Random assignments and outside options

Authors: Caterina Calsamiglia, Francisco Martinez-Mora and Antonio Miralles

Social Choice and Welfare, Vol. 57, No 3, 557–566 , March, 2021

Most environments where assignment mechanisms (possibly random) are used are such that participants have outside options. For instance private schools and private housing are options that participants in a public choice or public housing assignment problems may have. We postulate that, in cardinal mechanisms, chances inside the assignment process could favor agents with better outside options. By imposing a robustness to outside options condition, we conclude that, on the universal domain of cardinal preferences, any mechanism must be (interim) ordinal.