# Voting, Ice Cream, and the Classroom

29 Sep 2015In my public finance class, last night we got to public choice theory. I find public choice to be the hardest part of the class. I also kind of think that public choice is the quantum mechanics of economics. If you are not completely confused by it, you didn’t understand it. Now, by this same analogy, macroeconomics is astrology. But nevermind that drive-by insult, for now.

So rather than giving what passes for a lecture in my classroom, I asked everyone to pull out a sheet of paper and divide it in ballot. We were making ballots. And on the first, I said we are selecting ice cream. Pick one of chocolate or vanilla. And only those. Then pass their ballots to the front. Then on the second ballot, the options were vanilla and strawberry. And on the third, chocolate or strawberry. On the last ballot, they could select any of the three.

Generally, there’s an expectation of transitivity in voting outcomes. That is, if voters prefer B to C, and prefer A to B, we expect them to prefer A to C. This isn’t necessarily the case and it is known as Condorcet’s paradox. Because of this phenomenon, a majority rule system is not guaranteed to produce the most efficient allocation of governmental resources.

So we started counting the ballots and something neat happened. First, vanilla beat chocolate, 10 to 6. Then vanilla beat strawberry, 10 to 6. And then strawberry beat chocolate, 9 to 7. So mathematically, [latex]v > c[/latex], [latex]v > s[/latex], and [latex]s > c[/latex]. Also, we expect [latex]v > s > c[/latex], and that does not contradict our results. Well, so much for the class experiment.

But then we counted the fourth ballot. Here, vanilla received 9 notes, chocolate received 6, and strawberry received 1. So now the rank ordering is [latex]v > c > s[/latex]. That’s a different result.

And what flowed from here was an excellent discussion of preferences, grounded right in something we can all relate to and understand easily. We also got to see how preferences can change based on how the election is presented to them. After all, who doesn’t like ice cream? Of course, at a few points, the discussion did diverge into the relative merits of each flavor and at least one protest that swirl should have been an option, but I can live with that.

Now, four ballots were enough. But I kind of think I should have added a fifth where students would rank-order the three with points.

*Image by Meutia Widodo / Flickr.*