论文标题
代表代理投票
Representative Proxy Voting
论文作者
论文摘要
我们研究了代理投票模型，其中候选人，选民和代理人都位于实际线路上，而不是直接投票，而是将其投票委派给了最接近的代理。目的是找到一组代理，即$θ$的代表性，这需要对位于线上任何地方的任何选民来说，其最喜欢的候选人在其最接近的代理人最喜欢的候选人的距离$θ$之内。该财产保证了强大的代表形式，因为不需要提前确定一组选民，甚至是有限的。我们表明，对于位于一条线上的候选人，可以在多项式时间内计算最佳代理安排。此外，我们提供了形成$θ$代表集所需的代理数量的上限和下限，因此表明相对较少的代理足以捕获任何一组选民的偏好。 $θ$代表的代理安排的另一个有益财产是，对于严格的委员会投票规则，代理投票的结果与直接投票的结果相似。
We study a model of proxy voting where the candidates, voters, and proxies are all located on the real line, and instead of voting directly, each voter delegates its vote to the closest proxy. The goal is to find a set of proxies that is $θ$-representative, which entails that for any voter located anywhere on the line, its favorite candidate is within a distance $θ$ of the favorite candidate of its closest proxy. This property guarantees a strong form of representation as the set of voters is not required to be fixed in advance, or even be finite. We show that for candidates located on a line, an optimal proxy arrangement can be computed in polynomial time. Moreover, we provide upper and lower bounds on the number of proxies required to form a $θ$-representative set, thus showing that a relatively small number of proxies is enough to capture the preferences of any set of voters. An additional beneficial property of a $θ$-representative proxy arrangement is that for strict-Condorcet voting rules, the outcome of proxy voting is similarly close to the outcome of direct voting.
