare in public policy, but most (if not all) economists would assent to the abstract proposition that ceteris paribus more utility is a good thing. But this apparent agreement is at a very abstract and ambiguous level. There are many different ideas about what "utility" is.

Cardinal and Ordinal Interpretations of Utility One key divide is between cardinal and ordinal interpretations of utility. An ordinal utility function for an individual consists of a rank ordering of possible states of affairs for that individual. An ordinal function tells us that individual i prefers possible world X to possible world Y, but it doesn't tell us whether X is much better than Y or only a little better.

A cardinal utility function yields a real-number value for each possible state of affairs. If we assume that utility functions yield values expressed in units of utility or utiles, then individual's utility function might score possible world P at 80 utiles and possible world Q at 120 utiles. We might represent the utility function U of individual i for P and Q as follows:

Ui(P) = 80 Ui(Q) = 120

The distinction between cardinal and ordinal utilities is potentially important for utilitarianism, at least on certain interpretations. As a theory of evaluation, utilitarianism is the view that an action is the best action if and only if the action maximizes utility when compared with all possible alternative actions. For technical reasons, utilitarianism requires both cardinality and full interpersonal comparability. This point about utilitarianism is closely related to the history of welfare economics, the explicitly normative branch of economic theory.

Measurement Problems Both cardinality and interpersonal comparability pose measurement problems for economists. Even in the case of a single individual, it is difficult to reliability measure cardinal utilities. Measurements that support interpersonal comparisons are even more difficult to justify, and cardinal interpersonal comparisons seem to require the analyst (the person making the comparison) to make a variety of controversial value judgments. Market prices won't do as a proxy for utility, for a variety of reasons including wealth effects. The challenge for welfare economics was to develop a methodology that yields robust evaluations but does not require the cardinal interpersonally comparable utilities.

Pareto This is the point at which Pareto arrives on the scene. Suppose that all the information we have about individual utilities is ordinal and non-interpersonally comparable. In other words, each individual can rank order states of affairs, but we (the analysts) cannot compare the rank orderings across persons. The weak Pareto principle suggests that possible world (state of affairs) P is socially preferable to possible world (state of affairs) Q, if everyone's ordinal ranking of P is higher than their ranking of Q. Weak Pareto doesn't get us very far, because such unanimity of preferences among all persons is rare. The strong Pareto principle suggests that possible world (state of affairs) P is socially preferable to possible world (state of affairs) Q, if at least one person ranks P higher than Q and no one ranks Q higher than P. Unlike weak Pareto, strong Pareto does permit some relatively robust conclusions.

The New Welfare Economics The so-called new welfare economics was based on the insight that market transactions without externalities satisfy strong Pareto. If the only difference between state P and state Q is that in P, individuals i1 and i2 engage in an exchange (money for widgets, chickens for shoes) where both prefer the result of the exchange, then the exchange is Pareto efficient. A state of affairs where no further Pareto efficient moves (or trades) are possible is called Pareto optimal. The assumption about externalities is, of course, crucial. If there are negative externalities of any sort, then the trade is not Pareto efficient.

Weak Pareto and the Arrow Impossibility Theorem Weak Pareto plus ordinal utility information allows some social states (or possible worlds) to be ranked on the basis of everyone's preferences. A method for transforming individual utility information into such a social ranking is called a social utility function. Kenneth Arrow's famous impossibility theorem demonstrates that it is impossible to construct a social utility function that can transform individual ordinal rankings into a social ranking in cases not covered by weak Pareto, if certain plausible assumptions are made. Arrow's theorem has spurred two lines of development in welfare economics. One line of development relaxes various assumptions that Arrow made; for example, we might relax Arrow's assumption that the social ranking must be transitive (if X is preferred to Y and Y is preferred to Z, then X must be preferred to Z). The other line of development considers the possibility of allowing information other than individual, noncomparable ordinal utilities. It is this second line of development that is relevant to the use of social welfare functions in contemporary law and economics.

Social Welfare Functions Suppose that we allow full interpersonal comparability and cardinal utility information. This is sufficient to support what are called Bergson-Samuelson utility functions, which have the form:

W(x) = F (U1(x), U2(x), . . . UN(x))

Where

W(x) represents a real number social utility value for some state of affairs (or possible world) X,
F is some increasing function that yields a real number,
U1(x) is a cardinal, interpersonally comparable utility value yielded by some procedure for individual 1 for state of affairs X, and
N is the total number of individuals.

Bergson-Samuelson social welfare functions are named after Paul Samuelson and Avram Bergson.

What Are the Plausible Social Welfare Functions? There are a variety of different possible functions that can be substituted for F. Here are some of the most important possibilities:

Classical-utilitarian SWF--We could substitute summation for F, and simply add the individual utility values; this is sometimes called a Benthamite or classical-utilitarian social welfare function famously associated with Jeremy Bentham. The classical utility social welfare function can be represented as follows:

W(x)={U1(x) + U2(x) + U(3(x) . . . Un(x)}

Average-utilitarian SWF--The classical SWF adds the utilities. This raises some very interesting issues when the different states of the world (x or y) have different population sizes. When deciding whether to add additional individuals, the classical-utilitarian SWF says more is better until we reach the point where adding more actually reduces the overall level of utility. One way to avoid this implication is use the average level of utility instead of the sum, as in the following formula:

W(s){[U1(x) + U2(x) + U(3(x) . . . Un(x)]/n}

In other words, we divide the sum of utilities by the number of individuals!


