Politics and Calculus. In one place. At the same time. I’m sure I’ve got your attention now!
Go ahead and spool up those thinking machines, kids, because I’m dead serious. Fortunately, all you need recall of your calculus is that “integrals” are just the areas under the curves that they “integrate” and that a “derivative” is just slope. Right?
The key variable in political elections is, depending on who you ask, some variation on the theme of “public opinion.” Measuring the opinions of the public at large proves difficult at best, and at certain times has the eerie tone of the Dark Arts. However, we political scientists have little choice but to posit a public and posit that this public has measurable opinions, lest we become entirely irrelevant. That our methods of measure remain inadequate is actually an excellent selling point for some researchers. I digress.
We have a rich language for pronouncing public opinion. “The public respect Candidate Jones a great deal due to his legislative record,” or “President Smith’s support among moderates has waned in response to his reform plans.” Let “public opinion” equal “P.”
We also speak frequently about the course of public opinion, which we might call “change in public opinion over time.” Still with me? We use this first derivative of P when we say things like “Candidate Davis has the wind at his back,” or almost any time we talk about momentum.
We even have language for the second derivative of public opinion, “the change (over time) in the change (over time) in public opinion.” When was the last time you heard some talking head say that he or she thought that “Candidate Bryant has stopped the bleeding,” or “Candidate Nathan has defused the situation” or similar?
Is public opinion “turning?” My Calculus professor always reminded us that derivatives are most interesting when they look the most boring. Any time a derivative equals zero, that means that the thing it is derived from has flattened–that is, if Candidate Williams has “stemmed the tide” then she may soon “turn things around” and if things go well for her she might even become the “presumptive favorite.” That happens because a tiny shift in a derivative can propagate through the others and into the master curve.
Whew.
In spite of the mess, we do have one generally approved measure of public opinion: elections. Sure, they’re the thing we want to be predicting, but never you mind. The wisdom of the ancients in politics suggests that beyond the second derivative, most people’s brains start trickling out of their ears.
Thus we reach several common perceptions concerning the relationship between pre-election polling and the results themselves. We assume that public opinion is much less elastic than it appears to be, and we also tend to assume that elections, like polls, are inflexible flashes in history (instant obsolescence! Don’t tell Bill Gates!).
I think that we may need a new way to look at voting behavior, and I may elaborate upon it later. Suffice it to say that I wonder if voters do not, in part, take voting as a part of the grand narrative of elections and opinions. Who doesn’t like an underdog? And how many Ohioans voted for Ralph Nader in 2000, knowing that he could not win?