Abstract
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).
References
Aizerman, M., and F. Aleskerov. 1986. “Voting Operators in the Space of Choice Functions.”. Mathematical Social Sciences 11: 201–42. https://doi.org/10.1016/0165-4896(86)90027-2.Search 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.Search in Google Scholar
Arrow, K. 1950. “A Difficulty in the Concept of Social Welfare.” The Journal of Political Economy 58 (4): 328–46. https://doi.org/10.1086/256963.Search in Google Scholar
Cherepanov, V., T. Feddersen, and A. Sandroni. 2013. “Rationalization.” Theoretical Economics 8 (3): 775–800. https://doi.org/10.1016/j.jet.2017.04.004.Search 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. https://doi.org/10.1016/j.jet.2017.04.004.Search in Google Scholar
Manzini, P., and M. Mariotti. 2007. “Sequentially Rationalizable Choice.” American Economic Review 97–5: 1824–39. https://doi.org/10.1257/aer.97.5.1824.Search in Google Scholar
Masatlioglu, Y., D. Nakajima, and E. Ozbay. 2012. “Revealed Attention.” American Economic Review 102 (5): 2138–205. https://doi.org/10.1257/aer.102.5.2183.Search in Google Scholar
© 2020 Walter de Gruyter GmbH, Berlin/Boston