# Other Papers

## Working papers and unpublished versions of articles

"Accountability in Markovian Elections" (2021) with Jean Guillaume Forand. We study the ability of elections to solve the dynamic programming problem of a representative voter in a dynamic citizen-candidate framework. We assume a finite number of states and general utilities and state transition probability, thereby allowing for non-trivial dynamics. We prove existence of equilibrium; we show that politicians may manipulate the state to affect their electoral prospects, resulting in suboptimal payoffs for the voter; and we show that for equilibria satisfying a responsive voting condition, equilibria become approximately optimal as the voter becomes patient. This paper supercedes several past versions with different titles ("Markovian Elections," "The Power of Commitment in Dynamic Elections," and "Accountability via Delegation in Dynamic Elections"). Here are slides from a talk.

"Theorems of the Alternative: An Essay in Memory of Kim Border" (2021) This note collects a number of theorems of the alternative, which inform us about solutions to systems of linear equalities and inequalities. To each primary system is associated a secondary system, and the results establish two stark alternatives: either the primary system has a solution, or the secondary system does, but not both. I first learned of these results from Kim Border, who was one of my advisors at Caltech. Kim passed away on November 19, 2020. He dedicated his career to helping other scholars do better work, and this modest note is dedicated to his memory.

"Continuity Properties of the Pareto Correspondence in the Spatial Model of Politics" (2019) 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.

"Existence of Markov Electoral Equilibria" (2018) with Jean Guillaume Forand. We prove existence and upper hemicontinuity of a form of stationary equilibrium in a dynamic model of elections with a discrete (countable) state space and general policies and preferences..

"Bilateral Lobbying: Political Influence as a First Price Auction" (2018) This paper models lobbying as a type of auction, in which lobbyists simultaneously make offers consisting of a policy and transfer, and the politician chooses either one of the offers or implements the status quo. Pure strategy equilibria exist generally. With two lobbyists, the equilibrium outcome is "constrained efficient," and with multiple lobbyists, the possible winners are maximal with respect to an acyclic competitiveness relation. In the spatial model with quadratic utility, there is always an equilibrium in which the lobbyist furthest from the politician wins.

"Extreme Agenda Setting Power in Dynamic Bargaining Games" (2018) with Zizhen Ma. We investigate a canonical model of bargaining with a fixed agenda setter, and we show that when players are impatient or the set of alternatives is one-dimesional, the equilibrium outcome from the static model obtains; but when players are patient and the alternatives are multidimensional, the equilibrium outcome typically converges to the ideal point of the agenda setter. Here is a working paper with additional results on boundary equilibria and genericity in the Whitney topology. Here are some slides from a talk.

“The Political Economy of Dynamic Elections: A Survey and Some New Results” (2017) with Cesar Martinelli. This paper contains a survey and synthesis of the literature on electoral accountability, i.e., repeated elections in which politicians cannot commit their policy choices. We establish sets of conditions under which policy choices nevertheless reflect the preferences of the median voter. A shorter version with redacted proofs is published in *Journal of Economic Literature*, 2017, 55: 916--984.

“A Note on the Pareto Manifold in the Spatial Model of Politics” (2016) I provide sufficient conditions for the Pareto set to exhibit a manifold structure near a Pareto optimal alternative -- the analysis takes utility functions as given, rather than making genericity claims. I then investigate a natural parameterization of the Pareto manifold and the corresponding parameterized utilities. In contrast to Smale (1976), I do not assume an economic environment; rather, I consider a general model that includes the spatial model of politics as a special case.

“Sequential Median Location” (2015) This short note shows that in sequential location games in one dimension with single-peaked preferences, if the order of location alternates between agents on one side of the median and the other, then the unique pure strategy subgame perfect equilibrium outcome is the median. The result extends to sequential play of any Condorcet consistent game and to mixed strategies.

