Voting Paradoxes

The next issue I would like to introduce is  under the umbrella of public choice is the arbitrariness of putting decisions to vote. Let’s look at a particular voting scenario to illustrate this.

VOTER X: A >B >C

VOTER Y: C> A> B

VOTER Z: B> C >A

If the voters were voting on this issue, voter X would prefer law A over law B and law B over law C. In shorthand – A > B > C. To summarize all of the choices of the voters we see that 2/3 of the voters have preference A > B, 2/3 of the voters have preference B > C, but when voting A vs. C, 2/3 have preference C > A.

See if you follow the application of this. If we have two elections and the first is made between policy B and C, then B will win (2/3 of the voters have preference B > C). If this is followed by a second election A vs. B (Because C was eliminated in the first election) then A will be the law that ultimately passes by majority rule.

Now if the order is changed, in which the first election is between A and B, A will win (because 2/3 of the voters rank A > B). Then in the second election when A goes against C, C will be the law that passes by majority rule (again because 2/3 of the voters have preference C > A).

So when voting on these policies, the process becomes arbitrary. The outcome depends on the order of the vote, so a cycling of choices ensues. According to public choice economist Gordon Tullock, any outcome can be obtained in majority voting by at least one voting method. There is nothing magical and there is no ‘truth’ in the outcome just because it was reached by majority rule. Majorities can be irrational and dangerous. The exception to this is if preferences are single peaked. I will present this in a separate entry, because it presents problems of its own.