The Math of Politcal Platforms

A mathematician doing political commentary!

This may be as plausible to some as a sumo wrestler playing basketball, but some simple mathematics is relevant to the upcoming presidential election and to two very different electoral strategies.

Republicrats and Depublicans seem to be everywhere this year as both major political parties move to the center. Simultaneously, there is an opposite tendency for the parties to cater to special interests by adopting more extreme positions on particular issues.

Playing One or Several Issues

First, let’s consider the median theory of elections, which, despite its name, is quite commonsensical. One version maintains that if one issue or one set of highly related issues dominates an election, there is a strong tendency for both candidates to move toward the position of the median voter. That position is such that half the voters are on one side of it, half on the other side.

To illustrate, assume that the primary issue in an election is reducing taxes, with one party initially advocating a very large cut. The other party may favor keeping tax rates the same or even increasing them, but would be astute to plump for a cut in taxes slightly smaller than the opposition, thus capturing all the voters except those favoring very large tax cuts. Knowing this, the party favoring the large cut will probably call for a smaller cut so as not to be marginalized. Calculating in this way moves both parties toward the center.

This inclination to move toward the center holds if one issue dominates. If there are many issues, however, and if voters feel strongly about some of them, then candidates are often wiser to adopt less centrist positions. By doing so, they may be able to cobble together a majority out of a variety of special interest groups.

If, for example, the issues are taxes, education, abortion, gun control, affirmative action, and defense spending, taking the median position on each of them may result in a bland losing platform. Adopting a more extreme position on some of these issues might result in a controversial winning platform that attracts those voters who decide largely on the basis of only one of these issues.

A wild card in these calculations is voter intensity.

Consider, for example, a scenario in which 20 percent of the electorate is opposed to stricter gun controls, three-fourths of them (15 percent of the electorate) so strongly that they will vote against any candidate who supports controls. Suppose further that the 80 percent of the electorate in favor of tighter controls do not feel as intensely. Let’s say that only one-twentieth of them (4 percent) will treat this as a litmus issue and vote against any candidate who opposes controls.

Given these assumptions, it’s not hard to imagine a prudent politician trying to either ignore the issue entirely or else adopting a perfunctory opposition to gun control. Doing so loses him 4 percent of the vote; coming out for gun control loses him 15 percent of the vote. The difference of 11 percent would be significant in most elections. These single issue voters, 15 percent and 4 percent of the electorate, respectively, are often more determinative than are the 20 percent and 80 percent, respectively, from which they come. The same calculations apply to the abortion issue.

Paradox and Strategy

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.