Bernoulli-Nash SWF--In the alternative, we could substitute the product function (¡Ç) and multiply individual utilities. This is sometimes called a Bernoulli-Nash social welfare function, which can be represented as follows:

W(x)={U1(x) * U2(x) * U(3(x) . . . Un(x)}

Rather than adding individual utilities, we multiply them! And yes, the "Nash" in Bernoulli-Nash is John Nash of "A Beautiful Mind" fame.

What About the Problem of Interpersonal Comparison? Social welfare functions are much discussed in legal theory these days. One of the reasons for the contemporary debate over social welfare functions is that this approach has been championed by Louis Kaplow and Steven Shavell (both of the Harvard Law School). Their book, Welfare versus Fairness, has put the welfarist approach to normative economics "front and center."

One of the interesting theoretical questons about SWFs concerns the problem of interpersonal comparison. How do we get the values to plug into U1(x), U2(x), and so forth. That is, how do we compare up with a way of putting my utility and your utility on the same scale. As I understand the state of play, this is not a topic on which economists agree. Some economists believe that there is no objective way of producing interpersonally comparable cardinal utility values. But some economists believe that a third-party (the legal analyst or the economist) can do the job of assigning values to individual utilities.

Conclusion We've barely begun to scratch the surface of the many interesting theoretical issues that attend the use of social welfare functions in legal theory. Some of those issues were explored in a prior Legal Theory Lexicon entry on Balancing Tests. Even if you have absolutely no background in economics, there is no reason to shy away from the debates about social welfare functions. The notation, although at first intimidating, is actually very simple. The foundational ideas, although sometimes articulated in the jargon of economic theory, really go to fundamental questions in moral theory. I hope this post has given you the tools to begin to discuss these ideas!

Legal Theory Lexicon 011: Second Best

Introduction The post provides a very basic introduction to the idea of "second best." The term "second best" originated in a famous 1956 article by Lipsey and Lancaster (see bibliography), and it was originally used as a technical economic concept. Despite its technical origins, the idea behind the second best is very general: sometimes the ideal solution to a problem (or "optimal policy option") is infeasible. The best should not be the enemy of the good; so, when the first-best policy option is unavailable, then normative legal theorists should consider second-best solutions. In this post, we will take a hard look at the idea of the second best, beginning with a statement of the intuitive idea and then looking at the more formal idea of the second best in its original economic context.

As always, the Lexicon is aimed at law students, especially first-year law students, with an interest in legal theory.

The Intuitive Idea The intuition behind the idea of the second best is simple. We would like to have the best possible legal system. But sometimes the best legal policies are not in the cards; that is, the best policy may be impractical. Why? In legal theory, one common reason that we cannot adopt the best policy is politics. Given the political forces that operate, the best campaign finance system may be pie in the sky. So we ask the question, of those systems that might be politically feasible, which is the "second best"?

Although I've introduced the intuitive idea by talking about "political feasibility," the idea of the second best is more general than that. First-best solutions may be unavailable because of a variety of constraints, of which politics is only one. The intuitive idea of the second best is a bit broader and less technical than the way economists define "second best," so let's turn to the technical economic idea of second best now.

The Second Best in Economics The very general idea of the economic theory of the second best can be expressed as follows:

Assume a system with multiple variables. Take the most desirable state the whole system could assume and the associated values that all of the variables must assume to produce this state: call this condition, the first-best state of the system and call the associated values of the variables, the first-best values. Now assume that one variable will not (or cannot) assume the value necessary for the first-best state of the whole system: call this the constrained variable. Holding the constrained variable constant, consider the most desirable state the whole system could then assume and the associated values that all the nonconstrained variables must assume to produce this state: call this the second-best state of the system. There are systems in which achieving the second-best state will require that at least one variable other than the constrained variable must assume a value other than the first-best value: call these value(s) the second-best value(s).

And here is the way that Lipsey and Lancaster formulated the idea:

[I]f there is introduced into a general equilibrium system a constraint which prevents the attainment of one of the Paretian conditions, the other Paretian conditions, though still attainable, are in general, not desirable.

(If "Paretian" is unfamiliar to you, either ignore that term or click here.) Lipsey and Lancaster are making a normative (but technical) argument. They assert that if one variable is constrained and cannot assume its first-best value, then "in general" other variables should not assume their first-best values. The "in general" qualification is important. Lipsey and Steiner didn't and couldn't show that it is always (or necessarily) the case that constraint of one variable affects the most desirable value for other variables. Rather, their proof shows that this is possible. In the real world, whether nonconstrained variable should depart from their first-best variables depends entirely on the facts. In fact, if a policymaker lacks certain information about the second-best variables, it may turn out that the real world policy that will produce the best result is to try to move the constrained variable as close as possible to its optimal state, leaving the second-best variables in their first-best states. The possibility was called the "third best" by Ng (see bibliography below).

One or two additional points are necessary to complete the technical story.

First, the definition that I just gave assumes that only one variable is constrained. But there is no reason to limit the theory of the second best in this way, more than one variable may be constrained. In fact, in theory every variable could be constrained: in this limiting case, the second-best state would be the only possible state of the system.

Second, the second best is usually understood as relative to a constrained variable. We could use the phrase "second best" to refer to the second-best state the system could assume if all the variables were unconstrained, but this is not the way that Lipsey and Lancaster used that phrase.

Third, there is an important difference between the way economists understand "second best" and the way the same phrase is understood by noneconomists. What was interesting and powerful about Lipsey and Lancaster's proof is that it produced the counterintuitive result that sometimes when one variable is constrained, the best policy choice will involve moving other variables away from their first-best values.

