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Abstract:
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In order to study voting situations when voters can also abstain and the output is binary, i.e., either approval or rejection, a new extended model of voting rule was defined. Accordingly, indices of power, in particular Banzhaf’s index, were considered. In this paper we argue that in this context a power index should be a pair of real numbers, since this better highlights the power of a voter in two different cases, i.e., her being crucial when switching from being in favor to abstain, and from abstain to be contrary. We also provide an axiomatization for both indices, and from this a characterization as well of the standard Banzhaf index (the sum of the former two) is obtained. Some examples are provided to show how the indices behave. |
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Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Teoria de jocs
-Game theory
-Decision making -- Mathematical models
-Voting -- Mathematical models
-Voting -- Abstention
-Axioms
-Abstention
-Axioms
-Decision making process
-Power
-Voting systems in democratic organizations
-Jocs, Teoria de
-Decisió, Presa de -- Models matemàtics
-Vot -- Models matemàtics
-Abstencionisme electoral
-Axiomes
-Classificació AMS::05 Combinatorics::05C Graph theory
-Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science
-Classificació AMS::94 Information And Communication, Circuits::94C Circuits, networks |
