Affine Maximizers in Domains with Selfish Valuations

We consider the domain of selfish and continuous preferences over a “rich” allocation space and show that onto, strategyproof and allocation non-bossy social choice functions are affine maximizers. Roberts [1979] proves this result for a finite set of alternatives and an unrestricted valuation space. In this article, we show that in a subdomain of the unrestricted valuations with the additional assumption of allocation non-bossiness , using the richness of the allocations, the strategyproof social choice functions can be shown to be affine maximizers. We provide an example to show that allocation non-bossiness is indeed critical for this result. This work shows that an affine maximizer result needs a certain amount of richness split across valuations and allocations.