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Social Choice and Welfare
Published in: Social Choice and Welfare 2-3/2020

19-02-2020 | Original Paper

A modified version of Arrow’s IIA condition

Author: E. Maskin

Published in: Social Choice and Welfare | Issue 2-3/2020

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Abstract

I propose a modified version of Arrow's independence of irrelevant alternatives condition (IIA). The new version preserves the most attractive feature of traditional IIA, viz., that it rules out vote-splitting in elections (in which two or more popular candidates split the vote, allowing a relatively unpopular candidate to win). Moreover, it permits election outcomes to reflect voters' preference intensities, unlike the traditional condition.
previous article Editorial: Special issue in memory of Kenneth J. Arrow
next article Majority decision and Condorcet winners

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Footnotes
1
Arrow insisted, for a pragmatic reason, that a SWF should determine a social ranking of alternatives rather than merely the social choice of an optimal alternative. He imagined that which alternatives in X would turn out to be feasible might not be known in advance, and so a social ranking serves as a contingency plan: if the top-ranked alternative is not available, choose the next alternative, and so on.
 
2
\( x \succ_{i} y \) means that individual i strictly prefers x to y, i.e., \( x\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ \succ }_{i} y \) but \( y\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{\not \succ }\! {}_{i}\;x. \)
 
3
In runoff voting, there are two rounds. Each individual votes for one alternative in the first round, and if some alternative gets a majority, it is ranked first socially. If no alternative gets a majority, the top two vote-getters face each other in a runoff round, and the majority winner there is ranked first socially.
 
4
I also show that the Borda count continues to be uniquely characterized if we replace MIIA and positive association with a modified version of strategy-proofness (strategy-proofness is analyzed in Gibbard 1973 and Satterthwaite 1975).
 
Literature
Arrow KJ (1950) A difficulty in the concept of social welfare. J Polit Econ 58(4):328–346CrossRef
Arrow KJ (1951) Social choice and individual values, 1st edn. Wiley, New York
Arrow KJ (1963) Social choice and individual values, 2nd edn. Yale Univ. Press, New Haven
Arrow KJ (2012) Social choice and individual values, 3rd edn. Yale Univ. Press, New Haven
Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41(4):587–601CrossRef
Maskin E (2020) The Borda Count reconsidered
May KO (1952) A set of independent necessary and sufficient conditions for simple majority decisions. Econometrica 20:680–684CrossRef
Satterthwaite M (1975) Strategy-proofness and arrow’s conditions: existence and correspondence theorems for voting procedures and social welfare functions. J Econ Theory 10(2):187–217CrossRef
Metadata
Title
A modified version of Arrow’s IIA condition
Author
E. Maskin
Publication date
19-02-2020
Publisher
Springer Berlin Heidelberg
Published in
Social Choice and Welfare / Issue 2-3/2020
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI
https://doi.org/10.1007/s00355-020-01241-7

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