The Price of Majority Support
Robin Fritsch, Roger Wattenhofer

TL;DR
This paper analyzes the trade-off between majority support and representativeness in group decision-making on multiple binary topics, quantifying the 'price' of enforcing majority consensus and its impact on outcome quality.
Contribution
It introduces formal metrics for measuring the loss of representativeness due to majority support constraints and provides bounds and numerical results for these metrics across different numbers of topics.
Findings
Maximum guaranteed agreement with majority support is loor{(t+1)/2} for t topics.
For 3 topics, the ratio of matches guaranteed is 5/6 (~0.83).
As t increases, the upper bound approaches approximately 0.90.
Abstract
We consider the problem of finding a compromise between the opinions of a group of individuals on a number of mutually independent, binary topics. In this paper, we quantify the loss in representativeness that results from requiring the outcome to have majority support, in other words, the "price of majority support". Each individual is assumed to support an outcome if they agree with the outcome on at least as many topics as they disagree on. Our results can also be seen as quantifying Anscombes paradox which states that topic-wise majority outcome may not be supported by a majority. To measure the representativeness of an outcome, we consider two metrics. First, we look for an outcome that agrees with a majority on as many topics as possible. We prove that the maximum number such that there is guaranteed to exist an outcome that agrees with a majority on this number of topics and has…
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Taxonomy
TopicsGame Theory and Voting Systems · Opinion Dynamics and Social Influence · Complexity and Algorithms in Graphs
