A New Axiomatization of the Banzhaf Index for Games with Abstention

Giulia Bernardi

doi:10.1007/s10726-017-9546-6

A New Axiomatization of the Banzhaf Index for Games with Abstention

Giulia Bernardi^*

^*Corresponding author

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

(3, 2)-Simple games are a model for voting situation in which players can vote not only in favour or against a proposal but they can also abstain. Also in this model, power indices are used to evaluate the power of players. In particular, the Banzhaf index and the Shapley–Shubik index have been generalized to define analogous power indices in the context of games with abstention. In this work we provide a new axiomatization of the Banzhaf index for games with abstention, to underline its properties and increase the justification of the use of this index as a solution concept also in the family of games with abstention.

Original language	English
Pages (from-to)	165-177
Number of pages	13
Journal	Group Decision and Negotiation
Volume	27
DOIs	https://doi.org/10.1007/s10726-017-9546-6
Publication status	Published - 2018
Externally published	Yes

Keywords

Abstention
Arts and Humanities (miscellaneous)
Axioms
Decision Sciences (all)
Game theory
Management of Technology and Innovation
Power indices
Social Sciences (all)
Strategy and Management1409 Tourism, Leisure and Hospitality Management
Voting

Access to Document

10.1007/s10726-017-9546-6

Cite this

@article{ba051daadc10441390521a5ad8b4e20e,

title = "A New Axiomatization of the Banzhaf Index for Games with Abstention",

abstract = "(3, 2)-Simple games are a model for voting situation in which players can vote not only in favour or against a proposal but they can also abstain. Also in this model, power indices are used to evaluate the power of players. In particular, the Banzhaf index and the Shapley–Shubik index have been generalized to define analogous power indices in the context of games with abstention. In this work we provide a new axiomatization of the Banzhaf index for games with abstention, to underline its properties and increase the justification of the use of this index as a solution concept also in the family of games with abstention.",

keywords = "Abstention, Arts and Humanities (miscellaneous), Axioms, Decision Sciences (all), Game theory, Management of Technology and Innovation, Power indices, Social Sciences (all), Strategy and Management1409 Tourism, Leisure and Hospitality Management, Voting, Abstention, Arts and Humanities (miscellaneous), Axioms, Decision Sciences (all), Game theory, Management of Technology and Innovation, Power indices, Social Sciences (all), Strategy and Management1409 Tourism, Leisure and Hospitality Management, Voting",

author = "Giulia Bernardi",

year = "2018",

doi = "10.1007/s10726-017-9546-6",

language = "English",

volume = "27",

pages = "165--177",

journal = "Group Decision and Negotiation",

issn = "0926-2644",

publisher = "Springer Netherlands",

}

TY - JOUR

T1 - A New Axiomatization of the Banzhaf Index for Games with Abstention

AU - Bernardi, Giulia

PY - 2018

Y1 - 2018

N2 - (3, 2)-Simple games are a model for voting situation in which players can vote not only in favour or against a proposal but they can also abstain. Also in this model, power indices are used to evaluate the power of players. In particular, the Banzhaf index and the Shapley–Shubik index have been generalized to define analogous power indices in the context of games with abstention. In this work we provide a new axiomatization of the Banzhaf index for games with abstention, to underline its properties and increase the justification of the use of this index as a solution concept also in the family of games with abstention.

AB - (3, 2)-Simple games are a model for voting situation in which players can vote not only in favour or against a proposal but they can also abstain. Also in this model, power indices are used to evaluate the power of players. In particular, the Banzhaf index and the Shapley–Shubik index have been generalized to define analogous power indices in the context of games with abstention. In this work we provide a new axiomatization of the Banzhaf index for games with abstention, to underline its properties and increase the justification of the use of this index as a solution concept also in the family of games with abstention.

KW - Abstention

KW - Arts and Humanities (miscellaneous)

KW - Axioms

KW - Decision Sciences (all)

KW - Game theory

KW - Management of Technology and Innovation

KW - Power indices

KW - Social Sciences (all)

KW - Strategy and Management1409 Tourism, Leisure and Hospitality Management

KW - Voting

KW - Abstention

KW - Arts and Humanities (miscellaneous)

KW - Axioms

KW - Decision Sciences (all)

KW - Game theory

KW - Management of Technology and Innovation

KW - Power indices

KW - Social Sciences (all)

KW - Strategy and Management1409 Tourism, Leisure and Hospitality Management

KW - Voting

UR - http://hdl.handle.net/10807/133914

UR - http://www.kluweronline.com/issn/0926-2644

U2 - 10.1007/s10726-017-9546-6

DO - 10.1007/s10726-017-9546-6

M3 - Article

SN - 0926-2644

VL - 27

SP - 165

EP - 177

JO - Group Decision and Negotiation

JF - Group Decision and Negotiation

ER -

A New Axiomatization of the Banzhaf Index for Games with Abstention

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this