# Sh:782

- Shelah, S. (2005).
*On the Arrow property*. Adv. In Appl. Math.,**34**(2), 217–251. arXiv: math/0112213 DOI: 10.1016/j.aam.2002.03.001 MR: 2110551 -
Abstract:

Let X be a finite set of alternatives. A choice function c is a mapping which assigns to nonempty subsets S of X an element c(S) of S. A*rational*choice function is one for which there is a linear ordering on the alternatives such that c(S) is the maximal element of S according to that ordering. Arrow’s impossibility theorem asserts that under certain natural conditions, if there are at least three alternatives then every non-dictatorial social choice gives rise to a non-rational choice function. Gil Kalai asked if Arrow’s theorem can be extended to the case when the individual choices are not rational but rather belong to an arbitrary non-trivial symmetric class of choice functions. The main theorem of this paper gives an affirmative answer in a very general setting. - published version (35p)

Bib entry

@article{Sh:782, author = {Shelah, Saharon}, title = {{On the Arrow property}}, journal = {Adv. in Appl. Math.}, fjournal = {Advances in Applied Mathematics}, volume = {34}, number = {2}, year = {2005}, pages = {217--251}, issn = {0196-8858}, mrnumber = {2110551}, mrclass = {91B14 (05A10)}, doi = {10.1016/j.aam.2002.03.001}, note = {\href{https://arxiv.org/abs/math/0112213}{arXiv: math/0112213}}, arxiv_number = {math/0112213} }