通过迭代删除具有加性保证的公正选择

Javier Cembrano, Felix A. Fischer, David Hannon, Max Klimm
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引用次数: 6

摘要

公正的选择是根据群体中其他成员的提名从群体中选择个人,以这样一种方式,个人不能影响自己的选择机会。我们给出了一个确定性机制,在有n个个体的情况下,每个个体投O(nκ)项,其中κ∈[0,1],具有O(n(1+κ)/2)的加性性能保证。对于κ=0,即当每个个体最多投出一个常数的提名数时,这个界限是O(√n)。这与最著名的随机机制保证和单一提名相匹配。当κ=1时,边界为O(n)。这是微不足道的,因为即使是从不选择的机制也提供了n-1的附加保证。然而,我们表明,这也是最可能的:对于每一个确定性的公正机制,都存在这样一种情况,即某些个体被所有其他个体提名,而该机制要么不选择,要么选择一个没有被任何人提名的个体。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Impartial Selection with Additive Guarantees via Iterated Deletion
Impartial selection is the selection of an individual from a group based on nominations by other members of the group, in such a way that individuals cannot influence their own chance of selection. We give a deterministic mechanism with an additive performance guarantee of O(n(1+κ)/2) in a setting with n individuals where each individual casts O(nκ) nominations, where κ∈[0,1]. For κ=0, i.e. when each individual casts at most a constant number of nominations, this bound is O(√n). This matches the best-known guarantee for randomized mechanisms and a single nomination. For κ=1 the bound is O(n). This is trivial, as even a mechanism that never selects provides an additive guarantee of n-1. We show, however, that it is also best possible: for every deterministic impartial mechanism there exists a situation in which some individual is nominated by every other individual and the mechanism either does not select or selects an individual not nominated by anyone.
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