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Kurz, Sascha ; Mayer, Alexander ; Napel, Stefan:
The Art and Beauty of Voting Power.
In: Leroch, Martin A. ; Rupp, Florian
(Hrsg.):
Power and Responsibility : Interdisciplinary Perspectives for the 21st Century in Honor of Manfred J. Holler. -
Cham
: Springer International Publishing
,
2023
. - S. 125-141
ISBN 978-3-031-23014-1
DOI: https://doi.org/10.1007/978-3-031-23015-8
Abstract
We exhibit the hidden beauty of weighted voting and voting power by applying a generalization of the Penrose-Banzhaf index to social choice rules. Three players who have multiple votes in a committee decide between three options by plurality rule, Borda’s rule, and antiplurality rule, or one of the many scoring rules in between. A priori influence on outcomes is quantified in terms of how players’ probabilities are pivotal for the committee decision compared to a dictator. The resulting numbers are represented in triangles that map out structurally equivalent voting weights. Their geometry and color
variation reflect fundamental differences between voting rules, such as their inclusiveness and transparency.