Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relating Metric Distortion and Fairness of Social Choice Rules   One way of evaluating social choice (voting) rules is through a utilitarian
distortion framework. In this model, we assume that agents submit full rankings
over the alternatives, and these rankings are generated from underlying, but
unknown, quantitative costs. The \emph{distortion} of a social choice rule is
then the ratio of the total social cost of the chosen alternative to the
optimal social cost of any alternative; since the true costs are unknown, we
consider the worst-case distortion over all possible underlying costs.
Analogously, we can consider the worst-case \emph{fairness ratio} of a social
choice rule by comparing a useful notion of fairness (based on approximate
majorization) for the chosen alternative to that of the optimal alternative.
With an additional metric assumption -- that the costs equal the
agent-alternative distances in some metric space -- it is known that the
Copeland rule achieves both a distortion and fairness ratio of at most 5. For
other rules, only bounds on the distortion are known, e.g., the popular Single
Transferable Vote (STV) rule has distortion $O(\log m)$, where $m$ is the
number of alternatives. We prove that the distinct notions of distortion and
fairness ratio are in fact closely linked -- within an additive factor of 2 for
any voting rule -- and thus STV also achieves an $O(\log m)$ fairness ratio. We
further extend the notions of distortion and fairness ratio to social choice
rules choosing a \emph{set} of alternatives. By relating the distortion of
single-winner rules to multiple-winner rules, we establish that Recursive
Copeland achieves a distortion of 5 and a fairness ratio of at most 7 for
choosing a set of alternatives.

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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas