Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1997), we explore new conditions on prefernce domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set {0, 1/2, 1}: indeed, we show that, there exists a one-to-one correspondence between solutions of an integer program defined on this set and the set of all Arrovian social welfare functions - without restrictions on the range.

Integer Programming on Domains Containing Inseparable Ordered Paris

Using the integer programming approach introduced by Sethuraman, 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 Arrovian social welfare functions \without ties," but also Arrovian social welfare functions \with ties," since they satisfy the strictly decomposability 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).

An axiomatization of difference-form contest success functions

This paper presents an axiomatic characterization of difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. This axiomatization rests on the property of Equalizing Consistency, stating that the difference between winning probabilities in the grand contest and in the smaller contest should be identical across all participants in the smaller contest. This property overcomes some of the drawbacks of the widely-used ratio-form contest success functions. Our characterization shows that the criticisms commonly-held against difference-form contests success functions, such as lack of scale invariance and zero elasticity of augmentation, are unfounded.By clarifying the properties of this family of contest success functions, this axiomatization can help researchers to find the functional form better suited to their application of interest.