The Paradox Files: The Voting Paradox

Preferences are transitive relations―that is, if you prefer A to B and B to C, then you also prefer A to C. It's this fact which justifies the inference above that the Club must prefer R to I. Since groups are made up of individuals who have preferences, it is tempting to think that such groups will thereby have preferences of their own. Surely we think that we can determine what the majority of a group wants, and that will represent the wants of the group as a whole. However, the voting paradox shows that it is a mistake to treat the results of an election by majority rule as if they represent the preferences of the group. The assumption that the majority vote of the Club represents its preferences leads to a contradiction, showing that that assumption is false.

We naturally tend to think of groups or organizations as if they were big people made up of a lot of little people, with all of the psychological qualities that people have, including preferences. However, this is at best a metaphor. Groups and organizations are not people; they lack minds, and therefore do not have preferences. The voting paradox confounds our expectations only because we have treated a metaphor as if it were a literal truth.