衡量先验投票权——认真对待委托
Measuring a Priori Voting Power -- Taking Delegations Seriously
AI总结：
本文提出衡量流动民主中选民先验投票权的新权力指数，扩展了Penrose-Banzhaf指数，证明一般情形下计算临界性为#P难，但在二部图或完全图等特定网络中可伪多项式时间计算，并通过数值实验展示委托限制对投票权的影响。
摘要：
我们引入了新的权力指数，用于衡量流动民主选举中选民的先验投票权，其中底层网络限制了委托。我们认为，我们的权力指数是简单投票博弈中标准Penrose-Banzhaf指数的自然扩展。我们证明，即使投票权重在实例规模上多项式有界，计算选民的临界性也是#P难的。然而，对于特定设置，例如当底层网络是二部图或完全图时，递归公式可以在伪多项式时间内计算加权投票博弈的这些指数。我们强调了它们的理论性质，并提供了数值结果来说明限制可能的委托如何改变选民的投票权。
英文摘要：
We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard Penrose-Banzhaf index in simple voting games. We show that computing the criticality of a voter is #P-hard even when voting weights are polynomially-bounded in the size of the instance. However, for specific settings, such as when the underlying network is a bipartite or complete graph, recursive formulas can compute these indices for weighted voting games in pseudo-polynomial time. We highlight their theoretical properties and provide numerical results to illustrate how restricting the possible delegations can alter voters' voting power.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
