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We present a unifying framework encompassing many social choice settings.Viewing each social choice setting as voting in a suitable metric space, weconsider a general model of social choice over metric spaces, inwhich---similarly to the spatial model of elections---each voter specifies anideal element of the metric space. The ideal element functions as a vote, whereeach voter prefers elements that are closer to her ideal element. But it alsofunctions as a proposal, thus making all participants equal not only as votersbut also as proposers. We consider Condorcet aggregation and a continuum ofsolution concepts, ranging from minimizing the sum of distances to minimizingthe maximum distance.  We study applications of the abstract model to various social choicesettings, including single-winner elections, committee elections, participatorybudgeting, and participatory legislation. For each setting, we compare eachsolution concept to known voting rules and study various properties of theresulting voting rules. Our framework provides expressive aggregation for abroad range of social choice settings while remaining simple for voters, andmay enable a unified and integrated implementation for all these settings, aswell as unified extensions such as sybil-resiliency, proxy voting, anddeliberative decision making.

Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation