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From an Election Fable to Election Procedures
In: Basic Geometry of Voting, S. 1-27
Symmetry Extensions of 'Neutrality' I: Advantage to the Condorcet Loser
This is the first of three papers introducing a theory for positional voting methods that determines all possible election rankings and relationships that ever could occur with a profile over all possible subsets of candidates for any specified choices of positional voting methods. As such, these results extend to all positional voting systems what was previously possible only for the Borda Count and the plurality voting systems. In this first part certain mathematical symmetries based on neutrality are used 1) to generalize the basic properties that cause the desired features of the Borda Count and 2) to describe classes of positional voting methods with new types of election relationships among the election outcomes. Some of these relationships generalize the well-known results about the positioning of a Condorcet winner/loser within a Borda ranking, but now it is possible for the Condorcet loser, rather than the winner, to have the advantage to win certain positional elections. Included among the results are axiomatic characterizations of many positional voting methods.
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Susceptibility to manipulation
In: Public choice, Band 64, Heft 1, S. 21-41
ISSN: 1573-7101
Susceptibility to Manipulation
In: Public choice, Band 64, Heft 1, S. 21
ISSN: 0048-5829
Condorcet Domains: A Geometric Perspective
In: Studies in Choice and Welfare; The Mathematics of Preference, Choice and Order, S. 161-182
Hidden Mathematical Structures of Voting
In: Studies in Choice and Welfare; Mathematics and Democracy, S. 221-234
Reviews -
In: Perspectives on politics: a political science public sphere, Band 7, Heft 3, S. 703
ISSN: 1537-5927
Likelihood of voting outcomes with generalized IAC probabilities
In: Mathematical social sciences, Band 87, S. 1-10
Connecting pairwise and positional election outcomes
In: Mathematical social sciences, Band 66, Heft 2, S. 140-151
Finessing a point: augmenting the core
The "finesse point" introduced here extends the notion of a core; it is a position that minimizes what a candidate needs to do to counter moves that are made by an opponent. The definition, which is motivated by the "chaos theorem" as well as by the dynamics of positive and negative political campaigning, is also used to define a "malicious point," which is an optimal location from which a candidate can engage in "negative campaigning."
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Sen's Theorem: Geometric Proof, New Interpretations
In: Social Choice and Welfare, Band 31, S. 393-413
SSRN
Working paper
The Sum of the Parts Can Violate the Whole
In: American political science review, Band 95, Heft 2, S. 415-433
ISSN: 0003-0554
We develop a geometric approach to identify all possible profiles that support specified votes for separate initiatives or for a bundled bill. This disaggregation allows us to compute the likelihood of different scenarios describing how voters split over the alternatives & to offer new interpretations for pairwise voting. The source of the problems -- an unanticipated loss of available information -- also explains a variety of other phenomena, such as Simpson's paradox (a statistical paradox in which the behavior of the "parts" disagrees with that of the "whole") & Arrow's theorem from social choice. 6 Tables, 4 Figures, 1 Appendix, 23 References. Adapted from the source document.
ARTICLES - The Sum of the Parts Can Violate the Whole
In: American political science review, Band 95, Heft 2, S. 415-434
ISSN: 0003-0554
The Copeland Method I; Relationships and the Dictionary
A central political and decision science issue is to understand how election outcomes can change with the choice of a procedure or the slate of candidates. These questions are answered for the important Copeland method (CM) where, with a geometric approach, we characterize all relationships among the rankings of positional voting methods and the CM. Then, we characterize all ways CM rankings can vary as candidates enter or leave the election. In this manner new CM strengths and flaws are detected.
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