From Paired Comparisons and Cycles to Arrow’s Theorem

2019 ◽  
pp. 62-84
Author(s):  
Donald G. Saari
Keyword(s):  
Democratic Theory ◽  
Impossibility Result ◽  
Preference Aggregation ◽  
Pairwise Comparisons ◽  
Paired Comparisons ◽  
Arrow’S Theorem ◽  
Generic Type ◽  
Arrow's Theorem ◽  
Special Case

What makes paired comparisons so easy to accept is that they arise everywhere, and an appealing aspect of this approach is that it directly compares the merits of two opponents. However, paired comparisons can generate a wide array of difficulties that can lead to what appear to be paradoxes. Preference aggregation based solely on pairwise comparisons is at the heart of Arrow’s theorem. This chapter indicates that the Arrow impossibility result is a special case of a more generic type of problem involving parts and whole, and it offers an interpretation of it that shows that it does not have the implications for democratic theory that it is commonly assumed to have.

scholarly journals Seeking consistency with paired comparisons: a systems approach

2021 ◽  
Author(s):  
Donald G. Saari
Keyword(s):  
Systems Approach ◽  
Paired Comparisons ◽  
Arrow’S Theorem ◽  
Wide Range ◽  
Decision Methods ◽  
Arrow's Theorem

AbstractIt is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair is looked upon as a subsystem with an assigned task. In this manner, the source of several difficulties (including Arrow’s Theorem) is equated with the standard concern that the “whole need not be the sum of its parts.” These problems arise because the objectives assigned to subsystems need not be compatible with that of the system. Knowing what causes the difficulties leads to resolutions.

Arrow's Theorem and Engineering Design Decision Making

1999 ◽  
Vol 11 (4) ◽  
pp. 218-228 ◽  
Author(s):  
Michael J. Scott ◽  
Erik K. Antonsson
Keyword(s):  
Decision Making ◽  
Engineering Design ◽  
Design Decision ◽  
Arrow’S Theorem ◽  
Arrow's Theorem

Is abstention an escape from Arrow’s theorem?

2006 ◽  
Vol 28 (3) ◽  
pp. 439-442
Author(s):  
Murat Ali Çengelci ◽  
M. Remzi Sanver
Keyword(s):  
Arrow’S Theorem ◽  
Arrow's Theorem

Distributed Systems

2020 ◽  
pp. 143-198
Author(s):  
Andreas Bolfing
Keyword(s):  
Distributed Systems ◽  
Fault Tolerant ◽  
Deterministic Algorithm ◽  
Impossibility Result ◽  
Software Systems ◽  
Trade Off ◽  
Byzantine Failures ◽  
The Individual ◽  
Special Case

Chapter 5 considers distributed systems by their properties. The first section studies the classification of software systems, which is usually distinguished in centralized, decentralized and distributed systems. It studies the differences between these three major approaches, showing there is a rather multidimensional classification instead of a linear one. The most important case are distributed systems that enable spreading of computational tasks across several autonomous, independently acting computational entities. A very important result of this case is the CAP theorem that considers the trade-off between consistency, availability and partition tolerance. The last section deals with the possibility to reach consensus in distributed systems, discussing how fault tolerant consensus mechanisms enable mutual agreement among the individual entities in presence of failures. One very special case are so-called Byzantine failures that are discussed in great detail. The main result is the so-called FLP Impossibility Result which states that there is no deterministic algorithm that guarantees solution to the consensus problem in the asynchronous case. The chapter concludes by considering practical solutions that circumvent the impossibility result in order to reach consensus.

Confirmational Holism and Theory Choice: Arrow Meets Duhem

Mind ◽  
2019 ◽  
Vol 129 (513) ◽  
pp. 71-111 ◽  
Author(s):  
Eleonora Cresto ◽  
Diego Tajer
Keyword(s):  
Theory Choice ◽  
Impossibility Theorem ◽  
Arrow’S Theorem ◽  
Epistemic Virtues ◽  
Evidence Amalgamation ◽  
Arrow's Impossibility Theorem ◽  
Arrow's Theorem ◽  
The One ◽  
Different Sources ◽  
Positive Light

Abstract In a recent paper Samir Okasha has suggested an application of Arrow’s impossibility theorem to theory choice. When epistemic virtues are interpreted as ‘voters’ in charge of ranking competing theories, and there are more than two theories at stake, the final ordering is bound to coincide with the one proposed by one of the voters (the dictator), provided a number of seemingly reasonable conditions are in place. In a similar spirit, Jacob Stegenga has shown that Arrow’s theorem applies to the amalgamation of evidence; the ‘voters’ here are the different sources of evidence. As with Okasha’s proposal, it is not clear how to avoid Arrow’s pessimistic conclusion. In this paper we develop a novel argument that purports to show that, in typical examples, Arrow’s result does not obtain when dealing with evidence amalgamation. The reason is that we cannot escape the well-known Duhem problem: the evidence actually confirms (or disconfirms) complex conjunctions that include various auxiliary hypotheses. We argue that confirmational holism induces us to restrict the domain of a reasonable amalgamation function, thus violating one of Arrow’s conditions. The upshot is that we are now able to see the Duhem problem under a different, positive light – namely, as a phenomenon that makes the aggregation of the evidence possible in the first place, when there are at least three options on the table.

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