scholarly journals Recognizing majority-rule equilibrium in spatial voting games

1991 ◽  
Vol 8 (3) ◽  
pp. 183-197 ◽  
Author(s):  
J. J. Bartholdi ◽  
L. S. Narasimhan ◽  
C. A. Tovey
Keyword(s):  
Majority Rule ◽  
Spatial Voting ◽  
Voting Games

Stability and Centrality of Legislative Choice in the Spatial Context

1987 ◽  
Vol 81 (2) ◽  
pp. 539-553 ◽  
Author(s):  
Bernard Grofman ◽  
Guillermo Owen ◽  
Nicholas Noviello ◽  
Amihai Glazer
Keyword(s):  
Infinite Number ◽  
Majority Rule ◽  
Solution Concept ◽  
Spatial Context ◽  
Core Outcome ◽  
Legislative Voting ◽  
Spatial Voting ◽  
Voting Games ◽  
Legislative Choice ◽  
Copeland Winner

Majority-rule spatial voting games lacking a core still always present a “near-core” outcome, more commonly known as the Copeland winner. This is the alternative that defeats or ties the greatest number of alternatives in the space. Previous research has not tested the Copeland winner as a solution concept for spatial voting games without a core, lacking a way to calculate where the Copeland winner was with an infinite number of alternatives. We provide a straightforward algorithm to find the Copeland winner and show that it corresponds well to experimental outcomes in an important set of experimental legislative voting games. We also provide an intuitive motivation for why legislative outcomes in the spatial context may be expected to lie close to the Copeland winner. Finally, we show a connection between the Copeland winner and the Shapley value and provide a simple but powerful algorithm to calculate the Copeland scores of all points in the space in terms of the (modified) power values of each of the voters and their locations in the space.

On β-Plurality Points in Spatial Voting Games

2021 ◽  
Vol 17 (3) ◽  
pp. 1-21
Author(s):  
Boris Aronov ◽  
Mark De Berg ◽  
Joachim Gudmundsson ◽  
Michael Horton
Keyword(s):  
Spatial Voting ◽  
Voting Games ◽  
Equal Distance ◽  
Alternative Proposal

Let V be a set of n points in mathcal R d , called voters . A point p ∈ mathcal R d is a plurality point for V when the following holds: For every q ∈ mathcal R d , the number of voters closer to p than to q is at least the number of voters closer to q than to p . Thus, in a vote where each  v ∈ V votes for the nearest proposal (and voters for which the proposals are at equal distance abstain), proposal  p will not lose against any alternative proposal  q . For most voter sets, a plurality point does not exist. We therefore introduce the concept of β-plurality points , which are defined similarly to regular plurality points, except that the distance of each voter to p (but not to  q ) is scaled by a factor  β , for some constant 0< β ⩽ 1. We investigate the existence and computation of β -plurality points and obtain the following results. • Define β * d := {β : any finite multiset V in mathcal R d admits a β-plurality point. We prove that β * d = √3/2, and that 1/√ d ⩽ β * d ⩽ √ 3/2 for all d ⩾ 3. • Define β ( p, V ) := sup {β : p is a β -plurality point for V }. Given a voter set V in mathcal R 2 , we provide an algorithm that runs in O ( n log n ) time and computes a point p such that β ( p , V ) ⩾ β * b . Moreover, for d ⩾ 2, we can compute a point  p with β ( p , V ) ⩾ 1/√ d in O ( n ) time. • Define β ( V ) := sup { β : V admits a β -plurality point}. We present an algorithm that, given a voter set V in mathcal R d , computes an ((1-ɛ)ċ β ( V ))-plurality point in time O n 2 ɛ 3d-2 ċ log n ɛ d-1 ċ log 2 1ɛ).

In quest of the banks set in spatial voting games

2012 ◽  
Vol 41 (1) ◽  
pp. 43-71 ◽  
Author(s):  
Scott L. Feld ◽  
Joseph Godfrey ◽  
Bernard Grofman
Keyword(s):  
Spatial Voting ◽  
Voting Games ◽  
Banks Set

scholarly journals Computing the Yolk in Spatial Voting Games without Computing Median Lines

2019 ◽  
Vol 33 ◽  
pp. 2012-2019
Author(s):  
Joachim Gudmundsson ◽  
Sampson Wong
Keyword(s):  
Upper Bound ◽  
Linear Time ◽  
Search Technique ◽  
Important Concept ◽  
Uncovered Set ◽  
Spatial Voting ◽  
Voting Games ◽  
Parametric Search ◽  
Linear Time Algorithms

The yolk is an important concept in spatial voting games: the yolk center generalises the equilibrium and the yolk radius bounds the uncovered set. We present near-linear time algorithms for computing the yolk in the plane. To the best of our knowledge our algorithm is the first that does not precompute median lines, and hence is able to break the best known upper bound of O(n4/3) on the number of limiting median lines. We avoid this requirement by carefully applying Megiddo’s parametric search technique, which is a powerful framework that could lead to faster algorithms for other spatial voting problems.

The Core and the Stability of Group Choice in Spatial Voting Games

1988 ◽  
Vol 82 (1) ◽  
pp. 195-211 ◽  
Author(s):  
Norman Schofield ◽  
Bernard Grofman ◽  
Scott L. Feld
Keyword(s):  
Political Stability ◽  
Simple Majority ◽  
Small Perturbations ◽  
The Core ◽  
Spatial Voting ◽  
Voting Games ◽  
Voting Game ◽  
Stable Core ◽  
The Stability ◽  
Structurally Stable

The core of a voting game is the set of undominated outcomes, that is, those that once in place cannot be overturned. For spatial voting games, a core is structurally stable if it remains in existence even if there are small perturbations in the location of voter ideal points. While for simple majority rule a core will exist in games with more than one dimension only under extremely restrictive symmetry conditions, we show that, for certain supramajorities, a core must exist. We also provide conditions under which it is possible to construct a structurally stable core. If there are only a few dimensions, our results demonstrate the stability properties of such frequently used rules as two-thirds and three-fourths. We further explore the implications of our results for the nature of political stability by looking at outcomes in experimental spatial voting games and at Belgian cabinet formation in the late 1970s.

scholarly journals Limits on agenda control in spatial voting games

1989 ◽  
Vol 12 (4-5) ◽  
pp. 405-416 ◽  
Author(s):  
Scott L. Feld ◽  
Bernard Grofman ◽  
Nicholas R. Miller
Keyword(s):  
Agenda Control ◽  
Spatial Voting ◽  
Voting Games

scholarly journals Spatial voting games, relation algebra and RelView

2014 ◽  
Vol 83 (2) ◽  
pp. 120-134
Author(s):  
Rudolf Berghammer ◽  
Agnieszka Rusinowska ◽  
Harrie de Swart
Keyword(s):  
Relation Algebra ◽  
Spatial Voting ◽  
Voting Games

The half-win set and the geometry of spatial voting games

Public Choice ◽  
1991 ◽  
Vol 70 (2) ◽  
pp. 245-250
Author(s):  
Scott L. Feld ◽  
Bernard Grofman
Keyword(s):  
Spatial Voting ◽  
Voting Games
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