We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the spatial model of elections---each voter specifies an ideal element of the metric space. The ideal element functions as a vote, where each voter prefers elements that are closer to her ideal element. But it also functions as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of the abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters, and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making.

中文翻译：

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度量空间的聚合：在选举、预算和立法中提议和投票

我们提出了一个包含许多社会选择设置的统一框架。将每个社会选择设置视为在合适的度量空间中投票，我们考虑了度量空间上的社会选择的一般模型，其中——类似于选举的空间模型——每个选民指定了度量空间的理想元素. 理想元素起到投票的作用，每个投票者都喜欢更接近她理想元素的元素。但它也起到了提案的作用，从而使所有参与者不仅作为投票者而且作为提案者都是平等的。我们考虑 Condorcet 聚合和解决方案概念的连续统，范围从最小化距离总和到最小化最大距离。我们研究抽象模型在各种社会选择环境中的应用，包括单一获胜者选举、委员会选举、参与式预算和参与式立法。对于每个设置，我们将每个解决方案概念与已知投票规则进行比较，并研究结果投票规则的各种属性。我们的框架为广泛的社会选择设置提供了表达性聚合，同时对选民保持简单，并且可以为所有这些设置实现统一和集成的实施，以及统一的扩展，例如女巫弹性、代理投票和审议决策.