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.

scholarly journals In Search of the Uncovered Set

2007 ◽  
Vol 15 (1) ◽  
pp. 21-45 ◽  
Author(s):  
Nicholas R. Miller
Keyword(s):  
Computational Algorithm ◽  
Voting Theory ◽  
Legislative Action ◽  
Uncovered Set ◽  
Political Analysis ◽  
Spatial Voting ◽  
Voting Games ◽  
General Relevance ◽  
Straight Line ◽  
Theoretical Considerations

This paper pursues a number of theoretical explorations and conjectures pertaining to the uncovered set in spatial voting games. It was stimulated by the article “The Uncovered Set and the Limits of Legislative Action” by W. T. Bianco, I. Jeliazkov, and I. Sened (2004, Political Analysis 12:256—78) that employed a grid-search computational algorithm for estimating the size, shape, and location of the uncovered set, and it has been greatly facilitated by access to the CyberSenate spatial voting software being developed by Joseph Godfrey. I bring to light theoretical considerations that account for important features of the Bianco, Jeliazkov, and Sened results (e.g., the straight-line boundaries of uncovered sets displayed in some of their figures, the “unexpectedly large” uncovered sets displayed in other figures, and the apparent sensitivity of the location of uncovered sets to small shifts in the relative sizes of party caucuses) and present theoretical insights of more general relevance to spatial voting theory.

The Uncovered Set and the Limits of Legislative Action

2004 ◽  
Vol 12 (3) ◽  
pp. 256-276 ◽  
Author(s):  
William T. Bianco ◽  
Ivan Jeliazkov ◽  
Itai Sened
Keyword(s):  
Social Choice ◽  
Real World ◽  
Solution Concept ◽  
Collective Choice ◽  
Simulation Technique ◽  
Legislative Action ◽  
Uncovered Set ◽  
Spatial Voting ◽  
Voting Games

We present a simulation technique for sorting out the size, shape, and location of the uncovered set to estimate the set of enactable outcomes in “real-world” social choice situations, such as the contemporary Congress. The uncovered set is a well-known but underexploited solution concept in the literature on spatial voting games and collective choice mechanisms. We explain this solution concept in nontechnical terms, submit some theoretical observations to improve our theoretical grasp of it, and provide a simulation technique that makes it possible to estimate this set and thus enable a series of tests of its empirical relevance.

The uncovered set in spatial voting games

1987 ◽  
Vol 23 (2) ◽  
pp. 129-155 ◽  
Author(s):  
Scott L. Feld ◽  
Bernard Grofman ◽  
Richard Hartly ◽  
Marc Kilgour ◽  
Nicholas Miller ◽  
...  
Keyword(s):  
Uncovered Set ◽  
Spatial Voting ◽  
Voting Games

scholarly journals Almost Linear Time Algorithms for Minsum k-Sink Problems on Dynamic Flow Path Networks

2021 ◽  
Author(s):  
Yuya Higashikawa ◽  
Naoki Katoh ◽  
Junichi Teruyama ◽  
Koji Watase
Keyword(s):  
Linear Time ◽  
Flow Path ◽  
Dynamic Flow ◽  
Linear Time Algorithms

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).

scholarly journals Linear-Time Algorithms for Tree Root Problems

Algorithmica ◽  
2013 ◽  
Vol 71 (2) ◽  
pp. 471-495 ◽  
Author(s):  
Maw-Shang Chang ◽  
Ming-Tat Ko ◽  
Hsueh-I Lu
Keyword(s):  
Linear Time ◽  
Linear Time Algorithms

FAULT TOLERANT ROUTING IN HYPERCUBES AND STAR GRAPHS

1996 ◽  
Vol 06 (01) ◽  
pp. 127-136 ◽  
Author(s):  
QIAN-PING GU ◽  
SHIETUNG PENG
Keyword(s):  
Free Path ◽  
Fault Tolerant ◽  
Linear Time ◽  
Time Efficiency ◽  
Routing Problem ◽  
Star Graphs ◽  
Linear Time Algorithms ◽  
Better Than

In this paper, we give two linear time algorithms for node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn and star graphs Gn. The first algorithm, given at most n−1 arbitrary fault nodes and two non-fault nodes s and t in Hn, finds a fault-free path s→t of length at most [Formula: see text] in O(n) time, where d(s, t) is the distance between s and t. Our second algorithm, given at most n−2 fault nodes and two non-fault nodes s and t in Gn, finds a fault-free path s→t of length at most d(Gn)+3 in O(n) time, where [Formula: see text] is the diameter of Gn. When the time efficiency of finding the routing path is more important than the length of the path, the algorithms in this paper are better than the previous ones.

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
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