What is it about?
When choosing a committee, voters are often asked to rank candidates rather than assign them exact numerical values. But can we still choose a good committee when we only know these rankings? We study this question when voters and candidates can be placed along a one-dimensional spectrum, such as a political spectrum from left to right. We consider settings in which every member of the elected committee matters to every voter, and the goal is to choose a committee that is collectively as close as possible to the voters. We introduce a new voting method, the Polar Comparison Rule, which uses only voters’ rankings. The rule carefully compares candidates on different sides of the electorate when building the committee. We then measure how close the resulting committee is to the best committee that could have been chosen if voters’ exact preferences were known.
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Why is it important?
Collective decisions are often made using rankings because asking people to provide precise numerical preferences can be difficult or unrealistic. This makes it important to understand how good a decision can be when only rankings are available. Our results show that substantially better committees can be guaranteed by using the information in these rankings more carefully. For most committee sizes, our method improves the previously known worst-case guarantee from 3 to approximately 2.33. This shows that even without knowing voters’ exact preferences, we can make significantly better collective decisions by designing voting rules that make better use of ordinal information.
Perspectives
A natural starting point on the line is the median voter: when choosing a single candidate, the candidate ranked first by the median voter is an optimal choice. But when choosing a committee, it is less clear how the remaining members should be selected. Simply continuing down the median voter’s ranking may result in choosing several candidates from the same side of the median voter, leading to a substantially worse outcome. This observation motivates the main idea behind our Polar Comparison Rule. After choosing the median voter’s top-ranked candidate, the rule introduces a bias in favor of candidates on the opposite side of the median voter from the candidate already chosen. This encourages the committee to represent both sides of the median voter, while still taking the preferences of all voters into account. Importantly, even though we do not know the exact locations of the candidates, we can determine their relative order on the line from the voters’ rankings. This allows us to exploit the underlying geometry without requiring voters to report their exact numerical preferences.
Golnoosh Shahkarami
Max Planck Institute for Informatics
Read the Original
This page is a summary of: Distortion of Multi-Winner Elections on the Line Metric: The Polar Comparison Rule, ACM Transactions on Economics and Computation, August 2026, ACM (Association for Computing Machinery),
DOI: 10.1145/3843232.
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