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 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.)