Although technically, the definition of second best need not be limited to that special situation, that is the interesting result, and the use of the theory of the second best in economics may be limited to the special case. Outside of economics, however, the phrase "second best" tends to be used in a much looser sense. The important thing is not the terminology, but the ideas. To be clear, however, it is useful to explain what you mean by second best!

The Second Best and Nonideal Theory The idea of the second best that is used by economists is analogous to a distinction made famous by the political philosopher, John Rawls. Rawls distinguished between two ways of approaching political philosophy, ideal and nonideal theory. In ideal theory, we assume compliance with the normative requirements of our theory. Rawls used the phrase "well-ordered society" to refer to the situation that obtains in ideal theory. In a society that is well ordered by Rawls's principles of justice, citizens actually would be guaranteed a fully adequate scheme of basic liberties and the basic structure would actually work to the advantage of the least well off group in society. In nonideal theory, we relax the assumption that the society is well ordered by the principles of justice. Can you make that very abstract description more concrete? Yes, here is a really good example. In a society that is well-ordered by Rawls's principles of justice, we might assume that if there are local governmental units, they will comply with the restraints imposed by the freedom of speech. But in the real world, local governments might be more susceptible to political pressure to suppress unpopular speech than would be the central government (i.e. the national government in Washington, D.C., in the case of the United States). So, in the real world of nonideal theory, we might be very considered with constraining the jurisdiction and powers of local governments; whereas, this issue may not even arise in the case of ideal theory.

Pinpointing the Constrained Variable The notion of the second best and the related idea of nonideal theory get tossed around quite a lot in legal theory, but sometimes these terms are used carelessly or without precision. Whenever you hear or read the term "second best," ask yourself the question, "Which variable is constrained, and why is it constrained?" Because the "second best" is second best relative to a constrained variable, use of the concept of the second best doesn't mean anything unless and until the constrained variable is specified. Moreover, it is sometimes very important to know why the constrained variable is constrained. This is because it is easy to construct an argument for a second-best policy option that uses a double standard with respect to whether variables should be considered to be constrained. Here is a simple example:

Suppose our problem is racial justice with respect to the distribution of income and resources. Someone might make the case for reparations (a one time payment of a compensatory amount to descendents of the former slaves) on the ground that reparations are the second-best solution. The first-best solution would be a just economic order in which market mechanisms operate in a nondiscriminatory fashion to allocate income and wealth according to just criteria. (For this purpose, we don't need to specify what the just criteria are.) But the first-best solution is unavailable, because a just economic order is politically infeasible. Therefore, we ought to support reparations, which is the second-best policy.

So far, so good. But notice that there is a hidden assumption in this argument. The argument assumes that reparations are politically feasible. If this assumption is incorrect (which it may well be as an empirical matter), then it follows that the argument for reparations as the preferred second-best solution is fallacious. Of course, one can deploy double standards with respect to which variables are constrained (or which options are infeasible) so long as the double standard is made clear. But when the double standard is concealed and the argument is made in the context of policy evaluation, then we have either an innocent mistake or an attempt at manipulation.

The Feasible Choice Set Another way of approaching the general problem revealed by the theory of the second best is via the notion of the feasible choice set. Take all of the possible legal policy options with respect to a particular legal problem. Then lay out a set of well-defined criteria for feasibility. Apply the criteria to the set, sorting the options into the feasible choice set and the infeasible choice set. Practical policy discussion will usually be limited to the options within the feasible choice set, but legal theory is not limited to the practical. Frequently we can learn something important by considering options that are outside the feasible choice set. For example, a rule of strict liability might turn out to be the optimal rule of tort law. It could also turn out that strict liability regimes are politically infeasible--perhaps because the fault-based social norms are very strongly held. But that fact should not preclude legal theorists from examining the merits of strict liability regimes. Not only may such an examination be of intrinsic interest, but the insights gleaned from such an examination may well assist in the evaluation of the options that are within the feasible choice set.

The Bottom Line The notion of the second best, the distinction between ideal and nonideal theory, and the idea of the feasible choice set, are all essential tools for a legal theorist. As a first year student, you are likely to encounter these ideas in classroom discussion or in law review articles assigned as ancillary reading. The trick to mastering these concepts and using them effectively is to identify the constrained variable (or the nonideal conditions). Once you've done that, you can move to the next step, which is the question, "What criteria are used to identify the constrained variables?" And if you can answer that question, you are now in a position to respond in an intelligent and sophisticated way to applications of the theory of the second best!

Bibliography & Links

• R.G. Lipsey & Kelvin Lancaster, The General Theory of the Second Best, 24 REV. ECON. STUD. 11 (1956).
• Yew-Kwang, Ng, Welfare Economics (London: Macmillan, 1983).
• Karla Hoff, Second and Third Best Theories (pdf file).
• Steven Suranovic, The Theory of the Second Best
• Thomas McCarthy, Political Philosophy and Racial Injustice: From Normative to Critical Theory (explores Rawls's use of ideal and nonideal theory).
• Lawrence B. Solum, Constitutional Possibilities (2007).

(This entry was last updated on January 20, 2008.)

Legal Theory Lexicon 008: Utilitarianism

fiIntroduction This installment of the Legal Theory Lexicon is an introduction to utilitarian moral and political philosophy tailored to law students (especially first-year law students) with an interest in legal theory.

