Approval Voting: Three Examples

Francesco de Sinopoli (1) , Bhaskar Dutta (2) , Jean-François Laslier (3)

1 Department of Economics
2 University of Warwick [Coventry]
3 X-DEP-ECO - Département d'Économie de l'École Polytechnique

As proposed in various places, a set of propositional formulas, each associated with a numerical weight, can be used to model the preferences of an agent in combinatorial domains. If the range of possible choices can be represented by the set of possible assignments of propositional symbols to truth values, then the utility of an assignment is given by the sum of the weights of the formulas it satisfies. Our aim in this paper is twofold: (1) to establish correspondences between certain types of weighted formulas and well-known classes of utility functions (such as monotonic, concave or k-additive functions); and (2) to obtain results on the comparative succinctness of different types of weighted formulas for representing the same class of utility functions.

Mots clés: Preference representation; logic-based languages; expressive power comparative succinctness; computational complexity

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Francesco de Sinopoli, Bhaskar Dutta, Jean-François Laslier. Approval Voting: Three Examples. 2006. ⟨hal-00119323⟩