The Likelihood of the Consistency of Collective Rankings Under Preferences Aggregation with Four Alternatives Using Scoring Rules: A General Formula and the Optimal Decision Rule

Eric Kamwa and Vincent Merlin ()

Computational Economics, 2019, vol. 53, issue 4, No 4, 1377-1395

Abstract: Abstract In most of the social choice literature dealing with the computation of the exact probability of voting events under the impartial culture assumption, authors deal with no more than four constraints to describe voting events. With more than four constraints, most of the authors rely on Monte-Carlo simulations. It is usually more tricky to estimate the probability of events described by five constraints. Gehrlein and Fishburn (Appl Math Optim 6:241–255, 1980) have tried, but their conclusions are based on conjectures. In this paper, we circumvent this conjecture by having recourse to the technique suggested by Saari and Tataru (Econ Theory 13: 345–363, 1999) in order to compute the limit probability of the consistency of collective rankings when there are four competing alternatives given that the decision rule is a scoring rule. We provide a general formula for the limiting probability of the consistency and we determine the optimal decision rules among the scoring rules that provide the best guarantee of consistency. Given the collective ranking on a set A, we have consistency if the collective ranking on B a proper subset of A is not altered after some alternatives are removed from A.

Keywords: Consistency; Scoring rules; Optimization; Impartial culture; Probability; 91B14; 91B12; 46N10 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10614-018-9816-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
Working Paper: The Likelihood of the Consistency of Collective Rankings under Preferences Aggregation with Four Alternatives using Scoring Rules: A General Formula and the Optimal Decision Rule (2019)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:compec:v:53:y:2019:i:4:d:10.1007_s10614-018-9816-7

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

DOI: 10.1007/s10614-018-9816-7

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().