Lewis Carroll计分规则的$O(\log m)$、确定性、多项式时间可计算近似
A $O(\log m)$, deterministic, polynomial-time computable approximation of Lewis Carroll's scoring rule
摘要：
我们提供了确定性的，多项式时间可计算的投票规则，近似道奇森的和（“最小化版本”）杨的评分规则在对数因子。我们对道奇森规则的近似是紧到常数因子，因为道奇森规则是$\NP$ -很难近似到某个对数因子内。杨氏法则的"最大化版本“是已知的$\NP$ --很难用任何常数因子来近似。这两种近似都很简单，而且作为规则本身也很自然：给定一个我们希望评分的候选人，我们可以将其道奇森或杨得分视为给定的选民偏好集与候选人是孔多塞获胜者之间的编辑距离。(The两个评分规则之间的区别是允许的编辑类型。）我们认为一系列编辑的边际成本是编辑的数量除以编辑产生的减少数量（在与对手的成对竞争中，候选人对任何对手的赤字）。在一系列的回合中，我们的评分规则会自动选择一个编辑序列，该序列只修改一个投票者的偏好，并且其边际成本不大于任何其他单票修改序列。
英文摘要：
We provide deterministic, polynomial-time computable voting rules that approximate Dodgson's and (the ``minimization version'' of) Young's scoring rules to within a logarithmic factor. Our approximation of Dodgson's rule is tight up to a constant factor, as Dodgson's rule is $\NP$-hard to approximate to within some logarithmic factor. The ``maximization version'' of Young's rule is known to be $\NP$-hard to approximate by any constant factor. Both approximations are simple, and natural as rules in their own right: Given a candidate we wish to score, we can regard either its Dodgson or Young score as the edit distance between a given set of voter preferences and one in which the candidate to be scored is the Condorcet winner. (The difference between the two scoring rules is the type of edits allowed.) We regard the marginal cost of a sequence of edits to be the number of edits divided by the number of reductions (in the candidate's deficit against any of its opponents in the pairwise race against that opponent) that the edits yield. Over a series of rounds, our scoring rules greedily choose a sequence of edits that modify exactly one voter's preferences and whose marginal cost is no greater than any other such single-vote-modifying sequence.
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。
