The math behind the vote (AP)

"Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It)" (Farrar, Straus and Giroux, 352 pages, $25), by William Poundstone: Most analysts doubt Ralph Nader's bid for the White House will divide Democrats and tip the presidency to Republicans in 2008. After all, he received less than 0.4 percent of the vote in 2004, down from nearly 3 percent in 2000.

But according to William Poundstone's new book on voting, tipping the vote is exactly what Nader has sought to do.

To draw votes from Democrats, Republicans paid cash to get Nader on the 2004 ballot -- an enemy-of-my-enemy-is-my-friend tactic that both parties used to divide and cherry pick congressional opponents from San Diego to Pennsylvania in 2006, Poundstone says in "Gaming the Vote: Why Elections Aren't Fair (and What We Can Do About It)."

But spoilers are nothing new, having determined at least five presidential elections since popular voting for the White House widely began in 1828, Poundstone argues. James Polk, Zachary Taylor, Abraham Lincoln, Grover Cleveland, Woodrow Wilson, Bill Clinton and George W. Bush all benefited from a split vote, taking office even though a majority of voters preferred someone else.

How can that happen in a democracy? Poundstone looks for answers in an offshoot of mathematics called social choice theory.

The problem, it turns out, is that neither plurality voting, nor any other known method, is entirely fair. This depressing notion was proved in 1948 by Nobel Prize-winning economist Kenneth Arrow, whose "impossibility theorem" showed that when three or more candidates compete, no voting system yields truly representative results.

"Arrow's work was a death knell for any idealistic notion of democracy," causing concern at the cusp of the Cold War when many of the greatest American minds were bent on proving democracy superior, Poundstone writes.

That's not to say voting theorists and political strategists failed to seek alternatives. Many had long been looking for fairer voting methods -- and better ways to game the plurality system now in place.

In an avalanche of quirky anecdotes, Poundstone surveys their alternatives: The so-called "Borda count" lets voters rank choices on a ballot, while "Condorcet voting" pairs every possible combination of candidates in a one-on-one duel. "Approval voting" allows voters to give a thumbs up or down to multiple candidates, while an "instant runoff" redistributes losing votes to stronger, second choice contenders.

All alternatives are flawed, but Poundstone suggests that one method, "range voting" -- an internet favorite used, for example, to rate books on Amazon.com -- is actually the best among imperfect options, because it allows voters to express their degree of preference with a numerical score, rather than a simple yes or no.

Split into contentious camps, railing proponents of these different methods dismiss one another as "snake oil" salesmen and "mathematical zealots." But their feuding theories leave it unclear what general readers are meant to learn from the mess.

As Poundstone acknowledges: "This ongoing lack of expert consensus has been the biggest obstacle confronting those who would reform American voting."

To an extent, Poundstone's argument is obvious: Spoilers tip elections and political consultants game them because the math behind the vote allows it. What is surprising to hear, though, is that every other way of voting is also inherently flawed.

It seems it might be best, then, to just play the game and stop complaining about the rules.

"Democracy is the worst form of government," Poundstone recalls, citing Winston Churchill, "except all those other forms that have been tried."