Law students learn early on that classroom discussion of cases and statutes may begin with questions about what the rule is but is likely to turn to questions about what the rule should be. And in most law school classrooms, analysis of the “should” question is likely to go down one of two paths. The first path leads to fairness (which outcome in this case is fair to the parties; which rule will produce fair results in the future). The second path leads to policy (which rule will produce the best consequences in the future). Theories about fairness will be covered in future installments of the Legal Theory Lexicon; today, we focus on arguments of policy and the theoretical question, “What does it mean to say that a rule would produce the best consequences?” One answer to that question is “utilitarianism,” a theory of enormous interest and influence. But what exactly is “utilitarianism” and how might it be criticized or defended?

What is “utilitarianism”?
Just about every law student has some basic familiarity with the idea of utilitarianism, but unless you were a philosophy or economics major, you may have only a fuzzy notion of what this term really means. In this history of moral philosophy, utilitarianism is strongly associated with two historical figures, Jeremy Bentham and John Stuart Mill. Mill’s views are important and deeply interesting, but they are also extremely difficult to sort out properly. Jeremy Bentham, however, provides a wonderful entrée into the world of utilitarian moral and political philosophy. Law students should be especially fond of Bentham, because with only a bit of exaggeration, we can say than Bentham is the original disgruntled law student. Bentham, you see, was highly displeased with William Blackstone’s lectures on law at Oxford University. The common law, Bentham thought, was a disorganized body of rules. Common-law judges irrationally worshipped historical pedigree and had an immoral disregard of the consequences of legal rules.

Legal rules, Bentham believed, should be codified, and the codes should be written so as to produce “the Greatest Good, for the Greatest Number.” That is, we should adopt those legal rules that will maximize utility.

Consequentialism
Utilitarianism is just one member of a more general family of moral theories, which we might call “consequentialist.” Consequentialism is the view that morality is about consequences of decisions. Utilitarianism is a particular form of consequentialism, but not the only form. Consequentialism is sometimes contrasted to deontology, where deontological moral and political theories maintain that there are moral rules or principles, the violation of which cannot be justified on the ground that good consequences would result. Thus, a consequentialist might believe that one may tell lies, break promises, or injure innocent persons in order to accomplish a greater good, whereas a deontologist might believe that such actions are forbidden--even if good consequences will result.

Disambiguating Utilitarianism
Let’s pause for a moment. It turns out that “utilitarianism,” the term, refers to many different interrelated theories. “Utilitarianism” is ambiguous, and so we need to specify what we mean by utilitarianism by answering some questions:

• What is utility? That is, when we say, the greatest “good” for the greatest number, what do we mean by “good?”



• What is scope of decision? That is, what should maximize utility, individual actions, general rules, principles, or something else?



• What does it mean to maximize utility?



• Does the rightness of an action depend on actual or expected utilities?

What is utility?
What is utility? What is a good consequence? Or to use a bit of jargon, what is a “utile,” where the word “utile” stands for a unit of utility? There are many possible answers to this question, but here are three versions of utilitarianism that give three different answers to this question:

Hedonistic Utilitarianism. Bentham himself believed that utility was pleasure and the absence of pain. Suppose it were possible to measure and quantify pleasures and pains. We might then call one unit of pleasure a positive “hedon” and one unit of pain a negative “hedon.” Maximizing utility then, would simply be to maximize the sum of hedons. When we evaluated legal rules, we would engage in what Bentham called a “hedonic calculus.”

Eudaimonistic Utilitarianism. But is the good really just a matter of pleasures and pains? Many of Bentham’s critics argued that not all pleasures are good. Would you really want to live your life carrying around a device that constantly stimulated the pleasure center of your brain and suppressed the pain center? Rather than maximize pleasure, we might instead maximize “happiness”—eudaimonia in ancient Greek. Happiness may be related to pleasure, but it includes more abstract satisfactions. Climbing a mountain may involve much more pain than pleasure, but this activity may still contribute to the happiness of the climber.

Preference Satisfaction Utilitarianism. But if happiness seems a better candidate for “good” than pleasure, there are difficulties with the proposition that the law should maximize “happiness.” Happiness is notoriously difficult to define, and different persons have different views about what makes for a happy life. Moreover, happiness, like pleasure, is difficult to measure directly. For these reasons and others, some utilitarian theorists (especially economists) substitute “preference” for happiness as the “good” to be maximized. Preferences can be measured in a variety of ways. For example, we can ask individuals to simply rank order their preferences among various states of affairs, giving us an ordinal utility function for the individual. Economists have devised a variety of techniques for translating these rank orderings (1st best, 2nd best, etc.) into numerical values. Thus, we can construct a cardinal utility function for an individual. Because preference-satisfaction is measurable, most economists use a preference-based conception of utility. And because of the influence of economics on legal theory, this form of utilitarianism has had the greatest impact on contemporary legal theory as well.

There are other versions of utilitarianism, but you get the idea.

Scope of Decision
So let’s assume we have a working conception of utility. Our next question is: What exactly is the decision that is supposed to maximize utility? Is each individual action required to maximize utility? Or is it general rules that we are concerned with? Or principles? Or something else? I am going to call this question, the scope of decision question. Different forms of utilitarianism give different answers to the scope of decision question. Let’s take a quick look at some of the possibilities:

• Act Utilitarianism. (abbreviated AU) The first possibility is that each individual action should maximize utility. Given this answer to the scope of decision question, we might formulate utilitarianism as follows:

  Act so that your action maximizes utility as opposed to any alternative action that you could perform.

  Suppose, for example, that you must decide whether to break or keep a promise to have lunch with a friend. You would ask yourself, “Would keeping my promise produce greater utility than breaking it?” Thus, you would consider the costs of your decision, such as: (1) your friend will be hurt, (2) you will miss out on the satisfaction of having lunch with your friend, and (3) your friend may not trust your promises in the future if you break this promise. And you would consider the benefits, such as: (1) you will be able to use a free ticket to go to the baseball game if you break the promise, and (2) you will not have to listen to your friend's boring stories. You then add the utilities for each action, and choose the action that produces the greatest utility.

