Miscellany

"A Brief Survey on Rational Choice Models of Polling" (2008) with Dan Bernhardt and Francesco Squintani, in The Political Economy of Democracy, Enriquetta Aragones, Carmen Bevia, Humberto Llavador, and Norman Schofield, eds., Fundacion BBVA.

"Candidate Objectives and Electoral Equilibrium" (2006) in The Oxford Handbook of Political Economy, Barry Weingast and Donald Wittman, eds., Oxford: Oxford University Press. Here is the last version prior to publication.

“Probabilistic Voting in the Spatial Model of Elections: The Theory of Office-Motivated Candidates” (2005) in Social Choice and Strategic Decisions: Essays in Honor of Jeffrey S. Banks,David Austen-Smith and John Duggan, eds., New York: Springer. Here is the last version prior to publication.

Social Choice and Strategic Decisions: Essays in Honor of Jeffrey S. Banks, David Austen-Smith and John Duggan, eds., New York: Springer. Here is a review by Maggie Penn.

Special Issue in Honor of William Thomson, Social Choice and Welfare, 2017, Volume 48, Issue 1, with Paulo Barelli and Youngsub Chun. See ``Introduction to the Special Issue in Honor of William Thomson,'' pages 1--4.

Special Issues on Political Economy, International Journal of Game Theory, 2006, Volume 35, Issues 1 and 2, with Shlomo Weber.

"A Conditional Maximum Theorem" (2019) 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.

"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.

Elementary Proofs of Tests for Definiteness of a Matrix in Terms of Principal Minors" (2020) This note gives alternative (and I think nice) proofs that a matrix is positive definite if and only if its leading principal minors are positive, and that it is positive semi-definite if and only if all its principal minors are non-negative. The proofs use elementary matrix algebra and results from optimization theory. A byproduct is a bonus theorem that gives another test for positive semi-definiteness that requires calculation of fewer determinants.

"A Graphical Perspective on Kolmogorov's Inequality" (2010)

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

"Lemmas on Minimal (Positively) Dependent Sets" (2008)

"Making Determinants Less Weird" (2010) Just some notes I wrote giving some intuition behind determinants, including a geometric proof of Cramer's rule. Sorry the notes are so terse.

"A Note on Backward Induction, Iterative Elimination of Weakly Dominated Strategies, and Voting in Binary Agendas" (2003) This note was written in 2003 but did not include figures, which were at that time done by hand. Since that writing, the open questions I raised were closed by Patrick Hummel, ``Iterative Elimination of Weakly Dominated Strategies in Binary Voting Agendas with Sequential Voting,'' Social Choice and Welfare, 31: 257--269. This note is in the original form except that I have included figures (omitting two that were redundant) and added margin comments reflecting Hummel's findings. No other modifications (typo corrections or otherwise) were made.

"A Note on Continuity Properties of Parameterized Solutions to a Class of Equations" (2019) 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.

"A Note on Harsanyi's Social Aggregation Theorem" (1996)

"A Note on Lebesgue's Dominated Convergence Theorem for Multi-Indexed Sequences of Functions" (2007)

"A Note on Sensitivity Analysis for Local Solutions of Non-Linear Programs" (2007) with Tasos Kalandrakis

"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.

"Pseudo-rationalizability and Tournament Solutions" (1997)

"A Quadratic Triangle Inequality" (2019) 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.

"Quick Lemma on Convexity of the Aumann Integral of L1-Selections from a Correspondence on a Product Space" (2011)

"Quick Lemma on Upper Hemi-continuity of the Bochner Integrals of Lp-Valued Correspondences" (2012)

“A Simple Example of a Finite Stochastic Game with Sequential Moves and No Pure-strategy Stationary Markov Perfect Equilibrium” (2016)

"A Slight Variation on Glicksberg's Theorem" (2002)

"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.

“Remarks for John Ledyard’s 75th Birthday Celebration” (2015) Some remarks I wanted to make at a conference to celebrate John Ledyard’s 75th birthday. I was unfortunately not able to attend, but the sentiments still apply.

"Electoral and Policy Dynamics in US Politics" (2009) Slides from the presentation of an unfinished project with Tasos Kalandrakis.

"Generic Expansiveness of the Majority Top Cycle" (2008) Slides from the presentation of an unfinished project.

"Acceptance Speech for 2006 Social Choice and Welfare Prize" I thought it would be appropriate to post these comments for posterity. My wife and two-year old daughter were present for the ceremony; my daughter lost her patience and started crying right at the end of the speech. Perfect timing.

“Advice on Writing Papers in Political Science” (2013) A short seminar for Rochester grad students.

BibTeX style file that approximates the requirements for Social Choice and Welfare. Here is a link to the BibTeX style file I usually prefer.

"Biography of Jeffrey S. Banks" (2009) This is a short biography of Jeff Banks with proper citations of his work.

"Dynamic Social Choice" (2006) Slides from a plenary lecture at the 2006 Meetings of the Society for Social Choice and Welfare. This talk is based on joint work with Tasos Kalandrakis.

“The Formal Political Theory Field at Rochester” (2013) Slides from a graduate recruiting seminar.

"Formal Political Theory" (2006) Slides from a graduate recruiting seminar.

"How to Maximize Probability of Success in Political Science: Some Tips'' (2005) A short seminar for graduate students.

Bayesian Implementation

• Chapter 1: Introduction

• Chapter 2: Bayesian Implementability in Arbitrary Environments

• Chapter 3: A Full Characterization of Bayesian Implementability in Very General Environments

• Chapter 4: A Full Characterization of Virtual Bayesian Implementability in Quite General Environments