The Math of Politcal Platforms

Voter intensity is not the only imponderable. Outright election paradoxes have been around for a long time. One classic example demonstrates that a common element of an individual’s rationality is sometimes not present in groups. Imagine a political party split over the relative importance of various issues. Assume that one third of the party thinks that the most important issue in the election is taxes, then education, then defense spending (T-E-D for short). Another third of the party that the ranking of the issues should be education, then defense, then taxes (E-D-T), while the remaining third believes that the order should be defense, then taxes, then education (D-T-E).

If we go back and examine these rankings carefully, we see that two-thirds of the party thinks that tax policy is more important than education and that two-thirds think that education is more important than defense spending. It would be natural to assume then that a majority of the party believes tax policy is more important than defense spending.

Natural, but wrong.

Two-thirds of the party believes that defense spending is more important than tax policy! Even if the preferences of all the individual voters are transitive (i.e., whenever a voter prefers X to Y and Y to Z, then that voter prefers X to Z), it doesn’t necessarily follow that the electoral preferences determined by majority rule are transitive too.

Clearly, deciding which issues to prioritize in a platform is a tricky matter for a party. Often the choice a party must face is that between centrist blandness or an appeal to a collection of narrow constituencies. The two parties’ strategies seem to have made quite different choices this year.

The Republicans appear to be glossing over some of their more hard-edged stances and attempting to co-opt some traditional Democratic issues by moving toward the proverbial median voter, the “compassionate conservative” occupying a position somewhat to the fuzzy right of the Democrats. The Democrats, in contrast, seem to be trying to stress their many policy differences with the Republicans and hoping thereby to put together a winning coalition of diverse groups and agendas. Their lack of a simple slogan — maybe something like “tough-minded liberalism” — is telling.

Fearless Prediction

Finally, what about polls? In this volatile time when running mate selections and national conventions move them 20 points in a week, polls are a bit like weather vanes in a tornado — accurate at the moment, but not predictive of the weather next week. Besides we’d need 50 different state polls to say anything about the deciding electoral vote.

So who’s going to win? Probably Bush or Gore.

Professor of mathematics at Temple University, John Allen Paulos is the author of several bestselling books, including Innumeracy and A Mathematician Reads the Newspaper. His “Who’s Counting?” column on appears on the first day of every month.

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