• Rule Utilitarianism. (abbreviated RU) The case of promises reveals a potential problem with AU. If I calculate utilities every time, I decide whether to break or keep a promise, my promises may not be viewed by others as trustworthy. And if my promises are not trustworthy, then I will not be able to use the institution of promising to coordinate my behavior with that of other people. But the ability to coordinate through promises produces good consequences. One way out of these difficulties is to shift the scope of decision from individual actions to general rules. Thus, although the individual actions of breaking my promise might maximize utility as compared to the alternative, the general rule, “keep your promises,” might produce more utility than the alternative rules, such as “keep your promises, but only when there is nothing better to do.”

Rule utilitarianism itself has two important subvariants, and we can add a third, specifically legal, variant as well:

Ideal Rule Utilitarianism (IRU) says that you should act in accordance with the set of “ideal rules” that would maximize utility if everyone were actually to act in conformity with the rules.

Actual Rule Utilitarianism (ARU) says that you should act in accord with the set of “actual rules” that would maximize utility if it were adopted as the moral code of a real society in which persons will sometimes fail to live up to the requirements of the moral code.

Legal Rule Utilitarianism (LRU) responds to an obvious fact about the application of utilitarianism to the law. The law is concerned with individual acts (e.g. an individual judge's decision in an individual case at the trial level), but it is also concerned with rule-creating acts (e.g. the decision of a legislator to vote for or against a given bill). So it is reasonable for legal theorists to advance a more specialized version of utilitarianism, which we can call "Legal Rule Utilitarianism," as a theory about legal rules. Notice, however, that LRU will have a set of variants. So we can distinguish the utility of an ideal system of legal rules (with perfect compliance) versus an actual system of legal rules (with disobedience and enforcement costs) versus a single nonideal actual rule (where the status quo system of rules is assumed and we look at the utility of changing only a single rule).

• Utilitarian Generalization (abbreviated UG) There is one more answer to the scope of decision problem that is worth mentioning. UG is the view that one should act on the basis of principles (or maxims) that would produce the greatest utility if they were generalized (e.g. we acted upon by everyone. Because this form of utilitarianism, plays very little role in legal thought, I won't discuss it further.

What does it mean to maximize utility?
There is yet another ambiguity about utilitarianism that is really important to its application. What does "the greatest good for the greatest number" mean? Alternatively, what does it mean to maximize utility? This is a really complex topic. Right off the bat, it has both an intrapersonal and interpersonal dimension. To simplify, I will focus on the interpersonal problem. Let's assume we have utility values for individuals. What do we do with them? You may think the answer is obvious, "Add them up!," but it isn't so easy. Here are some alternatives:

• Classical Utilitarianism. "Add them up" is the classic answer. That is, we simply sum individual utilities. Sometimes this is called the "utilitarian social welfare function" by economists. This can lead to some confusion as this is what some economists think the term "utilitarianism" means.


• Average Utilitarianism. But we could average rather add. That is, we could take the sum of individual utilities and divide by the number of persons. You, gentle reader, undoubtedly have run way ahead of me and seen that this will make a big difference to things like population policy. We might have a choice between a larger population with a lower average utility but a greater sum, and a smaller population, with a higher average, but a lower sum.


• Bernoulli-Nash John Nash (of A Beautiful Mind fame) is associated with another alternative. We might multiply rather than add utilities. I won't go into the reasons why this might be a good idea, except to tell you that multiplication makes more sense if we our utility values for individuals are relative rather than absolute.

Actual or Expected Utilities
We rarely know with certainty what consequences will result from actions or rules. Utilitarianism might look to the actual consequences of rules. If so, then some actions that looked right at the time will turn out to be very wrong, because of some unanticipated effect of the action. The alternative is to say that the rightness or wrongness of an action depends on its expected consequences. Given the phenomenon of uncertainty, a given action may lead to several different possible future states of the world. If we could assign a probability to each state, then the expected consequences of a given action could be calculated by taking the product of the utility value for the state and the probability that the state will coming into being. Take the following choice situation:

Action A has a 50% chance of producing a utility of 10 and a 50% chance of producing a probability of 0. Since .5*10 + .5*0 = 5, the expected utility of action A is 5.

Action B has a 90% chance of producing a utility of 0, and a 10% chance of producing a utility of 100. Since .9*0 +.1*100 = 10, the expected utility of action A is 10.

And since 10 > 5, action A has the greater expected utility. Of course, it may turn out that action B produces a utility of zero, but if what counts is expected utility, then this ex post fact is irrelevant to the moral evaluation of action A.

Some Objections to Utilitarianism
Utilitarianism is an enormously controversial view, with adamant defenders and critics. It is worth our while to examine a few of the most prominent objections, but we will only be sliding across the surface of a deep and complex topic.

The Rights Objection. Utilitarianism evaluates actions on the basis of the consequences they produce, and therefore does not require respect for moral or legal rights. The literature is full of hypotheticals in which utilitarianism is alleged to justify intuitively unattractive rights violations. Suppose, for example, the slavery is contrary to a moral right, but that in a particular society, enslaving a small minority of the population would produce greater utility for the majority than it produced disutility for the enslaved minority. If these facts were true, the utilitarianism seems to say that slavery would be morally required. But most people would disagree, saying that slavery cannot be justified simply because it produces good consequences: “We have a moral right not to be enslaved." Utilitarians are likely to get quite huffy when this argument is made. They may say, “But slavery does not produce good consequences. It produces bad consequences, and that’s why we think slavery is so awful.” And then the critic might say, “But suppose slavery did produce good consequences, what then?” You can see how this debate could go on for quite some time before we made any progress. Notice, however, that act utilitarianism seems more open to the rights objection than does rule utilitarianism. Rules against rights violations may produce good consequences, even if individual acts of rights violation could be justified on utilitarian grounds.

