Topic: Fair division under objective constraints and ordinal input

Speaker: Anna Bogomolnaia, Professor, University of Glasgow

Time: April 10, 2024, 15:40

Venue: Room 121

Abstract:

   A set A of m indivisible objects is to be fully allocated between n agents; each agent i is to get exactly qi objects. Agents only report their ordinal preference orderings of single objects in A. Thus, a mechanism designer can only partially compare allocations of an agent, based on stochastic dominance.

   The paper shows the existence of an allocation rule, which satisfies Ordinal Efficiency (weaker condition than full efficiency, unreachable in this model), Ordinal Proportionality up to one object exchange (oPRO1) and Ordinal Envy-Freeness up to one object exchange (oEF1) (stronger conditions then cardinal ones). It is proven by demonstrating that an appropriate generalization of Round Robin rule (gRR) always exists for the case of different entitlements qi, and satisfies a plethora of attractive normative properties.

   Concepts of fairness "up to one object exchange" are introduced as necessary modifications for our new model of classical "up to one object" fairness properties used in standard fair division literature.

Guest Bio:

    Anna Bogomolnaia received her PhD in Economics from Universitat Autonoma de Barcelona, Spain, in 1998. She also holds Master degree in Mathematics from St. Petersburg University, Russia. Before joining University of Glasgow in 2013, she worked at University of Nottingham, Southern Methodist University, and Rice University.