# Irrationality of Aggregate Preferences

I was an economics major back in my undergraduate days and one of the common complaints about the subject (well, at least before the crash) was something along the lines: “Economists assume people are rational when they’re not.” A fair enough point, but usually the trouble with this assessment is like if someone said, the trouble with is that these people are assuming all numbers rational when they’re not. It’s certainly true, but that word probably doesn’t mean what you think it does. So one assumption that’s considered part of the assumption that people are rational is that their preferences form what mathematicians call a “preorder,” which basically consists of: (1) every thing is preferable to itself and (2) if thing A is preferable to thing B and thing B is preferable to thing C, then thing A is preferable to thing C. Here “preferable” means “at least as good as.” Now this assumption, in my view, seems fair provided that we’re only talking about any given moment, which we generally are. Preferences change over time, but we’re just talking about some moment not over long periods of time.

Now what’s interesting is that this notion of rationality fails once you consider groups of people. So if you consider three people considering three options: A, B and C. Person 1 prefers A to B to C; person 2 prefers C to A to B; and person 3 prefers B to C to A. Now they take a vote on what the preferences of the group should be: we see that 1 and 2 prefer A to B, so A is preferable to B, 1 and 3 prefer B to C, and lastly, 2 and 3 prefer C to A. So A is preferable to B which is preferable to C, but A is not preferable to C.

Aggregating preferences lead to inconsistent preferences, which is why the public demands inconsistent things like less taxes and more government programs, or why fans complain about some feature of a film and complain when it changes in the sequel. Some people might actually be irrational in this sense, but that’s not why we witness this behavior.