# John Duggan's Research Site

## Bio

I am a professor of political science and economics at the University of Rochester, chair of the Department of Political Science, and a research associate of the W. Allen Wallis Institute of Political Economy. I was director of the Wallis Institute for the period 2002--2012, and I was co-managing editor for the journal *Social Choice and Welfare* for the period 2008--2015. I received my PhD in social science from the California Institute of Technology in 1995. My specializations are game theory, political economy, and social choice theory. My current work is on equilibrium existence in non-cooperative games, dynamic models of bargaining and elections, multi-dimensional spatial models of political competition, and informational aspects of voting and elections.

## About my research

A mathematical model is a lens that can be helpful in aiding our understanding of a phenomenon, and as such, all models incorporate structure and assumptions that can color or distort that understanding. I tend to favor transparency, in the form of less restrictive assumptions, over resolution, even if that means trading off statistical analysis of testable hypotheses for general theoretical propositions. The main focus of my research has been the effect of dynamic and informational incentives on electoral and legislative politics, often using concepts from social choice theory as a benchmark for comparison and, sometimes, as a modeling tool. I've found political economy to be a rich source for theoretical problems: it turns out that discontinuities and non-convexities, which are often ruled out by assumption in economic theory, are a fundamental feature of politics. In some cases, this has led me to questions in pure game theory or social choice, e.g., the existence of equilibria in dynamic games, or the possibility of acyclic preference aggregation in the context of Arrow's impossibility theorem. Jeff Banks once told me that a theorist's choice of problems should follow his or her instincts: a problem should be chosen for its innate interest, not because it's easy or popular; in the long run, the interesting problems will reveal a more durable importance. The contents of this website reflect my attempt to pursue interesting problems, and to make a modest contribution to the field of theoretical political economy along the way.

## Recent work

In this section, I provide links to papers and other content added in the last year or so. Dates indicate the date of the post and sometimes differ from the date of the linked paper.

**August 31, 2020** “Subgame-Perfect Equilibrium in Games with Almost Perfect Information: Dispensing with Public Randomization” (with Paulo Barelli) Harris, Reny, and Robson (1995) show that correlated subgame perfect equilibrium exist in a general class of dynamic games. We show that when nature’s moves are atomless, every such equilibrium can be de-correlated: there is a payoff-equivalent subgame-perfect equilibrium of the original game. As a corollary, we obtain an existence result of He and Sun (2020) for subgame perfect equilibria in games with atomless moves by nature.

**August 30, 2020** "Representative Voting Games" (with Jean Guillaume Forand) We examine policy outcomes in dynamic elections in which the identity of a representative voter depends on an evolving state variable. We show that a subset of "reelection balanced" equilibria of the electoral model match the stationary Markov equilibria of a stochastic game played among representative voters, if politicians are sufficiently office motivated. We also provide general conditions for existence of a representative voter in each state. This paper is forthcoming at *Social Choice and Welfare*.

**July 18, 2020** "A One-page Statement and Proof of Arrow's Theorem" As if the world needed another short proof of Arrow's theorem... I couldn't help myself. This version significantly shortens and simplifies the previous one: by exploiting symmetry arguments (across groups and alternatives), the proof uses only two preference profiles. There are other short proofs, but I've also tried to make this as simple as possible.

**July 18, 2020** "A Model of Interest Group Influence and Campaign Advertising" (with Zuheir Desai) We propose a model in which interest groups contribute money for campaign advertising, which informs a proportion of voters about the policy position of the challenger. The model admits the possibility of positive and negative advertising (to help or hurt the challenger, respectively), but we show that in a given equilibrium, only one type of advertising is possible; the sort realized depends on voters' priors over the challenger. In a positive advertising equilibrium, challengers in a centrally located "funding interval" receive contributions, and in a negative advertising equilibrium, extreme challengers are targeted. This paper is forthcoming at *Quarterly Journal of Political Science*.

**July 18, 2020 **“Electoral Accountability and Responsive Democracy” (with Cesar Martinelli) We analyze a canonical two-period model of elections in which politicians’ preferences and actions are imperfectly observed by voters, i.e., elections are subject to adverse selection and moral hazard. We establish existence of electoral equilibrium, and we give a characterization of equilibria. We show that as politicians become more office motivated, policy is responsive to voter preferences in the sense that the expected level of effort exerted by politicians in the first period becomes arbitrarily large. We allow for the possibility that excessive effort is harmful to voters, and thus the welfare implications of the analysis depend on the properties of voter preferences. This paper is published in *The Economic Journal, *130: 675-715.

**July 18, 2020** "Lobbying as a Multidimensional Tug of War" (with Jacque Gao) We analyze lobbying as a contest in which each lobbyist exerts effort, and effort levels continuously determine a policy outcome in a multidimensional space. We solve for the unique pure strategy equilibrium, and we examine comparative statics with respect to a preference parameter, e.g., if lobbyists become more sensitive to large policy losses, then the equilibrium outcome converges to the Rawlsian policy, which maximizes the payoff of the worst-off lobbyist. The model has the additional interpretation of committee deliberation, in which members each attempt to pull the outcome in their preferred directions. This paper is published in *Social Choice and Welfare, *54: 141-166.

**January 28, 2020** "A Formal Theory of Democratic Deliberation" (with Hun Chung) We provide a framework to model three forms of democratic deliberation: myopic discussion, constructive discussion, and debate. The debate game has a unique subgame perfect equilibrium outcome, which is a compromise of the preferences of the participants. In contrast to the first two forms, debate always concludes with a single outcome (rather than a cycle) and this outcome is path independent (does not depend on the status quo). Here is a link to the technical appendix. This paper is published in the *American Political Science Review, *114: 14-35.

**October 1, 2019** "Continuity Properties of the Pareto Correspondence in the Spatial Model of Politics" This note contains reflections on the upper and lower hemicontinuity of the Pareto correspondence, with an emphasis on lower hemicontinuity, which is generally harder to come by. These results are doubtless known in some form (at least in the setting of an exchange economy), but they were fun to work out.

**September 9, 2019** "Introduction to the Formal Political Theorist's Basic Toolkit of Rational Choice Models" The title says it all: notes for graduate students giving a run down of a number of basic models in rational choice modeling.

**August 24, 2019** "Accountability via Delegation in Dynamic Elections" (with Jean Guillaume Forand) We study the ability of elections to solve the dynamic programming problem of a representative voter. We examine conditions under which the corresponding politician type is a "faithful delegate," and the possibility that delegation allows the voter to achieve optimal policies. We demonstrate the possibility of political failures due to existence of suboptimal equilibria, and we provide relatively narrow conditions precluding such equilibria.

**August 24, 2019** "A `Conditional' Maximum Theorem" (with Paulo Barelli) This note contains a version of the maximum theorem that permits non-compact feasible sets by strengthening the continuity assumption on the objective function being maximized.

**August 24, 2019** "A Quadratic Triangle Inequality" A very short, simple version of the triangle inequality that holds for weighted sums of squared norms of vectors. This is something that came up in a different project, and I thought it might be of small, but positive, interest.

**August 24, 2019** "A Note on Continuity Properties of Parameterized Solutions to a Class of Equations" This is a short note looking at solutions to a integral equation and examining continuity properties of those solutions with the topology of pointwise convergence. The key is to impose uniform continuity over compact sets over the integrand. This will be of limited interest, but I wanted to write this down.