Editing Arrow's impossibility theorem (section)

=== Intuitive argument ===
[[Condorcet paradox|Condorcet's example]] is already enough to see the impossibility of a fair [[Ranked voting|ranked voting system]], given stronger conditions for fairness than Arrow's theorem assumes.<ref name="McLean-1995">{{Cite journal |last=McLean |first=Iain |date=1995-10-01 |title=Independence of irrelevant alternatives before Arrow |url=https://dx.doi.org/10.1016/0165-4896%2895%2900784-J |journal=Mathematical Social Sciences |volume=30 |issue=2 |pages=107–126 |doi=10.1016/0165-4896(95)00784-J |issn=0165-4896}}</ref> Suppose we have three candidates (<math>A</math>, <math>B</math>, and <math>C</math>) and three voters whose preferences are as follows:

{| class="wikitable" style="text-align: center;"
! Voter !! First preference !! Second preference !! Third preference
|- 
! Voter 1 
| A || B || C
|- 
! Voter 2 
| B || C || A
|- 
! Voter 3 
| C || A || B
|}

If <math>C</math> is chosen as the winner, it can be argued any fair voting system would say <math>B</math> should win instead, since two voters (1 and 2) prefer <math>B</math> to <math>C</math> and only one voter (3) prefers <math>C</math> to <math>B</math>.  However, by the same argument <math>A</math> is preferred to <math>B</math>, and <math>C</math> is preferred to <math>A</math>, by a margin of two to one on each occasion. Thus, even though each individual voter has consistent preferences, the preferences of society are contradictory: <math>A</math> is preferred over <math>B</math> which is preferred over <math>C</math> which is preferred over <math>A</math>.

Because of this example, some authors credit [[Condorcet]] with having given an intuitive argument that presents the core of Arrow's theorem.<ref name="McLean-1995" /> However, Arrow's theorem is substantially more general; it applies to methods of making decisions other than one-person-one-vote elections, such as [[Market (economics)|markets]] or [[weighted voting]], based on [[Ranked voting|ranked ballots]].