Saturday, August 21, 2010

Book Review: Numbers Rule

After being directed to it by The New Yorker Book Review (and getting involved in the debate about the review and the response to it) I borrowed a copy of Numbers Rule, by George G. Szpiro, from my local library.

Numbers shares a similar concept to Gaming the Vote, of presenting the somewhat dry topic of voting theory via the colorful true stories of the great thinkers who have wrestled with the subject over the centuries. And I do mean centuries; we start with Plato, who is harshly criticized for his didactic and entirely unscientific approach to the issue. Quickly, the realization that it's hard to decide among three or more choices is brought out, as Pliny the Younger presides over a choice between the innocence, banishment, or execution of an Athenian slave.

Next, we are introduced to Ramon Llull and Nikolaus Cuanus, who, Szpiro tells us, developed the Borda count and the Condorcet method, over 350 years before the stars of the following chapters, Borda and Condorcet, were born. While the rediscovery and repetition for these two pairs of chapters is interesting and historically relevant, unfortunately it doesn't add anything to the readers knowledge about elections. To further the irrelevance, each chapter ends with entirely irrelevant (but still interesting) additional historical information on the main characters.

In the following chapter on Laplace—a contemporary of both Borda and Condorcet—the clever idea to "guarantee" majority-choices is introduced: If a vote doesn't result in a majority decision, vote again. Laplace's original thought was that voters would, eventually, settle on a compromise. Instead, his legacy is France's consistent use of top-two runoff, and the mathematically-unsound claims of instant runoff proponents. I think Laplace, as a mathematician of the highest caliber, would be displeased.

And then we go through much of the same material one last time—only with accusations of pedophillia—thanks to Charles Dodgson; better known as Lewis Carroll. Again, interesting, but the repetition is not especially helpful for learning the issue at hand.

It's here that the book takes a two-chapter and mostly-unconnected side trek to discuss the difficulties of apportioning seats in a legislature to its constituent districts. Even the impending re-apportionment that will soon occur on the heels of the 2010 census couldn't bring me to really care about the issue. A one-seat difference, out of 435, every 30 or 40 years, just seems insignificant to me. (Or maybe it's just that my new home state will certainly continue to have just one representative.)

When we return to elections proper, we are following Kenneth Arrow, to learn about the impossibility of perfection. Numbers gives a more in-depth explanation of why Arrow only considered ranked-order ballots, but armed with that understanding, I am now more confident both that Arrow's work can't be applied, for good or bad, to approval voting and score voting, and that the election simulations I often refer to can still be valid. A strange parallel is drawn between Arrow's work on voting, Hisenberg's work on physics, and Godel's work on logic; the point of which seems to be "Give up; nothing in the world works!" Again; interesting, but even more so than the chapters on districting, it seems out of place.

The book closes with one final chapter on districting—with an extra side of impossibility, for good measure—followed by a short and un-directed prance through the modern issues. This is the first, and only time, that any sort of proportional representation is mentioned, or that approval voting is brought up. (And the misleading description of approval voting that led off the New Yorker review? Not present at all.) Instant runoff voting is not mentioned by name, but single transferable vote is, and that it can be used for single-winner elections is discussed. But Szpiro avoids discussing them in any depth, and keeps far away from taking any sides. Having now spent a year and a half myself participating in the argument, perhaps this is a wise move on his part; but if the intent of the book is to educate, it's a missed opportunity to avoid what's happening in the world today.

If you love historical trivia (and I admit, I do) Numbers Rule is great. But if you're looking to get a handle on the issue of elections, Gaming the Vote is not only better focussed, but is more engaging to read. While Gaming sucked me in and inspired me to get involved and make this blog what it is today, I had to pull myself back into Numbers each time; happy that I would get a few more interesting tidbits, but knowing that I wasn't going to learn anything about voting that I didn't already know.

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