Schedule

An introduction to social choice theory covering its history, famous voting rules and basic axiomatic properties.

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Two prominent theorems that analyze voting rules through their axiomatic properties: May's Theorem (which characterizes majority voting) and Arrow's Theorem (which establishes the nonexistence of "perfect" voting rules over three or more alternatives).

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The Gibbard-Satterthwaite Theorem (nonexistence of "reasonable" rules that are immune to strategic manipulation) and the complexity-theoretic approach to circumventing it.

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Strategyproof rules in restricted domains, including single-peaked preferences and facility location.

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A view of voting rules as maximum likelihood estimators: the Condorcet Jury Theorem (for the case of two alternatives), the Mallows Model and the Kemeny Rule.

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Two models of liquid democracy, which allows transitive delegation of votes: an "objective" model where liquid democracy fails to consistently outperform direct democracy and a "subjective" model where it succeeds.

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Instructor: Dominik Peters

Approval voting asks voters which alternatives they approve and selects the alternative approved by the most voters. This rule has many axiomatic virtues, including being resistant to certain types of strategic manipulation.

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Instructor: Dominik Peters

Approval-based rules that select multiple winners, including proportional approval voting, which was proposed by Thiele in 1895 and selects a committee that proportionally represents voters.

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Instructor: Dominik Peters

Elections that allow residents of a city to vote over how a portion of the city budget is spent, with a focus on commonly used voting rules and recently proposed improvements.

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An introduction to fair division through cake cutting: proportionality and envy-freeness, prominent protocols that guarantee these properties and complexity-theoretic analysis through the Robertson-Webb Model.

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Two models and corresponding algorithms for envy-free rent division: a geometric approach relying on Sperner's Lemma versus quasi-linear utilities and the maximin solution.

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Provable fairness guarantees for the allocation of indivisible goods, including the maximin share guarantee and envy-freeness up to one good, as well as algorithms for achieving them (such as maximum Nash welfare).

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Randomized algorithms for allocating indivisible goods when each person only requires one good, with a focus on random serial dictatorship and the Probabilistic Serial Mechanism.

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Algorithms for randomly selecting a panel that is representative of the population and fair to volunteers.

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Methods proposed by the founding fathers for the apportionment of seats in the House of Representatives, as well as the paradoxes some of them have given rise to.

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Modern apportionment methods such as Huntington-Hill and the Balinkski-Young impossibility theorem.

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Instructor: Jamie Tucker-Foltz

Fair-division-based methods for redistricting a state and alleviating the problem of gerrymandering.

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Instructor: Moon Duchin

Statistical techniques for identifying when a map has been engineered to be biased to one party.

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An analysis of a class of cooperative games that models weighted voting, with an emphasis on methods for quantifying the power of states in the Electoral College.

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Instructor: Samuel Dishaw

A discussion of selected questions in political philosophy: abstention vs. uninformed voting, referendum vs. sortition, and epistocracy vs. universal suffrage.

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Groups: Chu-Li-Zhang-Zhu, Kan-Shin-Sirohi-Tan, Sadhuka-Srinivasan, Plotnick-Xu-York

Groups: Veluswamy-Yang, Hawa-Kelner, Hong-Hong-Sun, Cabral-Cheng-Mbaye

Groups: Lin-Halpern-Revel, Panday-Shanehsazzadeh-Zhang, Rees-Venkata-Skoczylas, Oatman-Rowley-Wu