Editing Arrow's impossibility theorem (section)

==== Infinite populations ====
[[Peter C. Fishburn|Fishburn]] shows all of Arrow's conditions can be satisfied for [[Uncountable set|uncountably infinite sets]] of voters given the [[axiom of choice]];<ref name="Fishburn197022">{{Cite journal |last=Fishburn |first=Peter Clingerman |year=1970 |title=Arrow's impossibility theorem: concise proof and infinite voters |journal=Journal of Economic Theory |volume=2 |issue=1 |pages=103–106 |doi=10.1016/0022-0531(70)90015-3}}</ref> however, Kirman and Sondermann demonstrated this requires disenfranchising [[Almost surely|almost all]] members of a society (eligible voters form a set of [[Measure (mathematics)|measure]] 0), leading them to refer to such societies as "invisible dictatorships".<ref>See Chapter 6 of {{cite book |last=Taylor |first=Alan D. |title=Social choice and the mathematics of manipulation |publisher=Cambridge University Press |year=2005 |isbn=978-0-521-00883-9 |location=New York |postscript=none}} for a concise discussion of social choice for infinite societies.</ref>