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On the Size of Minimum Super Arrovian Domains

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Dasgupta, Samit
Copyright Year	1999
Abstract	Arrow's celebrated impossibility theorem states that a sufficiently diverse domain of voter preference profiles cannot be mapped into social orders of the alternatives without violating at least one of three appealing conditions. Following Fishburn and Kelly, we define a set of strict preference profiles to be super Arrovian if Arrow's impossibility theorem holds for this set and each of its strict preference profile supersets. We write $\sigma(m,n)$ for the size of the smallest super Arrovian set for m alternatives and n voters. We show that $\sigma(m,2) = \lceil \frac{2m}{m-2} \rceil$ and $\sigma(3,3)=19.$ We also show that $\sigma(m,n)$ is bounded by a constant for fixed n and bounded on both sides by a constant times $2^n$ for fixed $m.$ In particular, we find that $\lim_{n\rightarrow \infty} \sigma(3,n)/2^n = 3.$ Finally, we answer two questions posed by Fishburn and Kelly on the structure of minimum and minimal super Arrovian sets.
Starting Page	524
Ending Page	534
Page Count	11
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480198332521
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	12
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	voter preference profiles minimum profile sets Arrow's impossibility theorem Permutations, words, matrices
Content Type	Text
Resource Type	Article
Subject	Mathematics

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