On the price of diversity for multiwinner elections under (weakly) separable scoring rules
研究了在（弱）可分计分规则下，多赢家选举中为满足多样性约束而付出的代价，提出了“多样性代价”和“个体多样性代价”两个概念并给出上界，发现关注候选人表现比关注多样性约束能更准确估计代价。
We consider a model of multi-winner elections, where each voter expresses a linear preference over a finite set of alternatives. Based on voters’ preferences, the primary goal is to select a subset of admissible alternatives, forming what is referred to as a committee. We explore (weakly) separable committee scoring rules, the voting mechanisms that assess each alternative individually using a scoring vector and select the top k alternatives, where k represents the committee’s size. Furthermore, we operate under the assumption that alternatives are categorized based on specific attributes. Within each attribute category, there exists a targeted minimum number of alternatives that the selected committee should encompass, emphasizing the necessity for diversity. In this context, we assess the cost associated with imposing such a diversity constraint on the voting process. This assessment is conducted through two methodologies, referred to as the “price of diversity” and the “individual price of diversity”. We set the upper bounds for both prices across all (weakly) separable committee scoring rules. Additionally, we show how the maximum price of diversity can be used to discriminate between different voting rules in this context. Ultimately, we illustrate that concentrating on the candidates’ performance yields a more accurate estimation of the price of diversity compared to a focus on the enforced diversity constraint.