It’s been more than a week since the polls closed and we still don’t know who the winner is in three Senate races. Georgia is headed to a runoff. Minnesota is going to have a potentially ugly recount, with only 206 votes out of nearly 3 million separating Coleman and Franken. Alaska is still counting and the difference there could also be small enough to trigger a state-funded recount. Supposedly these new tallies in Minnesota and Alaska will tell us who “really” won the elections. But will they actually mean anything?

Leonard Mlodinow writes about an election strikingly similar to Minnesota’s in his excellent book The Drunkard’s Walk:

In the 2004 governor’s race in the state of Washington, for example, the Democratic candidate was eventually declared the winner although the original tally had the Republican winning by 261 votes out of about 3 million. Since the original vote count was so close, state law required a recount. In that count the Republican won again, but by only 42 votes. It is not known whether anyone thought it was a bad sign that the 219-vote difference between the first and second vote counts was several times larger than the new margin of victory, but the upshot was a third vote count, this one “entirely by hand.” The 42-vote victory amounted to an edge of just 1 vote out of every 70,000 cast, so the hand-counting effort could be compared to asking 42 people to count from 1 to 70,000 and then hoping they averaged less than 1 mistake each. Not surprisingly, the result changed again. This time it favored the Democrat by 10 votes. That number was later changed to 129 when 700 newly discovered “lost votes” were included.

Neither the vote-counting process nor the voting process is perfect… Elections, like all measurements, are imprecise, and so are the recounts, so when elections come out extremely close, perhaps we ought to accept them as is, or flip a coin, rather than conducting recount after recount.

It might be true that, for procedural reasons, later vote counts really are more accurate than the initial one. For example, running the ballots through a counting machine a second time picks up votes that were missed due to infamous hanging chads. In that case a recount could be worthwhile (see a discussion here as it relates to Florida in 2000). Even so, there’s some level at which the difference ceases to tell you anything reliable about who actually received more votes. There’s appeal in this idea of choosing an acceptable level of statistical significance and, when it’s not met, simply letting the original count stand or deciding the election by a random process.

Replacing recounts with with a random selection process would be a tough sell though. One objection is that potential voters may not participate unless we make sure that “every vote counts.” That’s a nice ideal, but we know it’s not achievable in practice. That’s why we have recounts in the first place — we don’t know how to make every count. The best we can hope for is that the recounting process will be more accurate than the initial tally. If we instead accepted the chance that a random event would decide the outcome, people would still have an incentive to vote for their candidate; the baseline would simply be moved from winning by at least one vote to winning by a significant margin. In either case a single vote has a vanishingly small chance of making a difference and voters will presumably be motivated by the same things that motivate them now, such as civic duty, the desire to express their beliefs, or showing support for their party.

Another objection is that deciding a hotly contested election by a coin toss would decrease faith in the democratic process. That might be true, but so do recounts and other tight races. Many Democrats complained throughout the Bush presidency that he stole the 2000 election in Florida and the 2004 election in Ohio. Similarly, Republicans suspected voter fraud long after the resolution of the Washington governor’s race described above. The opposing camps in Minnesota are already gearing up to follow a similar path, with lawyers ready to take their arguments to court when the counting’s through. Regardless of who is declared the winner, we can be sure that the other side will doubt the result and allege wrongdoing. None of this would happen if the winner were decided randomly. He would go to office with the knowledge that he didn’t win a clear mandate from the state’s voters and the voters would know that he at least was given the position through a transparent and fair procedure.

And then there’s the fiscal savings. Minnesota’s Secretary of State Mark Ritchie pegs the cost of the recount at 3 cents per ballot, or a little over $86,000. That’s small change in government terms, but the lawyers’ fees, court challenges, and time consumed add up too. And for what? A result that will likely remain disputed and may not tell us anything about Minnesota voters that we didn’t already know. (Hint: They’re closely divided.) A coin toss costs only a quarter, which can then be given to the loser as a consolation prize.

Regardless, proposals like this aren’t going to gain any traction. That’s partly because people don’t understand statistics, but perhaps more so because they enjoy a good spectacle — and that’s one thing our system of recounts provides with absolute certainty.