Resources for students

This page contains material that is potentially useful for grad students (or at least, it would’ve been useful to me when I was a grad student).

Lecture notes

Abbreviated Notes on Social ChoiceNotes from PEC 575, Fall, 2014.


Basic Concepts in Mathematical Analysis: A Tourist BrochureA math survey that starts from the basics.


Formal Models in Political Science”   Lecture notes from PSC281/ECO 282, Fall, 2014.


Notes on Optimization and Pareto OptimalityNotes from PSC 408, Spring, 2013.


Notes on Spatial Bargaining and Stochastic GamesNotes from PEC 575, Fall, 2014.


"Notes on Rational Choice under UncertaintyNotes from PSC 408, Spring, 2013.


Notes on Social Choice Rules”   Notes from PSC 408, Spring, 2012.

Surveys in political economy

The Political Economy of Dynamic Elections: A Survey and Some New Results” (2015) with Cesar Martinelli.


A Survey of Equilibrium Analysis in Spatial Models of Elections” (2014)

Probabilistic Voting in the Spatial Model of Elections: The Theory of Office-Motivated Candidates" (2006) with Jeff Banks.

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.

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

Mathematical stuff
A Simple Example of a Finite Stochastic Game with Sequential Moves and No Pure-strategy Stationary Markov Perfect Equilibrium” (2016) A small example that might be interesting to someone.

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.

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

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

"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 Graphical Perspective on Kolmogorov's Inequality" (2010) Nothing deep here, but some nice 3-d pictures (check out p.2). I actually first drew them in grad school to enhance my intuition for the result.

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

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

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

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

Presentations and other information for grad students
A Comparison of PhD Programs in Formal Political Theory” (2015) This report summarizes my findings on training in formal political theory in five PhD programs, in addition to the University of Rochester, in political science. It represents my best effort to form a picture from the websites of these departments.

The Formal Political Theory Field at Rochester” (2015) Slides from a graduate recruiting seminar. Here are some slides from a seminar I gave in 2013.

Advice on Writing Papers in Political Science (2013)

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

"How to Maximize Probability of Success in Political Science: Some Tips'' (2005)