Three wealthy candidates have poured a collective $243 million into their campaigns this season, according to Politico. Meg Whitman of California, Linda McMahon of Connecticut, and Rick Scott of Florida have together outspent the biggest advocacy groups in the country, yet none of the three has a commanding lead in the polls. * How much does a candidate have to spend to buy a vote?

Somewhere between $5 and $175. In the contested 2008 House races, the average winner spent $1.3 million and received about 185,000 votes, for a total cost of about $7 per vote. Losers spent an average of $493,000 for 91,000 votes, at a unit cost of $5.42. Neither of those gives an accurate picture of the true cost of a vote, however, since so many people fill in their ballots along party lines, regardless of campaign spending. For politicians (and political scientists), the real question is how much it costs to convince an undecided voter to break in your direction.

In 1994, Freakonomist Steven Levitt used election rematches—congressional races that featured the same two candidates in more than one election cycle—to argue that increased spending has virtually no impact on the outcome of elections. Levitt found that doubling campaign spending brings only about 1 percent of the voting pool into a candidate’s column. If we go back to the numbers from the 2008 election, that means the average loser could have netted just a few thousand additional votes by doubling his spending to $986,000, for a cost of about $175 for each one.

There are many ways to do this sort of calculation, and economists have come up with a wide range of results. In a 2009 study, George Mason University economist Thomas Stratmann estimated that an average candidate could secure 1,686 votes by spending an additional $100,000. That comes out to $59 per vote.

Candidates should also consider that some forms of spending are more efficient than others. Just before the 2004 election, Yale political scientist Donald P. Green calculated that $50 directed toward voter mobilization could produce one vote, suggesting that door-to-door canvassing, rather than pricey television commercials, is the thriftiest way to scrounge up a few extra votes.

In practice, the candidate who spends the most money in an election almost always wins: The bigger spender has been the victor in 95 percent of all House races since 2004, according to the Center for Responsive Politics. But that doesn’t prove that vote-buying is economical or effective. It might also be that the leading candidate had more momentum and racked up more contributions—which in turn allowed for more spending. When a candidate spends his or her own money (independent of fundraising success), the return is negligible. In 2008, about 50 congressional candidates pitched in more than $500,000 from private bank accounts. Just 11 of them won their elections.

Got a question about today’s news? Ask the Explainer.

Explainer thanks Anthony J. Corrado, Jr. of Colby College and the Brookings Institution, Jeff Milyo of the University of Missouri, and Thomas Stratmann of George Mason University.Like Slate and the Explainer on Facebook. Follow us on Twitter.

Correction, Oct. 28, 2010: This article originally misidentified Rick Scott as a candidate from California. Scott is running for governor of Florida. (Return to the corrected sentence.)