Improved Metric Distortion for Deterministic Social Choice Rules
Improved Metric Distortion for Deterministic Social Choice Rules
复制标题
改进确定性社会选择规则的度量失真
DOI：
10.1145/3328526.3329550
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Wang, Kangning
中科院分区：
文献类型：
--
作者：
Munagala, Kamesh;Wang, Kangning
在本文中，我们研究了确定性社会选择规则的度量扭曲，该规则根据选民偏好从一组候选人中选择获胜候选人。选民和候选人位于底层度量空间中。选民的成本等于她与获胜候选人的距离。序数社会选择规则只能访问假设与度量距离一致的选民的序数偏好。我们的目标是设计一个具有最小失真的序数社会选择规则，这是在所有一致指标中，规则的社会成本与了解底层度量空间的最优全知规则的社会成本之间的最坏情况比率。已知最佳确定性社会选择规则的失真度在 3 到 5 之间。据推测，任何仅查看候选者加权锦标赛图的规则的失真度都不可能优于 5。在我们的论文中，我们通过提出失真度为 4.236 的加权锦标赛规则来反驳这一点。我们通过推广经典的未覆盖集概念来设计该规则，并进一步证明此类规则不能具有比 4.236 更好的失真度。然后，我们通过未覆盖集的替代概括提出一个新的投票规则。我们证明，如果存在满足该投票规则标准的候选者，那么选择这样的候选者会产生失真界限 3，与下限匹配。我们提出了一个隐含扭曲的组合猜想，并通过计算机实验对少数候选人和选民进行了验证。使用我们的框架，我们还表明，当加权锦标赛图是循环对称时，选择任何候选者可以保证最多 3 的失真。
In this paper, we study the metric distortion of deterministic social choice rules that choose a winning candidate from a set of candidates based on voter preferences. Voters and candidates are located in an underlying metric space. A voter has cost equal to her distance to the winning candidate. Ordinal social choice rules only have access to the ordinal preferences of the voters that are assumed to be consistent with the metric distances. Our goal is to design an ordinal social choice rule with minimum distortion, which is the worst-case ratio, over all consistent metrics, between the social cost of the rule and that of the optimal omniscient rule with knowledge of the underlying metric space. The distortion of the best deterministic social choice rule was known to be between 3 and 5. It had been conjectured that any rule that only looks at the weighted tournament graph on the candidates cannot have distortion better than 5. In our paper, we disprove it by presenting a weighted tournament rule with distortion of 4.236. We design this rule by generalizing the classic notion of uncovered sets, and further show that this class of rules cannot have distortion better than 4.236. We then propose a new voting rule, via an alternative generalization of uncovered sets. We show that if a candidate satisfying the criterion of this voting rule exists, then choosing such a candidate yields a distortion bound of 3, matching the lower bound. We present a combinatorial conjecture that implies distortion of, and verify it for small numbers of candidates and voters by computer experiments. Using our framework, we also show that selecting any candidate guarantees distortion of at most 3 when the weighted tournament graph is cyclically symmetric.
登录
查看更多内容
投票直到你们两个同意：失真小且样本复杂的机制
DOI：
--
发表时间：
2017
期刊：
AAAI Conference on Artificial Intelligence
影响因子：
--
作者：
Stephen Gross;Elliot Anshelevich;Lirong Xia
通讯作者：
Lirong Xia
DOI：
10.1609/aaai.v32i1.11469
发表时间：
2017
期刊：
SIAM J. Comput.
影响因子：
--
作者：
Yu Cheng;S. Dughmi;D. Kempe
通讯作者：
D. Kempe
尽管沟通有限，投票几乎使社会福利最大化
影响因子：
14.4
作者：
I. Caragiannis;Ariel D. Procaccia
通讯作者：
Ariel D. Procaccia
DOI：
10.1145/3033274.3085155
发表时间：
2017
期刊：
Proceedings of the 2017 ACM Conference on Economics and Computation
影响因子：
--
作者：
Yu Cheng;S. Dughmi;D. Kempe
通讯作者：
D. Kempe
将度量扭曲与社会选择规则的公平性联系起来
DOI：
10.1145/3230654.3230658
发表时间：
2018
期刊：
Systems and Computation
影响因子：
--
作者：
Goel, Ashish;Hulett, Reyna;Krishnaswamy, Anilesh K.
通讯作者：
Krishnaswamy, Anilesh K.