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A Comment on Arrow’s Impossibility Theorem

Alec Sandroni and Alvaro Sandroni


Arrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

Keywords: Arrow; aggregators; WARP

Corresponding author: Alvaro Sandroni, Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston, IL 60208, USA, E-mail:


Aizerman, M., and F. Aleskerov. 1986. “Voting Operators in the Space of Choice Functions.”. Mathematical Social Sciences 11: 201–42. in Google Scholar

Aizerman, M., and F. Aleskerov. 1995. “Theory of Choice.” In Studies in Mathematical and Managerial Economics, Vol. 38, edited by H. Gleiser, and S. Martin, North-Holland: Elsevier Science B.V.Search in Google Scholar

Aleskerov, F. 2002. “Categories of Arrovian Voting Schemes.” In Chapter 2 in the Handbook of Social Choice and Welfare, Vol. 1, 95–129. edited by K. Arrow, A. Sen, and K. Suzumura. North-Holland: Elsevier Science B.V.10.1016/S1574-0110(02)80006-6Search in Google Scholar

Aleskerov, F. 2010. “Arrovian Aggregation Models.” In Studies B: Mathematical and Statistical Methods, Vol. 39, edited by W. Leinfellner, and G. Eberlein. Kluwer Academic Publishers.10.1007/978-1-4757-4542-9Search in Google Scholar

Arrow, K. 1950. “A Difficulty in the Concept of Social Welfare.” The Journal of Political Economy 58 (4): 328–46. in Google Scholar

Cherepanov, V., T. Feddersen, and A. Sandroni. 2013. “Rationalization.” Theoretical Economics 8 (3): 775–800. in Google Scholar

Lleras, J., Y. Masatlioglu, D. Nakajima, and E. Ozbay. 2017. “When More is Less: Limited Consideration.” Journal of Economic Theory 170: 70–85. in Google Scholar

Manzini, P., and M. Mariotti. 2007. “Sequentially Rationalizable Choice.” American Economic Review 97–5: 1824–39. in Google Scholar

Masatlioglu, Y., D. Nakajima, and E. Ozbay. 2012. “Revealed Attention.” American Economic Review 102 (5): 2138–205. in Google Scholar

Received: 2019-11-24
Accepted: 2020-05-08
Published Online: 2020-07-06

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