Proportional Rankings
This work addresses the need for fair and proportional rankings in applications like hiring decisions, liquid democracy platforms, and recommender systems, offering a novel approach to ranking that is not incremental but introduces a new principle.
The paper tackles the problem of extending proportional representation to rankings based on approval preferences, ensuring cohesive voter groups are proportionally represented in each initial segment of the ranking. It provides theoretical guarantees and experimental evaluations to identify suitable methods for producing such proportional rankings.
In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that cohesive groups of voters are represented proportionally in each initial segment of the ranking. Proportional rankings are desirable in situations where initial segments of different lengths may be relevant, e.g., hiring decisions (if it is unclear how many positions are to be filled), the presentation of competing proposals on a liquid democracy platform (if it is unclear how many proposals participants are taking into consideration), or recommender systems (if a ranking has to accommodate different user types). We study the proportional representation provided by several ranking methods and prove theoretical guarantees. Furthermore, we experimentally evaluate these methods and present preliminary evidence as to which methods are most suitable for producing proportional rankings.