Two principles for two-person social choice

We consider two-person ordinal collective choice from an axiomatic perspective. We identify two principles: minimal Rawlsianism (the chosen alternatives belong to the upper-half of both individuals’ preferences) and the equal loss principle (the chosen alternatives ensure that both individuals concede “as equally as possible” from their highest ranked alternative). The equal loss principle has variants of different strength, depending on the precise definition of “as equally as possible”. We consider all prominent ordinal two-person social choice rules of the literature and explore which of these principles they satisfy. Moreover, we show that minimal Rawlsianism is logically incompatible with one version of the equal loss principle that we call the minimal dispersion principle. On the other hand, there are social choice rules that satisfy the Rawlsian minimal dispersion principle where the minimal dispersion principle is restricted to alternatives within the upper-half of both individuals’ preferences.