# Construction of aggregation paradoxes through load-sharing models

TL;DR: In this article , the authors show that load sharing models can be used to obtain basic results about a multivariate extension of stochastic precedence and related paradoxes, which can be applied in several different fields.

Abstract: Abstract We show that load-sharing models (a very special class of multivariate probability models for nonnegative random variables) can be used to obtain basic results about a multivariate extension of stochastic precedence and related paradoxes. Such results can be applied in several different fields. In particular, applications of them can be developed in the context of paradoxes which arise in voting theory. Also, an application to the notion of probability signature may be of interest, in the field of systems reliability.

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TL;DR: In this paper , it was shown that it is possible to observe any arbitrary set of elections' outcomes, no matter how paradoxical it may appear, and that a population of voters can be constructed that realize all the rankings of it.

Abstract: Abstract Referring to a standard context of voting theory, and to the classic notion of voting situation , here we show that it is possible to observe any arbitrary set of elections’ outcomes, no matter how paradoxical it may appear. In this respect, we consider a set of candidates $$1, 2, \ldots , m $$ 1 , 2 , … , m and, for any subset A of $$\{1, 2, \ldots , m \}$$ { 1 , 2 , … , m } , we fix a ranking among the candidates belonging to A . We wonder whether it is possible to find a population of voters whose preferences, expressed according to the Condorcet’s proposal, give rise to that family of rankings. We will show that, whatever be such family, a population of voters can be constructed that realize all the rankings of it. Our conclusions are similar to those coming from D. Saari’s results. Our results are, however, constructive and allow for the study of quantitative aspects of the wanted voters’ populations.

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01 Jan 1994

TL;DR: General Theory.

Abstract: General Theory. Applications in Statistics. Applications in Biology. Applications in Economics. Applications in Operations Research. Applications in Reliability Theory.

2,242 citations

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TL;DR: The key notion of the correlation of two strings is introduced, which is a representation of how the second string can overlap into the first, and this notion is used to state and prove a formula for the generating function that enumerates the q -ary strings of length n which contain none of a given finite set of patterns.

419 citations

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17 Oct 2007

TL;DR: This paper presents a meta-analysis of the application of Signature-Based Closure, Preservation and Characterization Theorems to Network Reliability and its applications in Reliability Economics and Signature-based Analysis of System Lifetimes.

Abstract: Background on Coherent Systems.- System Signatures.- Signature-Based Closure, Preservation and Characterization Theorems.- Further Signature-Based Analysis of System Lifetimes.- Applications of Signatures to Network Reliability.- Applications of Signatures in Reliability Economics.- Summary and Discussion.

387 citations

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01 Jan 1999

TL;DR: This chapter discusses the paradoxes of voting, including Borda's Paradox, Condorcet's paradox, and Schwartz's Paradox of Representation.

Abstract: Introduction.- Basic Concepts and Tools.- Alternatives and Opinions.- Preference Profile.- Pairwise Comparison and Tournament Matrix.- McGarvey`s Theorem.- Paradoxes of the Enlightenment Era.- Borda`s Paradox.- Condorcet`s Paradox.- Borda and Condorcet Compared.- How Frequent Are the Paradoxes?.- The Geometry of Voting.- The Saari Triangles.- The Conditions of Paradoxes.- The Paradoxical Act of Voting.- The Cost Calculus.- The No-Show Paradox.- Monotonicity Paradoxes.- Additional Support Paradox.- Preference Truncation Paradox.- How to Deal with Monotonicity Paradoxes?.- Compound Majority Paradoxes.- Ostrogorski`s Paradox.- Anscombe`s Paradox.- The Paradox of Multiple Elections.- The Referendum Paradox.- Simpson`s Paradox.- How to Deal With Compound Majority Paradoxes.- Intra-Profile Paradoxes.- Pareto Violations.- Inconsistency Paradox.- Choice Set Variance Paradoxes.- The q-Rules and Pareto Violations.- Tournament Solutions to Voting Paradoxes.- Paradoxes of Representation.- The Alabama Paradox.- Other Paradoxes of Hamilton Apportionments.- Schwartz`s Paradox of Representation.- How to Deal with Representation Paradoxes.- Classification of Paradoxes.- Hard and Soft Solutions.

287 citations