Integer Programming on Domains Containg Inseparable Ordered Pairs

Using the integer programming approach introduced by Sethura- man, Teo, and Vohra (2003), we extend the analysis of the preference domains containing an inseparable ordered pair, initiated by Kalai and Ritz (1978). We show that these domains admit not only Ar- rovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decom- posability condition introduced by Busetto, Codognato, and Tonin (2012). Moreover, we go further in the comparison between Kalai and Ritz (1978)'s inseparability and Arrow (1963)'s single-peak restrictions, showing that the former condition is more \respectable," in the sense of Muller and Satterthwaite (1985)