Political Numeracy: A Mathematical Perspective on Voting, Affirmation Action, Abortion and the Rest of Our Chaotic Constitution [Hardcover]

Of course, I very much enjoyed his chapter on self-referential problems with the constitution, because I thought it was funny and interesting. However, the interesting part was not the application of mathematics in politics but the discussion of odd situations that can arise in politics. (He correctly argues that Godel's result yields no substantial conclusions for politics. Then why talk about it in a book on politics? Its only value is as a metaphor, and a weak one at that.)

On a side note, I know this isn't a forum, but the pedant in me must correct the previous reviewer. If we define a function, f(x)=(x^2-1)/(x-1), then f(x) is defined only when x is not equal to 1. In that case f(1) is undefined (because f(1)=0/0), and it makes no sense to cancel the common factors (x-1). Or to put it another way, this cancellation is only valid when x is not equal to 1. Otherwise, we would be cancelling a factor zero from the numerator and denominator (and no number except 0 has 0 as a factor). To put it yet another way, suppose we want to say that f(x) is equivalent to (x+1), as the previous reviewer does. If we do this, we must remember that we reached this result only by assuming we could cancel (x-1) from the numerator and denominator. Again this cancellation is only valid when x is not 1. Therefore, f(x)=(x+1) only when x is not equal to 1. Sorry, but I couldn't stand the thought of someone out there being misled on this point.

The speed of Mr. Meyerson's survey may account for two mathematical lapses. First, there is the awkward statement that "Bush received more than 150,000 fewer popular votes than Al Gore." (pp. 54-55) Although published in 2002, this statement seems frozen in the first half of November 2000, before Gore's popular vote plurality over Bush was finalized at 537,000 votes.

Second, in discussing the theory of limits, the book recounts an interesting experience of David Berlinski, recalled in his book, A Tour of the Calculus, in which a function, (x squared -1) divided by (x-1), gets closer and closer to its limit (where x=1), but never reaches that limit because the resulting fraction, zero divided by zero, is impossible, leaving a limit that is as unattainable as God. (pp. 209-210) This is an evocative story, but it fails to disclose an identity of factors that turn what seems a quadratic function into a simple, linear one that, contrary to Berlinski, has no limit. As (x squared - 1) is the product of (x+1) and (x-1), then the function described by Berlinski and by Meyerson is actually equivalent to (x+1), once identical factors (x-1) in both parts of the fraction are eliminated. Viewed in that way, this function involves no division and has no limit. A simple alteration, e.g. (x squared -2) divided by (x-1), could have conveyed the same story without relying on a function whose simplification would remove any limits.

One additional mathematical topic worthy of a future edition: the theory of statistical sampling, in the context of the debates over the relative accuracy of direct counts and sampling for purposes of the Census required every ten years by the Constitution.