Kemeny Consensus Complexity

Fitzsimmons, Zack; Hemaspaandra, Edith

doi:10.24963/ijcai.2021/28

“…It is axiomatically attractive (Young and Levenglick 1978;Can and Storcken 2013;Bossert and Sprumont 2014) and has an interpretation as a maximum likelihood estimator (Young 1995) making it wellsuited to epistemic social choice that assumes a ground truth. indeed a Kemeny ranking (Fitzsimmons and Hemaspaandra 2021). Thus, third parties cannot easily audit, interpret, or understand the outcome, making systems based on Kemeny's method potentially unaccountable.…”

Section: Introductionmentioning

confidence: 99%

Rank Aggregation Using Scoring Rules

Boehmer

¹

,

Bredereck

²

,

Peters

³

2023

AAAI

2

0

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To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the top, and ranking by repeatedly choosing a loser that we delete and rank at the bottom. The latter method captures the frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, and Baldwin. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect the "true" ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for STV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates.

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“…However, Kemeny's method is hard to compute [Bartholdi et al, 1989, Hemaspaandra et al, 2005 which makes the method problematic to use, especially when there are many candidates to rank (for example, when ranking all applicants to a university). Even if computing the ranking is possible, it is coNP-hard to verify if a ranking is indeed a Kemeny ranking [Fitzsimmons and Hemaspaandra, 2021]. Thus, third parties cannot easily audit, interpret, or understand the outcome, making systems based on Kemeny's method potentially unaccountable.…”

Section: Introductionmentioning

confidence: 99%

Rank Aggregation Using Scoring Rules

Boehmer¹,

Bredereck²,

Peters³

2022

Preprint

1

0

View full text Add to dashboard Cite

To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the top, and ranking by repeatedly choosing a loser that we delete and rank at the bottom. The latter method captures the frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, and Baldwin. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect the "true" ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for STV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates.

show abstract