Gamson's Law in Dynamic Legislative Bargaining

15:30-16:30, Sunday, June 25, 2023

I-206, Boxue Building, DUFE


Dr. Quan WEN is Robert R. Rechards Professor of Economics at University of Washington. He received his Ph.D. in Economics from University of Western Ontario in 1991. His research fields are Game Theory and Microeconomic Theory. His work has appeared in Econometrica, Games and Economic Behavior, Journal of Economic Theory, among others.

In modern democratic society, conflicts of interest at various levels are often resolved through some collective decision-making process such as committee voting and dynamic legislative bargaining. There are generally multiple parties, each of which controls a certain fraction of votes. If several parties control a majority of votes, they would form a winning coalition in the majority voting to implement the policy that they agree on. The dynamic process continues in the same fashion, by which a new winning coalition may form and pass a new policy to replace the status quo. The following research questions naturally arise. First, how does the distribution of voting weights affect the composition of winning coalitions? Second, whether and when will winning collations be minimal in size and stable in composition? Third, how do parties in a winning coalition share the surplus? Answering these questions is of fundamental importance in understanding how various institutions work in practice and how to fine-tune them to achieve a certain social goal.

Following the existing literature (e.g., Kalandrakis, 2004, 2010; Anesi and Seidmann, 2015; Baron, 2019), we study a tractable model of dynamic legislative bargaining with a general voting weight distribution among n≥3 parties. Both the winning coalition and the status quo policy evolve endogenously via recurrent majority voting. We characterize a class of pure-strategy stationary Markov perfect equilibria, namely, simple equilibria, featuring a persistent winning coalition and stable status quo policy. Our equilibrium characterization generalizes that of Anesi and Seidmann (2015) from a symmetric one-party-one-vote setting to a general setting with arbitrary voting weight distribution. Like in Anesi and Seidmann (2015), there are multiple simple equilibria that are qualitatively different from each other in terms of key properties they exhibit. In particular, the persistent winning coalition in a simple equilibrium is not necessarily minimal in size and it may implement an inefficient policy, the stable status quo policy may allocate a positive share of the surplus to parties outside the winning coalition, and within the winning coalition, each party's share of the surplus may not depend on its voting weight at all.

We establish the existence of a special simple equilibrium in which the persistent winning coalition is minimal in size (i.e., the size principle due to Riker, 1962) and within the minimal winning coalition (MWC henceforth), each party receives a share of the surplus proportional to its voting weight (i.e., Gamson's Law due to Gamson, 1961b). More precisely, we show that (1) there is a set of stable policies and each stable policy is associated with one MWC; (2) each stable policy allocates each member of the associated MWC a share of the surplus proportional to its voting weight; (3) each party is indifferent among all the stable policies for which this party is contained in the associated MWC; (4) if the status quo policy is not in the set of stable policies, the proposing party will immediately propose to form an MWC containing itself to enforce the associated stable policy; (5) once a policy in the set of stable policies becomes the status quo, it will then persist forever.

We further explore the intrinsic robustness of this special simple equilibrium. It is shown that if the enforceable collection of MWCs, which may form in the simple equilibrium, satisfies an independence condition, then Gamson's Law must hold. In the three-party legislature without a veto party, there is a unique enforceable collection of MWCs and it satisfies the independence condition. Hence, in this case, if the size principle is satisfied, so is Gamson's Law.

The construction of the special simple equilibrium also enables us to obtain a set of non-trivial and interesting comparative statics results and corresponding testable hypotheses. In the case of a symmetric voting weight distribution, the size principle and Gamson's law simply imply that members of MWC will share the surplus equally. Once we depart from this symmetric case and consider an asymmetric voting weight distribution while fixing the size of the legislator, then Gamson's law predicts that surplus is divided in a non-trivial way depending on the voting weights.

Based on our theoretical findings, we can use controlled laboratory experiments to test whether the special simple equilibrium, satisfying the size principle and Gamson's law, is most likely to arise in reality.

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