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Mathematical INstitute @ Tel Aviv

Coordinators

  • Noga Alon
  • Michael Krivelevich
  • Leonid Polterovich

The Institute supports a variety of research-related activities at the School of Mathematical Sciences of TAU, including distinguished lectures, visitors, organization of workshops and travel of research students.

Advisory Board

  • Yakov Eliashberg (Stanford University)
  • Peter Sarnak (Princeton University and IAS)
  • Alain-Sol Sznitman (ETH, Zürich)
Stay updated using our calendar.

Upcoming MINT Distinguished Lectures

Rida Laraki (Université Paris Dauphine)

Date Day Time Location Title
2019-01-07 Mon 12:15 Schreiber 006 Majority judgment: a new voting method
2019-01-08 Tue 16:15 Schreiber 007 Acyclic Gambling Games

Rida Laraki (Université Paris Dauphine)

Date Day Time Location Title
2019-01-07 Mon 12:15 Schreiber 006 Majority judgment: a new voting method
2019-01-08 Tue 16:15 Schreiber 007 Acyclic Gambling Games

Abstracts:


Majority judgment: a new voting method

The traditional theory of social choice offers no good solution to the problems of how to elect, to judge, or to rank. We propose a more realistic model where voters evaluate the candidates in a common language of ordinal grades. This small change leads to a new theory and method « majority judgment ». It is at once meaningful, resists strategic manipulation, and is not subject to the paradoxes encountered in practice, notably Condorcet’s and Arrow’s. We offer theoretical, practical, and experimental evidence—from national elections to figure skating competitions—to support the arguments.

References:
Balinski M. and R. Laraki (2007), A Theory of Measuring, Electing and Ranking, PNAS, 104(2), 8720-8725.
B & L (2011), Majority Judgment: Measuring, Ranking, and Electing, MIT Press.
B & L (2014). Judge: Don’t vote. Operations Research, 28, 483-511.
B & L (2017), Majority Judgment vs Majority Rule, preprint.
B & L (2018), Majority Judgment vs Approval Voting, preprint.


Acyclic Gambling Games

Joint work with Jérome Renault (TSE, France)
We consider 2-player zero-sum stochastic games where each player controls his own state variable living in a compact metric space. The terminology comes from gambling problems where the state of a player represents its wealth in a casino. Under natural assumptions (such as continuous running payoff and non expansive transitions), we consider for each discount factor the value vλ of the λ-discounted stochastic game and investigate its limit when λ goes to 0 (players are more and more patient). We show that under a new acyclicity condition, the limit exists and is characterized as the unique solution of a system of functional equations: the limit is the unique continuous excessive and depressive function such that each player, if his opponent does not move, can reach the zone when the current payoff is at least as good than the limit value, without degrading the limit value. The approach generalizes and provides a new viewpoint on the Mertens-Zamir system coming from the study of zero-sum repeated games with lack of information on both sides. A counterexample shows that under a slightly weaker notion of acyclicity, convergence of (vλ) may fail.

Paper link:
https://bfi.uchicago.edu/sites/default/files/research/WP_2018-34.pdf