Leo Katz and Alvaro Sandroni (University of Pennsylvania Law School and University of Pennsylvania - The Ronald O. Perelman Center for Political Science and Economics (PCPSE)) have posted The Inevitability and Ubiquity of Cycling in All Feasible Legal Regimes: A Formal Proof (Journal of Legal Studies, Vol. 46, Pg. 237, 2017) on SSRN. Here is the abstract:
Intransitive choices, or cycling, are generally held to be the mark of irrationality. When a set of rules engenders such choices, it is usually held to be irrational and in need of reform. In this article, we prove a series of theorems, demonstrating that all feasible legal regimes are going to be rife with cycling. Our first result, the legal cycling theorem, shows that unless a legal system meets some extremely restrictive conditions, it will lead to cycling. The discussion that follows, along with our second result, the combination theorem, shows exactly why these conditions are almost impossible to meet. All of this has numerous implications to which we can only allude here. For one, it suggests why law is as susceptible to manipulation and exploitation of loopholes as it has proved to be.
Very interesting and recommended.