Positional Voting and Doubly Stochastic Matrices

2019/08/18 by Jacqueline Anderson, Anderson, Jacqueline, Brian Camara +3
Economics, Econometrics and Finance · Mathematics · #15B51 #32S22 #91B12 #91B14 #Combinatorics (math.CO) #FOS: Economics and business #FOS: Mathematics #History and Overview (math.HO) #Theoretical Economics (econ.TH) #econ.TH #math.CO #math.HO #msc:15B51 #msc:32S22 #msc:91B12 #msc:91B14

paper · pdf · doi:10.48550/arxiv.1908.06506

13 pages. The title has been changed and various revisions have been made based on referee comments

arxiv created 2020/08/14 · arxiv updated 2020/08/17

Abstract

We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles, and we also demonstrate how to choose weights that realize desirable results from a given profile. The analysis ultimately boils down to thinking about positional voting systems in terms of doubly stochastic matrices.

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