Agenda scientifique

Multiwinner voting aims to select a subset of alternatives (a committee) from a larger set of admissible alternatives, according to the votes cast by voters. We consider in this paper that each voter is endowed with a preference order in which the alternatives are ranked from the best to the worst. In this setting, we can define committee scoring rules as multiwinner analogues of positional scoring rules which constitute a well-known subclass of single-winner voting rules. A special class of committee scoring rules – (weakly) separable scoring rules – have gained considerable attention recently. Under this class, when the aim is to select a committee of size exactly k, we can first compute a separate score for each alternative using a single-winner scoring rule and then pick the k alternatives with the top scores. When the underlying single-winner scoring rule does (not) depend on the size k of the target committee then the rule is referred to as (weakly) separable. In this paper, we consider a model of multiwinner voting using (weakly) separable scoring rules where, moreover, alternatives have certain attributes and for each attribute there is a minimal desired number that the selected committee should fit. In this setting, enforcing attribute constraints on the winning committee must naturally have a cost since the feasible space of committees becomes smaller and hence the optimal score may decrease. We measure this cost, that we refer to as the price of diversity, by considering the ratio between the score of the optimal unconstrained committee and the score of the optimal constrained committee. We study to what extent the price of diversity changes regarding the choosen rule.