# Sh:782

• Shelah, S. (2005). On the Arrow property. Adv. In Appl. Math., 34(2), 217–251.
• 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}
}