Schedule

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

[ slides| video (poor audio) ]

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).

[ slides | video (poor audio) ]

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

[ slides | video (poor audio) ]

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

[ slides | video (poor audio) ]

Analysis of Nash equilibria in the Hotelling model of electoral competition and in extensions thereof (preceded by an introduction to game theory).

[ slides | video ]

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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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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Elections that allow residents of a city to vote over how a portion of the city budget is spent, with a focus on voting rules that guarantee new notions of representation.

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A class-wide discussion of which approach (axiomatic, game-theoretic, epistemic) is relevant to the design of real-world democratic systems, and which voting rule (plurality, Borda, STV, Kemeny, Approval) to use in a mayoral election.

[ video ]

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.

[ slides | video ]

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.

[ slides | video ]

Instructor: Krupa Patel

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

[ slides | handout | video ]

Groups: Chen, Chen, Jong, Tobin | D’Amico-Wong, Liang, Pyne, Zhang | Encalada-Stuart, Zhang, Zhou | Feng, Ganireddy, Zhou, Zhang

Groups: Berker, Casacuberta, Ong, Robinson | Guo, Li, Wei | Jafri, Mack, Siebel, Xie | Knorr, Shah, Zhang

Groups: Guo, Wise, Lee, Zhang | Huang, Li, Sun, Xiao | Li, Nehme, Zhu | Liu, Pombra, Pruneri