Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It) (GtV) by William Poundstone is a maddening book, full of interesting stories about voting, but flawed as a book. (Before you ask, William is a cousin of comedian Paula Poundstone.)
One of the fascinating results in mathematical economics is the proof by Kenneth Arrow of what is called the impossibility theorem, which demonstrates that, given a set of desirable criteria, no voting scheme can be devised that is totally fair. Obviously, this applies to voting in which there are three or more candidates; normal pick-one voting works fine for two-candidate races. One of the most common demonstrations is to show that transitivity is violated: A may be preferred to B, B to C, and C to A, which strikes most of us as wrong.
GtV begins with a lengthy recap of the 1991 Louisiana governor race in which former governor Edwin Edwards manipulated the incumbent governor out of the runoff, where Edwards defeated former Klansman David Duke. The book contains other stories of cases where the "wrong" candidate was elected, even for president - the 1912 campaign, in which Teddy Roosevelt split off the Republican vote from Taft, giving the White House to Woodrow Wilson, is the best known.
Poundstone has written a lot more books than I have, so I'm going to assume he has his reasons for jumping around in his topic. For me, though, I found it tedious. After the long prologue about Louisiana (which is a fascinating story, with outsized personalities, and Poundstone didn't really capture it), GtV launches into the theory behind the problem. The story jumps from person to tiny bits of math and back to person, in what I can only feel is a sop to the popular reader. You come out with the flavor of the Arrow impossibility theorem without any deep understanding; the impression is simply that normal plurality voting (voting for your favorite) is flawed beyond redemption.
If you want a flavor for this book, let me quote from the table of contents. Here is a list of topics in order from one of the chapters: ""syphilis; slavery; mother murder; Lyndon Johnson; farm animals; television; Rush Limbaugh; Arthur Finkelstein; the $12 Man; Jesus," and on and on. This list, by the way, gets us from page 95 to page 97. It is an impressive feat to weave these disparate topics into three pages, but it takes away from the coherence of Poundstone's arguments.
And there is an underlying argument here. After taking us through the often-entertaining stories of the origins of Borda Count, Condorcet voting, instant-runoff voting, and so forth, Poundstone shows us why these are all inferior to range voting.
Range voting is the kind used on Amazon to rate books, where there is a fixed scale (0 to 5, but it can be as much as 0 to 100 in Poundstone's examples) and a voter can pick any number for any of the candidates. For example, if Hillary were to stay in the current presidential race (and there's no guarantee that we can get her out), a voter who didn't want to perpetuate the Bush legacy could (on a 0 to 10 system) give Obama 10 points, Hillary 9, and McCain 0 or 1. In theory, this system minimizes the chance that voters will vote strategically instead of due to their real preferences.
DtV presents some, but not conclusive, evidence that range voting is superior to all other voting schemes. That may be true, but it remains to be seen how we explain the results of a sample presidential vote (on a range voting advocacy site,
http://rangevoting.org), in which the winner among all U.S. presidents is...Chester A. Arthur. The result comes from, as of this writing, 2428 ballots. Perhaps some of those people are fooling around, but you have to wonder about results in which the list of presidents over 80 (on a 0-100 scale) are W.H. Harrison, Polk, Taylor, Grant, Garfield, Arthur, B. Harrison, McKinley, and Eisenhower. (If you're curious, those ranked under 30 are Cleveland, Wilson, F. Roosevelt, Truman, and L. Johnson.)
Specific examples aside, there really isn't enough here to convince anyone that range voting minimizes the probability of Arrow's theorem creating undesirable results. The conclusion seems to be that it's worth a try, but that politics will get in the way. After all, political candidates and consultants have adjusted to the existing system, and it will be difficult to effect change. (In a curious omission, Poundstone tells us that Cleveland, Cincinnati, and New York all adopted single transferable voting in the early part of the 20th century, but doesn't explain how politicians were convinced that these systems were preferable.)
So I have to give a thumbs-sideways review here. I was already reasonably familiar with the formal literature on voting schemes, being a reformed math guy, and GtV is a pleasant, gentle introduction. As a book, however, it was repetitious (we understood the problems with Condorcet voting the first time), disorganized (there are references to things that weren't previously mentioned), and, at times, simplistic. So, read it if you're interested in voting schemes, but understand that you'll have more reading to do if you want to appreciate the fullness of this topic.
