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Robustness Among Multiwinner Voting Rules

Robert Bredereck (TU Berlin)

We investigate how robust are results of committee elections to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates in a single preference order is either that (1) at most one committee member can be replaced, or (2) it is possible that the whole committee can be replaced. Under mild assumptions, we show that if a rule exhibits the first ype of behavior then there is a polynomial-time algorithm that computes a winning committee under this rule. We also show that the problem of computing the smallest number of swaps that lead to changing the election outcome is typically \(\mathrm{NP}\)-hard, but there are natural \(\mathrm{FPT}\) algorithms. Finally, for a number of rules we assess experimentally the average number of random swaps necessary to change the election result.



Robert Bredereck
TEL 512

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