3 credits (3-0-0)
Pre-requisites: COL202 (or MTL 180) & COL351 (or MTL342)
Matchings: Deferred-acceptance algorithm and lattice structure; strategic manipulation, LP approach for fair (median) stable matchings: many-to-one matchings and rural hospitals theorem; housing markets and kidney exchange; popular matchings.
Fair Division: Proportional and envy-free cake cutting; rent division via Sperner’s lemma; fair allocation of indivisible goods and chores; Pareto optimality and Nash social welfare; fairness of randomised allocations.
Voting: Voting rules and axioms; strategic manipulation, Gibbard-Satterthwaite theorem, computational barriers against manipulation; structured preferences.
Modern Paradigms: Multiwinner voting axioms and Thiele methods; rank aggregation via Kemeny rule, NP-hardness and approximation algorithms; distortion of voting rules; participatory budgeting; liquid democracy: apportionment methods and paradoxes.