That idea that voting methods can be gamed has been so warmly embraced that Donald Saari, a prominent theorist, says: “For a price, I will come to your organization just prior to your next important election. You tell me who you want to win. I will talk with the voters to determine their preferences over the candidates. Then I will design a ‘democratic voting method’ which involves all candidates. In the election, the specified candidate will win.” Mr. Saari was joking, but some politicians understood this to be a serious offer.

In “Gaming the Vote,” Mr. Poundstone enumerates some of the major theoretical systems that could reshape voting. Two of the most influential methods are traced back to rival 18th-century French intellectuals who devised conflicting systems and also displayed a prescient scholarly hostility.

The Marquis de Condorcet, an important theorist in the field, once said of Jean-Charles de Borda, who advocated a weighted ballot on which voters ranked candidates in descending order: “Some of his papers display talent, although nothing follows from them and nobody has ever spoken of them or ever will.” This same collegiality is found among rival voting theorists even today. (Some of the most interesting work quoted here can be found on the Internet. But it has not met the publication standards of scholarly journals like Homo Oeconomicus.)

Among the points explained by “Gaming the Vote” is that the mad-tea-party absurdities of voting systems actually do owe something to Lewis Carroll. (Under his real name, the Rev. Charles Dodgson, he analyzed election paradoxes and advocated treating voting as a game of skill.) Mr. Poundstone cites leading scholars, among them Steven J. Brams and the Nobel laureate Kenneth J. Arrow, both of whom give their endorsement to this valuable book. He describes alternative voting systems known as Approval, Range, Cumulative, Condorcet and Instant-Runoff voting. Only rarely and humorously must he render this confusing.

“The thing is, it’s impossible to explain Condorcet voting any further without talking about cycles and ‘beat-paths’ and ‘cloneproof Schwartz sequential dropping,’ ” he says. “This is where the android’s mask falls off and it’s all wires and microchips inside. Non-Ph.D.’s run screaming for the exits. So far, Condorcet voting has tended to appeal to the kind of people who can write Javascript code for it.”

Mr. Poundstone’s preference is for a system called range voting, advanced by Warren D. Smith, a mathematician. Range voting, in which voters rate the candidates numerically, is akin to the weighted, collective tallies used for Internet product ratings, the Web site Hot or Not (which has elicited more votes than all American presidential contests combined) and restaurant guides shaped by consumers.

Range voting outstrips yes-or-no plurality voting in revealing voters’ nuanced opinions. It has been admired even by Ralph Nader  and that, Mr. Poundstone writes with typical dry panache, “is something like a spirochete endorsing penicillin.” Mr. Nader’s spoiler effect is exactly what “Gaming the Vote” means to assail.

Speaking of spoilers, the way Candidate A could lose with 9,999 votes would be on an approval ballot that allowed each voter to list more than one choice. If A alienated even one voter, while B, as a mediocrity, appealed to all of them, then B would be elected. If approval ballots had been used in 1992, and Ross Perot had appeared on every single ballot, and at least one voter chose not to vote for Bill Clinton or George Bush, President Perot would be in the history books. In the opinion of “Gaming the Vote,” this is reason enough to explain why voting systems warrant close scrutiny and major change.