# Student Resources

## Lecture notes

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

## Surveys in political economy

“The Political Economy of Dynamic Elections: A Survey and Some New Results” (2017) with Cesar Martinelli.

“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.

“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.

"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.

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

## 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.

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