“Choice-theoretic Solutions for Strategic Form Games” (2014) with Michel Le Breton. This is the continuation of an old project with Michel Le Breton in which we assume common knowledge of players’ choice sets, rather than mixed strategies. The approach allows for probability-free theories of how players resolve strategic uncertainty and generalizes known results for rationalizable strategies. Here is a working paper version with additional results on choice based on pessimistic conjectures.

“The State of Nature as a Spatial Contest” (2014) I model the state of nature as a spatial contest, in which the final outcome is a deterministic and continuous function of individual effort levels. I establish existence and uniqueness of equilibrium, I characterize the equilibrium of the game, and I perform comparative statics on the cost of effort and risk aversion of the players. This paper evolved into "Lobbying as a Multidimensional Tug of War," with Jacque Gao.

“Value Restriction, Median Voters, and the Core” (2013) I extend results on value restriction to general voting rules and synthesize forms of median voter theorems and representative voter theorems. For a more general analysis of social rationality, see “Preference Exclusions for Social Rationality,” *Social Choice and Welfare*, 46: 93--118.

"Limits of Acyclic Voting and Nash Implementation" (2012) An Arrovian result for acyclic social choice under the independence of irrelevant alternatives. This is version features a much shorter proof of a more general theorem; see the working paper for the case of four or more alternatives. Note the "throwback" typesetting, including typewriter math font; see the modern version, if you don’t like the old mimeograph style. Here are slides from a talk. A shorter version of this paper, without the Nash implementation results, is published in *Journal of Economic Theory*, 163: 658--683.

"Mixed Strategy Equilibrium and Deep Covering in Multidimensional Electoral Competition" (2006) with Matt Jackson. Here are some slides from a talk.

"Existence of Equilibria on Convex Sets" (2004) with Jeff Banks.

"Robust Implementation" (2001) with Joanne Roberts.

"Non-cooperative Games Among Groups" (2001)

"Equilibrium Non-existence in a Model of Representative Democracy" (2001) with Arantxa Jarque-Llamazares.

"Equilibrium Equivalence Under Expected Plurality and Probability of Winning Maximization" (2000) Incomplete: one section missing.

"Implementing the Efficient Allocation of Pollution" (1999) with Joanne Roberts. This paper has been published (American Economic Review, 2002, 92:1070-1078), but the unpublished version contains an analysis of the model with incomplete information.

"Mixed Refinements of Shapley's Saddles and Weak Tournaments" (1999) with Michel Le Breton. This paper has been published (Social Choice and Welfare, 2001, 8:65-78), but the unpublished version contains a more comprehensive analysis of solutions of weak tournaments and an appendix with several additional examples.

"A Bargaining Model of Collective Choice" (1999) with Jeff Banks. This paper has been published (American Political Science Review, 2000, 94:73-88), but the unpublished version contains an appendix showing that our assumption of "limited shared weak preference" is satisfied in a variety of economic environments.

"Dominance-based Solutions for Strategic Form Games" (1998) with Michel Le Breton. Here are some slides from a talk.

"More Bogosity Results for Monotonic Social Choice Rules" (1995) with Tom Schwartz. From the archives: One of my unpublished "classics," related to some results in my paper "Limitations of Acyclic Voting and Implementation."

"Strategic Manipulability is Inescapable: Gibbard-Satterthwaite without Resoluteness" (1992) with Tom Schwartz. This paper is published as "Strategic Manipulability without Resoluteness or Shared Beliefs: Gibbard-Satterthwaite Generalized" (2000) *Social Choice and Welfare,* 17: 85--93. The earlier version is Caltech Social Science Working Paper no. 817, which contains a version of our result with a stronger range condition and weaker non-dictatorship condition.

"Contracting Theory with Coincidence of Interest" (1992) From the archives: This was my second-year paper in the PhD program at Caltech -- in other words, this is ancient history. The paper looks at optimal contracting when the principal and agent both care about the quality of a project. I liked it at the time, but I can't vouch for the quality of this particular project!