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<p>In this note we review some recent results concerning two related problems: how to build, starting from a ranking over a finite set <i>A</i> of alternatives, a compatible extension to a ranking over all subsets of <i>A</i>; and, conversely, how to derive a ranking over the alternatives from a ranking over the subsets of a set of alternatives. These two problems are studied in Social Choice because of their wide range of applications. The reported results are taken from Lucchetti et&#xa0;al. (<CitationRef CitationID="CR25">2015</CitationRef>); Bernardi et&#xa0;al. (<CitationRef CitationID="CR8">2019</CitationRef>).</p>

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Connecting preferences over a set with preferences over its power set, and conversely

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Roberto Lucchetti

摘要

In this note we review some recent results concerning two related problems: how to build, starting from a ranking over a finite set A of alternatives, a compatible extension to a ranking over all subsets of A; and, conversely, how to derive a ranking over the alternatives from a ranking over the subsets of a set of alternatives. These two problems are studied in Social Choice because of their wide range of applications. The reported results are taken from Lucchetti et al. (2015); Bernardi et al. (2019).