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Part I: Voting

January 25, 2021: Voting Rules

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

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January 27, 2021: The axiomatic approach

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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February 1, 2021: Strategic manipulation

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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February 3, 2021: Restricted preferences

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

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February 8, 2021: The epistemic approach

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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February 10, 2021: Liquid democracy

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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February 15, 2021: University holiday

February 17, 2021: Approval voting

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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February 22, 2021: Committee elections

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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February 24, 2021: Participatory budgeting

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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March 1, 2021: Wellness day

March 3, 2021: Discussion of voting

Part II: Allocation

March 8, 2021: Cake cutting

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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March 10, 2021: Rent division

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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March 15, 2021: Indivisible goods

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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March 17, 2021: Random assignment

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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March 22, 2021: Sortition

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

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March 24, 2021: Apportionment in the 19th century

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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March 29, 2021: Apportionment in the 20th century

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

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March 31, 2021: Wellness day

April 5, 2021: Redistricting as cake cutting

Instructor: Jamie Tucker-Foltz

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

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April 7, 2021: Identifying gerrymandered maps

Instructor: Moon Duchin

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

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April 12, 2021: The Electoral College

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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April 14, 2021: Discussion of allocation

Part III: Miscellanea

April 19, 2021: Embedded EthiCS

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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April 21, 2021: Course project presentations

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

April 26, 2021: Course project presentations

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

April 28, 2021: Course project presentations

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