The Self-Defeating Objection
Another objection is that utilitarianism may be self-defeating. Suppose that everyone tried to deliberate as a utilitarian. It might turn out that nonetheless they would make decisions that led to bad consequences. For example, some people may be extremely bad at predicting the consequences of their actions. Others may systematically overestimate their own utilities while systematically underestimating those of others. One answer to this objection is famously associated with the British moral philosopher R.M. Hare. Hare proposed a two-level theory of morality. Utilitarianism, Hare argued, operates at the level of detached moral theorizing. Ultimately, an action is deemed good or bad based on its utility. But ordinary moral deliberation, Hare continued, operates at a different level. Ordinary folks should deliberate on the basis of moral rules of thumb, such as keep your promises, don’t steal, and don’t enslave your enemies when you vanquish them. As you might guess, there are many criticisms of two-level theories, but you get the general idea.

The Impossibility of Interpersonal Utility Comparisons
This one gets very complicated, very fast. So let me just state the general idea. Suppose we are trying to add up individual utilities for everyone in society. How do we come up with values that are truly comparable across persons. That is, how do we know that X amount of my pleasure or happiness or preference satisfaction is equal to Y amount of yours? This problem is especially vexing for economists, and one solution is simply to limit the conclusions of economics to cases that involve making everyone better off—hence obviating the need for interpersonal comparisons.

The Demandingness Objections
The list of objections goes on and on, but let’s do just one more. It is frequently argued that utilitarianism (especially act utilitarianism) is too demanding. Why? Imagine that it is your day off. You have two choices. You can either read a novel or your can work for Oxfam. If you read a novel, you will produce some positive utility—your enjoyment of the novel. But if you worked for Oxfam, you would save 1.7 starving children in the third world from death. Well, of course, you should work for Oxfam. But the problem is that it will always be the case that I could produce more utility for others if I dedicated my time to helping the least fortunate. Utilitarianism seems to require me to work for Oxfam after work and to stay up as late as I possibly can. In fact, I may be able to maximize utility by neglecting my health and family. If this is true, many would find utilitarianism too demanding and hence implausible.

Utilitarianism and Legal Theory
In the law, utilitarian thinking is most associated with normative law and economics. It is useful to review the various forms of utilitarianism in this context:

--Normative law and economics uses preferences rather than pleasure or happiness as its concept of utility.

--Normative law and economics usually assumes that the system of legal rules (as opposed to individual actions or ideal moral rules) provide the relevant scope of decision.

--Normative law and economics usually assumes that utilities are to be summed—although this issue is rarely addressed in any detail.

--Normative law and economics usually assumes that it is expected utilities, rather than actual utilities, that are to be maximized.

If you are interested in the relationship between utilitarianism and legal theory, you will definitely want to check out Kaplow and Shavell’s book, Fairness versus Welfare. Kaplow and Shavell don’t take a stand on the question as to whether utilities should be summed, multiplied, or combined in some other way, but they do offer a trenchant defense of consequentialism as well as an attack on nonconsequentialist approaches to legal theory.

Links

• Utilitarianism Resources
• Ethics Updates: Utilitarianism
• The Bentham Project
• International Society for Utilitarian Studies

Bibliography
The literature on utilitarianism is vast, but here are some good starting points:

• J.J.C. Smart & Bernard Williams, Utilitarianism: For and Against (1973)
• Utilitarianism and Beyond (Amartya Sen & Bernard Williams eds., 2002)
• Consequentialism (Stephen Darwall ed. 2002)
• Robert E. Goodin, Utilitarianism as a Public Philosophy (1995)
• Consequentialism and Its Critics (Samuel Scheffler, ed. 1988)

For past and future installments of the Legal Theory Lexicon, go here.

(This post was last modified on December 29, 2007.)

Legal Theory Lexicon 007: The Prisoners' Dilemma

Introduction One of the most useful tools in analyzing legal rules and the policy problems to which they apply is game theory. The basic idea of game theory is simple. Many human interactions can be modeled as games. To use game theory, we build a simple model of a real world situations as a game. Thus, we might model civil litigation as a game played by plaintiffs against defendants. Or we might model the confirmation of federal judges by the Senate as a game played by Democrats and Republicans. This week's installment of the Legal Theory Lexicon discusses one important example of game theory, the prisoner's dilemma. This introduction is very basic--aimed at a first year law student with an interest in legal theory.


An Example Ben and Alice have been arrested for robbing Fort Knox and placed in seperate cells. The police make the following offer to each of them. "You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice gets a heavy sentence. Likewise, if your accomplice confesses while you remain silent, he or she will go free while you get the heavy sentence. If you both confess I get two convictions, but I'll see to it that you both get light sentences. If you both remain silent, I'll have to settle for token sentences on firearms possession charges. If you wish to confess, you must leave a note with the jailer before my return tomorrow morning." This is illustrated by Table One. Ben's moves are read horizontally; Alice's moves read vertically. Each numbered pair (e.g. 5, 0) represents the payoffs for the two players. Ben's payoff is the first number in the pair, and Alice's payoff is the second number.

