# Correction to: On minimum sum representations for weighted voting games

Correction to: On minimum sum representations for weighted voting games Ann Oper Res https://doi.org/10.1007/s10479-018-2893-0 CORRECTION Correction to: On minimum sum representations for weighted voting games Sascha Kurz © Springer Science+Business Media, LLC, part of Springer Nature 2018 Correction to: Ann Oper Res (2012) 196:361–369 https://doi.org/10.1007/s10479-012-1108-3 1 Introduction A weighted voting game is a yes–no voting system speciﬁed by nonnegative voting weights w ∈ R for the voters and a quota q ∈ R . A proposal is accepted iff w(Y ) := w ≥ i ≥0 >0 i i ∈Y q,where Y is the set of voters which are in favor of the proposal. Restricting weights and quota to integers poses the question for minimum sum representations, where the sum of weights of all voters is minimized. For at most 7 voters, these representations are unique. For 8 voters, there are exactly 154 weighted voting games with two minimum sum integer weight representations. Two voters i and j are called equivalent if for all subsets S ⊆ {1,..., n}\{i, j } we have that w(S ∪{i }) and w(S ∪{ j }) either both are strictly less than q or both values are at least q. Adding the extra condition that equivalent voters should get the same weight, we http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Operations Research Springer Journals

# Correction to: On minimum sum representations for weighted voting games

, Volume OnlineFirst – May 31, 2018
3 pages

/lp/springer_journal/correction-to-on-minimum-sum-representations-for-weighted-voting-games-sQpvfP1s6v
Publisher
Springer US
Subject
Business and Management; Operations Research/Decision Theory; Combinatorics; Theory of Computation
ISSN
0254-5330
eISSN
1572-9338
D.O.I.
10.1007/s10479-018-2893-0
Publisher site
See Article on Publisher Site

### Abstract

Ann Oper Res https://doi.org/10.1007/s10479-018-2893-0 CORRECTION Correction to: On minimum sum representations for weighted voting games Sascha Kurz © Springer Science+Business Media, LLC, part of Springer Nature 2018 Correction to: Ann Oper Res (2012) 196:361–369 https://doi.org/10.1007/s10479-012-1108-3 1 Introduction A weighted voting game is a yes–no voting system speciﬁed by nonnegative voting weights w ∈ R for the voters and a quota q ∈ R . A proposal is accepted iff w(Y ) := w ≥ i ≥0 >0 i i ∈Y q,where Y is the set of voters which are in favor of the proposal. Restricting weights and quota to integers poses the question for minimum sum representations, where the sum of weights of all voters is minimized. For at most 7 voters, these representations are unique. For 8 voters, there are exactly 154 weighted voting games with two minimum sum integer weight representations. Two voters i and j are called equivalent if for all subsets S ⊆ {1,..., n}\{i, j } we have that w(S ∪{i }) and w(S ∪{ j }) either both are strictly less than q or both values are at least q. Adding the extra condition that equivalent voters should get the same weight, we

### Journal

Annals of Operations ResearchSpringer Journals

Published: May 31, 2018

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