Schedule

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

[ slides (overview) | slides (voting rules) | video ]

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 ]

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

[ slides | video ]

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

[ slides | video ]

Analysis of Nash equilibria in the Hotelling model of electoral competition and in extensions thereof.

[ 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.

[ slides | video ]

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. 

[ slides | video ]

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. 

[ slides | video ]

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.

[ slides | 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. 

[ slides | video ]

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. 

[ slides | video ]

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).  

[ slides | video ]

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. 

[ slides | video ]

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

[ slides | video ]

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. 

[ video (HarvardKey required) ]

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. 

[ slides | video ]

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

[ slides | video ]

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: Camila Flowerman

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

Groups: Abreu-Boussard-Ribot | DePaolo-Ha-Ramassamy | Ding-Ennis-Li-Shaotran | Kuchlous-Mohri-Morwani-Wu

Groups: D'Antonio-Lopez-Tang-Zhao | Acharya-Arango-Wang-Zhang | Huang-Huang-Marks-Lu-Romeo | Eshoa-Pisuttisarun-Singh-Shah

Groups: Zhang-Zhao-Zhao | Huang-Kitch-Melas-Kyriazi | Feng-Xiong-Yue | An-Li-Oliva-Paschalidis