Table One: Example of the Prisoner's Dilemma.




Suppose that you are Ben. You might reason as follows. If Alice confesses, then I have two choices. If I confess, I get a light sentence (to which we assign a numerical value of 1). If Alice confesses and I do not confess, then I get the heavy sentence and a payoff of 0. So if Alice confesses, I should confess (1 is better than 0). If Alice does not confess, I again have two choices. If I confess, then I get off completely and a payoff of 5. If I do not confess, we both get light sentences and a payoff of 3. So if Alice does not confess, I should confess (because 5 is better than 3). So, no matter what Alice does, I should confess. Alice will reason the same way, and so both Ben and Alice will confess. In other words, one move in the game (confess) dominates the other move (do not confess) for both players.
But both Ben and Alice would be better off if neither confessed. That is, the dominant move (confess) will yield a lower payoff to Ben and Alice (1, 1) than would the alternative move (do not confess), which yields (3, 3). By acting rationally and confessing, both Ben and Alice are worse off than they would be if they both had acted irrationally.


The Real World The prisoner's dilemma is not just a theoretical model. Here is an example from Judge Frank Easterbrook's opinion in United States v. Herrera, 70 F.3d 444 (7th Cir. 1995):

Cynthia LaBoy Herrera survived a nightmare. She and her husband Geraldo Herrera were arrested after a drug transaction. The couple, separated by the agents, then played and lost a game of Prisoner's Dilemma. See Page v. United States, 884 F.2d 300 (7th Cir.1989); Douglas G. Baird, Robert H. Gertner & Randal C. Picker, Game Theory and the Law 312-13 (1994). Cynthia told agents who their suppliers were. Learning of this, Geraldo talked too. When both were out on bond, Geraldo decided that Cynthia should pay for initiating the revelations. Geraldo clobbered Cynthia on the back of her head with a hammer; while she tried to defend herself, Geraldo declared that she talked too much to the DEA. As Cynthia grappled with the hand holding the hammer, Geraldo used his free hand to punch her in the face. Geraldo got the other hand free and hit Cynthia repeatedly with the hammer; she lapsed into unconsciousness.

Communication and Bargains How can we overcome a prisoner's dilemma? You have probably noticed that the prisoner's dilemma assumed that the two prisoner's were isolated from each other. This was not an accident. If the two prisoner's can communicate with each other, then they might reach an agreement. Alice might say to Ben, "I won't confess if you won't," and Ben might say, "I agree." Of course, this might not solve the prisoner's dilemma. Why not? Suppose they do agree not to confess, but each is then taken to a separate room and given a confession to sign. Ben might reason as follows, "If I keep the bargain, and Alice does not, then she will get off while I get a heavy sentence." So Ben may be tempted to defect from their agreement. And Alice may reason in exactly the same way. On the other hand, it may be that Ben and Alice have a reason to trust one another. For example, they may have had prior dealings in which each proved trustworthy to the other. Of course, trust can be established in another way. If each party can make a credible threat of retaliation against the other, then those threats may change the payoff structure in such a way as to make the cooperative strategy dominant. One situation in which the threat of retaliation is built into the model is the iterative (repeated) prisoner's dilemma.


Iterated Game As described above, the prisoner's dilemma is a one-shot game. But in the real world, may prisoner's dilemmas involve repeated plays. You can imagine a series of moves, for example:

Round One--Alice Confesses, Ben Does Not Confess Round Two--Alice Confesses, Ben Confesses Round Three--Alice Does Not Confess, Ben Does Not Confess

We can imagine various strategies of play for Ben and Alice. One of the most important strategies is called tit for tat. Alice might say to herself, "If Ben Confesses, then I will retaliate and confess, but if Ben does not confess, then neither will I." Add one more element to this strategy. Suppose both Ben and Alice say to themselves, on the first round of play, I will cooperate and not confess. Then we would get the following pattern:

Round One--Alice Does Not Confess, Ben Does Not Confess Round Two--Does Not Confess, Ben Does Not Confess Round Three--Alice Does Not Confess, Ben Does Not Confess

Thus, if both Ben and Alice play tit for tat, the result might be a stable pattern of cooperation, which benefits both Ben and Alice.

If you want to get a really good feel for the iterative prisoner's dilemma, go to this website, where you can actually try out various strategies.

One more twist. Suppose that this game is finite, i.e. it has a fixed number of moves, e.g. ten. How will Ben and Alex play in the "end game." Ben might reason as follows. If I defect and confess on the tenth move, Alice cannot retaliate on the eleventh move (because there is no eleventh round of play). And Alice might reason the same way, leading both Ben and Alice to confess in the final round of play. But now Ben might think, since it is rational for both of us to defect in the tenth round, I need to rethink my strategy in the ninth round. Since I know that Alice will confess anyway in the tenth round, I might as well confess in the ninth round. But once again, Alice might reason in exactly this same way. Before we know it, both Alice and Ben have decided to defect in the very first round.


Conclusion This has been a very basic introduction to the prisoner's dilemma, but I hope that it has been sufficient to get the basic concept across. As a first year law student, you are likely to run into the prisoner's dilemma sooner or later. If you have an interest in this kind of approach to legal theory, I've provided some references to much more sophisticated accounts. Happy modeling!


