论文标题
排名选择投票的噪声稳定性
Noise Stability of Ranked Choice Voting
论文作者
论文摘要
我们猜想，Borda Count是排名的选择投票方法，它可以最好地保留以随机损坏的选票的选举结果，其中包括满足Condorcet失败者标准的所有公平投票方法。这种猜想是对多数的改编，这是对排名选择投票的设定的最稳定的猜想。由于复数函数无法满足Condorcet失败者标准，因此我们的新猜想与多数构想直接相关是最稳定的猜想。然而，我们表明多数是最稳定的猜想，这意味着我们的新博尔达人数是最稳定的猜想。因此，我们推断出，当损坏的选票与原始选票几乎不相关时，Borda Count是最稳定的选举。我们还适应了缩小尺寸的论点，以表明最佳排名选择投票方法是“低维”。 Condorcet失败者标准断言，如果彼此在头对头比较中，候选人彼此优先，则必须失去选举。最后，我们将condorcet冠军标准作为约束而不是condorcet失败者标准讨论了猜想的变体。在这种情况下，我们没有猜测最稳定的排名选择投票方法。
We conjecture that Borda count is the ranked choice voting method that best preserves the outcome of an election with randomly corrupted votes, among all fair voting methods with small influences satisfying the Condorcet Loser Criterion. This conjecture is an adaptation of the Plurality is Stablest Conjecture to the setting of ranked choice voting. Since the plurality function does not satisfy the Condorcet Loser Criterion, our new conjecture is not directly related to the Plurality is Stablest Conjecture. Nevertheless, we show that the Plurality is Stablest Conjecture implies our new Borda count is Stablest conjecture. We therefore deduce that Borda count is stablest for elections with three candidates when the corrupted votes are nearly uncorrelated with the original votes. We also adapt a dimension reduction argument to this setting, showing that the optimal ranked choice voting method is "low-dimensional." The Condorcet Loser Criterion asserts that a candidate must lose an election if each other candidate is preferred in head-to-head comparisons. Lastly, we discuss a variant of our conjecture with the Condorcet Winner Criterion as a constraint instead of the Condorcet Loser Criterion. In this case, we have no guess for the most stable ranked choice voting method.
