Impossibility results for weak strategy-proofness and respect for improvements in random assignment with priorities
Keisuke Bando, Souta Takase · Economics Letters · 2025
We consider a random assignment problem where each agent has a strict preference and each object has a weak priority. We introduce a weak fairness notion called weak equal-top fairness , which requires that if two agents rank an object as their top choice, and the object also ranks both agents at the top, then they must be assigned to that object with equal probability. We show that even this mild fairness requirement is incompatible with other desirable properties; no mechanism satisfies weak equal-top fairness, ex ante stability, and weak strategy-proofness. Moreover, no mechanism satisfies weak equal-top fairness, ex ante stability, and respect for improvements.