Simple Games versus Weighted Voting Games

Frits Hof; Walter Kern; Sascha Kurz; Daniël Paulusma

doi:10.48550/arXiv.1805.02192

Simple Games versus Weighted Voting Games

Frits Hof
, Walter Kern
, Sascha Kurz
, Daniël Paulusma

Discrete Mathematics and Mathematical Programming

Research output: Working paper › Preprint › Academic

7 Downloads (Pure)

Abstract

A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $\alpha= \min_{p\geq 0}\max_{W\in {\cal W},L\in {\cal L}} \frac{p(L)}{p(W)}0$.

Original language	English
Publisher	ArXiv.org
Number of pages	13
DOIs	https://doi.org/10.48550/arXiv.1805.02192
Publication status	Published - 6 May 2018

Keywords

cs.GT
91B12, 94C10

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10.48550/arXiv.1805.02192

Article-v1Final published version, 247 KB

1 Conference contribution
1 Article
1 Preprint

Simple games versus weighted voting games: bounding the critical threshold value
Hof, F., Kern, W., Kurz, S., Pashkovich, K. & Paulusma, D., 1 Apr 2020, In: Social choice and welfare. 54, 4, p. 609–621 13 p.
Research output: Contribution to journal › Article › Academic › peer-review

Open Access
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Simple games versus weighted voting games
Hof, F., Kern, W., Kurz, S. & Paulusma, D., 2018, Algorithmic Game Theory: 11th International Symposium, SAGT 2018, Beijing, China, September 11-14, 2018, Proceedings. Deng, X. (ed.). Cham: Springer, p. 69-81 13 p. (Lecture Notes in Computer Science; vol. 11059).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review
3 Citations (Scopus)

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Simple Games versus Weighted Voting Games: Bounding the Critical Threshold Value
Hof, F., Kern, W., Kurz, S., Pashkovich, K. & Paulusma, D., 20 Oct 2018, ArXiv.org, 10 p.
Research output: Working paper › Preprint › Academic

Open Access
File
10 Downloads (Pure)

Cite this

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title = "Simple Games versus Weighted Voting Games",

abstract = "A simple game \$(N,v)\$ is given by a set \$N\$ of \$n\$ players and a partition of \$2\textasciicircum{}N\$ into a set \$\textbackslash{}mathcal\{L\}\$ of losing coalitions \$L\$ with value \$v(L)=0\$ that is closed under taking subsets and a set \$\textbackslash{}mathcal\{W\}\$ of winning coalitions \$W\$ with \$v(W)=1\$. Simple games with \$\textbackslash{}alpha= \textbackslash{}min\_\{p\textbackslash{}geq 0\}\textbackslash{}max\_\{W\textbackslash{}in \{\textbackslash{}cal W\},L\textbackslash{}in \{\textbackslash{}cal L\}\} \textbackslash{}frac\{p(L)\}\{p(W)\}0\$. ",

keywords = "cs.GT, 91B12, 94C10",

author = "Frits Hof and Walter Kern and Sascha Kurz and Dani{\"e}l Paulusma",

note = "13 pages, 2 figures",

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N2 - A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $\alpha= \min_{p\geq 0}\max_{W\in {\cal W},L\in {\cal L}} \frac{p(L)}{p(W)}0$.

AB - A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of $2^N$ into a set $\mathcal{L}$ of losing coalitions $L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$ with $v(W)=1$. Simple games with $\alpha= \min_{p\geq 0}\max_{W\in {\cal W},L\in {\cal L}} \frac{p(L)}{p(W)}0$.

KW - cs.GT

KW - 91B12, 94C10

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DO - 10.48550/arXiv.1805.02192

M3 - Preprint

BT - Simple Games versus Weighted Voting Games

PB - ArXiv.org

ER -

Simple Games versus Weighted Voting Games

Abstract

Keywords

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Research output

Simple games versus weighted voting games: bounding the critical threshold value

Simple games versus weighted voting games

Simple Games versus Weighted Voting Games: Bounding the Critical Threshold Value

Cite this