References Here are some links to game theory and prisoner's dilemma resoures on the web:

• Steve Kuhn, Entry on Prisoner's Dilemma in the Stanford Internet Encyclopedia of Philosophy.
• "Comprehsive Repository" for information about the iterated PD (compiled by group at Laboratoire d'Informatique Fondamentale de Lille).
• Axelrod and D'Ambrosio's annotated bibliography (1988-1994).
• Spatial IPDs by Norman Siebrasse
• Spatial IPDs by Jason Alexander.
• Spatial IPDs by William Harms.
• Site designed to accompany Axelrod's Complexity of Cooperation.
• Miscellaneous PD Resources (compiled by Constitution Society).
• Interactive Prisoner's Dilemma (at the Serendip pages at Bryn Mawr).

(Last revised on December 23, 2007.)

Legal Theory Lexicon 002: The Coase Theorem

This week the Legal Theory Lexicon investigates the Coase theorem. Ronald Coase is a member of the law and economics faculties at the University of Chicago and a winner of the Nobel Prize in Economics. The idea that we call the Coase Theorem was advanced in a very famous paper:

Coase, R.H., The Problem of Social Cost, Journal of Law and Economics 3, 1-44 (1960).

To understand the Coase theorem, we first need to introduce another idea, the externality. Roughly speaking, an economic externality is cost imposed by an activity that is not accrued by the person or firm who engages in the activity. That's a mouthful. Here's an example:

The Reading Railroad has track that goes by Farmer Jones's farm. The locamotives cast off sparks that cause a fire that damages Farmer Jones's crop, imposing a cost on Jones of $100. That ocst is an externality.

If the Reading Railroad owned the farm, then it would bear the cost, and there wouldn't be an externality. Before Coase, we thought that the existence of externalities justified some kind of government intervention. For example, we could create a liability rule that required the Reading Railroad to pay for the damage to his crops. Without a liability rule, the railroad wouldn't have any incentive to prevent the damage if there was a cost-effective means of doing so. Let's add a fact to our hypothetical:

The Reading Railroad can purchase and install a 100% effective spark arrestor for $50.

We want the railroad to install the spark arrestor for $50 to prevent $100 worth of damage. Before Coase, we said, "internalize the external diseconomies!" Really! That is, use tort law to transform the external cost imposed by the railroad into an internal cost.

This is where Coase came in. But to understand what Coase said, we need to add another bit of economic jargon. By transaction cost, we mean the cost of reaching a bargain. In the real world, lawyers are frequently part of transaction costs, but the time and expense that it takes to strike a deal are transaction costs as well--even if you don't actually lay out any cash. One more little move, if we assume that there are zero transaction costs, we are simply assuming that it costs absolutely nothing to strike a deal--no time, no effort, no lawyers, not even any paper on which to write it up.

Coase said, "Let's assume zero transaction costs!" Okey dokey, what next! If we assume zero transaction costs, then when there are externalities, the market will reach the efficient outcome irrespective of how entitlements are assigned. Another mouthful! Let's go back to our hypo:

Assuming zero transaction costs, it doesn't matter whether the law assigns the right to generate sparks to the railroad or the right to be free from sparks to the farmer. Why not? Let's work it out. There are two possibilities:

If we assign the entitlement to the farmer, the railroad will pay $100 in damages to the farmer for vioalting the farmer's right to be spark free. The railroad will realize that it can save this $100 cost by investing $50 in a spark arrestor. So the railroad will buy the spark arrestor.

If we assign the entitlement to the railroad, the farmer will incur $100 in costs from the fire. The farmer will realize that he can save this $100 cost by entering into a contract whereby he pays $50 (plus some extra enducement, say $51 total) to the railroad in exchange for the railroad installing the spark arrestor. Since we have assumed zero transaction costs, the railroad and the farmer both benefit from this deal.

That's it! It doesn't matter whether we assign the right to the farmer or the railroad. Either way, we get the efficient outcome.

If you are a first year law student, the Coase theorem is a very powerful analytic tool for understanding the economics of tort law. When you study a new rule or problem, ask yourself, "How would this come out assuming zero transaction costs?" Then ask, "If we assume positive transaction costs, how does the problem change?"
One word of warning, the zero-transaction-costs assumption is just an assumption. In the real world, there are always (or almost always) transaction costs. Nonetheless, in some situations, transactions costs are sufficiently low so that the efficient bargain can be struck. In other situations, this is not the case. That's where the action is!

Links

The World According to Coase
Bill Edmundson's Handout on the Coase Theorem

(This entry was last revised on November 25, 2007.)

Legal Theory Lexicon 001: Ex Ante/Ex Post

If I had to select only one theoretical tool for a first-year law student to master, it would be the ex post/ex ante distinction. (Of course, this is cheating, because there is a lot packed into the distinction.) The terminology comes from law and economics, and here is the basic idea:

• The ex post perspective is backward looking. From the ex post point of view, we ask questions like: Who acted badly and who acted well? Whose rights were violated? Roughly speaking, we associated the ex post perspective with fairness and rights. The ex post perspective in legal theory is also loosely connected with deontological approaches to moral theory. In general jurisprudence, we might associate the ex post perspective with legal formalism.
• The ex ante perspective is forward looking. From the ex ante point of view, we ask questions like: What affect will this rule have on the future? Will decision of a case in this way produce good or bad consequences? Again, roughly speaking we associate the ex ante perspective with policy and welfare. The ex ante perspective in legal theory is loosely connected with consequentialist (or utilitarian or welfarist) approaches to moral theory. In general jurisprudence, we might associate the ex ante perspective with legal instrumentalism (or legal realism).

Of course, this very basic introduction to the distinction is oversimplified. For example, a fairness-based theory of torts might consider future consequences in assessing legal rules, and even utilitarian legal theories must use ex ante information when evaluating particular cases.

Why is the distinction between ex ante and ex post so important? Because it marks an import