The uncovered set and its applications

Abstract Social choice theory demonstrates that majority rule is generically indeterminate. However, from an empirical perspective, large and arbitrary policy shifts are rare events in politics. The uncovered set (UCS) is the dominant preference-based explanation for the apparent empirical predictability of majority rule in multiple dimensions. Its underlying logic assumes that voters act strategically, considering the ultimate consequences of their actions. I argue that all empirical applications of the UCS rest on an incomplete behavioral model assuming purely egoistically motivated individuals. Beyond material self-interest, prosocial motivations offer an additional factor to explain the outcomes of majority rule. I test my claim in a series of committee decision-making experiments in which I systematically vary the fairness properties of the policy space while keeping the location of the UCS constant. The experimental results overwhelmingly support the prosociality explanation.

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Computing the Yolk in Spatial Voting Games without Computing Median Lines

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33012012 ◽

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.

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The uncovered set and indifference in spatial models: A fuzzy set approach

Fuzzy Sets and Systems ◽

10.1016/j.fss.2010.10.016 ◽

2011 ◽

Vol 168 (1) ◽

pp. 89-101 ◽

Cited By ~ 6

Author(s):

John N. Mordeson ◽

Terry D. Clark ◽

Nicholas R. Miller ◽

Peter C. Casey ◽

Michael B. Gibilisco

Keyword(s):

Fuzzy Set ◽

Spatial Models ◽

Uncovered Set

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A topological characterization of the non-emptiness of the Banks set and the uncovered set

Topology and its Applications ◽

10.1016/j.topol.2019.107026 ◽

2020 ◽

Vol 275 ◽

pp. 107026

Author(s):

Athanasios Andrikopoulos ◽

Katerina Zontou

Keyword(s):

Topological Characterization ◽

Uncovered Set ◽

Banks Set

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Uncovering Evidence of Conditional Party Government: Reassessing Majority Party Influence in Congress and State Legislatures

American Political Science Review ◽

10.1017/s0003055405051713 ◽

2005 ◽

Vol 99 (3) ◽

pp. 361-371 ◽

Cited By ~ 26

Author(s):

WILLIAM T. BIANCO ◽

ITAI SENED

Keyword(s):

Spatial Models ◽

State Legislatures ◽

Legislative Process ◽

Real World Data ◽

Majority Party ◽

Party Government ◽

One Dimensional ◽

Uncovered Set ◽

Dimensional Version ◽

Search Program

This paper aims at enriching the debate over the measurement of majority party influence in contemporary American legislatures. Our use of a new analytic technique, a grid-search program for characterizing the uncovered set, enables us to begin with a better model of legislative proceedings that abandons the simple one-dimensional spatial models in favor of the more realistic two-dimensional version. Our conclusions are based on the analysis of real-world data rather than on arguments about the relative merits of different theoretic assumptions. Our analysis confirms that when legislators' preferences are polarized, outcomes will generally be closer to the majority party's wishes, even if the majority-party leadership does nothing to influence the legislative process. This conclusion notwithstanding, our analysis also shows that at the margin of the majority party's natural advantage, agenda setting by the majority party remains a viable and efficacious strategy.

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Possible and Necessary Winners of Partial Tournaments

Journal of Artificial Intelligence Research ◽

10.1613/jair.4856 ◽

2015 ◽

Vol 54 ◽

pp. 493-534 ◽

Cited By ~ 8

Author(s):

Haris Aziz ◽

Markus Brill ◽

Felix Fischer ◽

Paul Harrenstein ◽

Jerome Lang ◽

...

Keyword(s):

Polynomial Time ◽

Sharp Contrast ◽

Pairwise Comparisons ◽

Solution Concepts ◽

Uncovered Set

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them, possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

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