Low Information Manipulations of Stable School Choice Mechanisms

Abstract

I consider the problem of assigning a set of agents to a set of schools (Abdulkadiroğlu and Sönmez, 2003). Agents have strict, transitive and complete preferences over schools and an outside option. The main normative criterion for assignments is stability. A stable outcome is such that (i) no agent desires entry at a school occupied by a second agent over whom she has priority, (ii) no agent prefers a school with remaining availability to that which she attends and (iii) no agent attends a school which she considers unacceptable. The appeal of a mechanism certain to yield a stable outcome is evident, as such an outcome is fair towards all agents. Regrettably, with the exception of the agent-proposing deferred acceptance mechanism (Dubins and Freedman, 1981; Roth, 1982), all such mechanisms are vulnerable to strategic manipulations (Alcade and Barberà, 1994). A mechanism in which truthful preference revelation is a dominant strategy is strategy-proof. Strategy-proofness entails that, in all possible states, an omniscient agent is unable to successfully manipulate the mechanism. Although strategy-proofness is a desirable property, it is also stringent, particularly when one considers that agents seldom possess detailed information regarding the preferences of other agents.