Impartial Selection with Additive Approximation Guarantees

Caragiannis, Ioannis; Christodoulou, George; Protopapas, Nicos

doi:10.1007/s00224-022-10081-0

Cited by 7 publications

(11 citation statements)

References 17 publications

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“…This is the first sublinear bound for a deterministic mechanism and any κ ∈ [0, 1], and is sublinear for all κ ∈ [0, 1). For settings with constant maximum outdegree, which includes the setting of Holzman and Moulin where all outdegrees are equal to one, our bound matches the best known bound of O( √ n) for randomized mechanisms and outdegree one, due to Caragiannis et al (2019).…”

Section: Our Contributionsupporting

confidence: 66%

“…Starting from the observation that impossibility results for randomized mechanisms in particular are obtained from graphs with very small indegrees, Bousquet et al (2014) developed a randomized mechanism that is optimal in the large-indegree limit, i.e., that chooses a vertex with indegree arbitrarily close to the maximum indegree as the latter goes to infinity. Caragiannis et al (2019Caragiannis et al ( , 2021 used the same observation as motivation to study mechanisms with additive rather than multiplicative guarantees. They developed new mechanisms that achieve such guarantees, established a relatively small but nontrivial lower bound of 3 for deterministic mechanisms in the approval setting, and gave improved deterministic mechanisms for a setting with prior information.…”

Section: Related Workmentioning

confidence: 99%

“…On the other hand, a multiplicative guarantee of n − 1 is easy to obtain by always following the outgoing edge of a fixed vertex. As multiplicative guarantees do not allow for a meaningful distinction among deterministic impartial mechanisms, Caragiannis et al (2019Caragiannis et al ( , 2021 proposed to instead consider an additive guarantee, i.e., the worst-case over all nomination graphs of the difference between the maximum indegree and the indegree of the selected vertex. A mechanism due to Holzman and Moulin, majority with default, achieves an additive guarantee of ⌈n/2⌉.…”

Section: Introductionmentioning

confidence: 99%

“…A mechanism due to Holzman and Moulin, majority with default, achieves an additive guarantee of ⌈n/2⌉. Caragiannis et al (2019Caragiannis et al ( , 2021 further propose a randomized mechanism with an additive guarantee of O( √ n). It remains open, however, whether there exists a deterministic mechanism with a sublinear additive guarantee.…”

Section: Introductionmentioning

confidence: 99%

“…The impossibility results of Holzman and Moulin regarding multiplicative guarantees carry over to the more general approval setting, where outdegrees can be arbitrary, but here even less is known about possible additive guarantees. While Caragiannis et al (2019) have shown that deterministic impartial mechanisms cannot provide a better additive guarantee than 3, no mechanism is known that improves on the trivial guarantee of n − 1 achieved by selecting a fixed vertex. Caragiannis et al also gave a randomized mechanism for the approval setting with an additive guarantee of Θ(n 2/3 ln 1/3 n).…”

Section: Introductionmentioning

confidence: 99%

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Impartial Selection with Additive Guarantees via Iterated Deletion

Cembrano¹,

Fischer²,

Hannon³

et al. 2022

Preprint

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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(n κ ) 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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Section: Our Contributionsupporting

confidence: 66%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Impartial Selection with Additive Guarantees via Iterated Deletion

Cembrano¹,

Fischer²,

Hannon³

et al. 2022

Preprint

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Optimal Impartial Correspondences

Cembrano

Fischer

Klimm

2022

Lecture Notes in Computer Science

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We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent of the outgoing edges of that vertex. For graphs with maximum outdegree d, we give a mechanism that selects at most d + 1 vertices and only selects vertices whose indegree is at least the maximum indegree in the graph minus one. We then show that this is best possible in the sense that no impartial mechanism can only select vertices with maximum degree, even without any restriction on the number of selected vertices. We finally obtain the following trade-off between the maximum number of vertices selected and the minimum indegree of any selected vertex: when selecting at most k vertices out of n, it is possible to only select vertices whose indegree is at least the maximum indegree minus ⌊(n − 2)/(k − 1)⌋ + 1.

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