Way back in podcast 172, I proposed a solution for the issue of contentious election recounts and legal battles over very close vote totals. With all the anger, bitterness, and waste that handling these close-margin races causes, I thought it would be good to review this proposal again, and really give it some serious thought.

Our nation collectively spends millions of dollars during each election cycle on such issues, and the number of contentious races seems to have exploded in recent years. One example is the recent Florida senate race, where over 8 million votes were cast, and the victory margin was within 10000, around an eighth of one percent. Due to the increasing partisan divide, these close margins are now universally accompanied by accusations of small-scale cheating in local precincts or at the margins. And we can’t deny that due to the all-or-nothing stakes, and the ability of a relatively tiny set of local votes to swing an election with national ramifications, the temptation for local partisans on both sides to cheat in small ways, if they spot an opportunity, must be overwhelming.

Now a lot of people will shrug their shoulders and say these contentious battles and accompanying waste are an inevitable consequence of democracy. But as I pointed out in the earlier podcast, if we think carefully, that’s not quite true. The first key point to recognize, as pointed out by authors such as Charles Seife, is that there is a *margin of error* to the voting process. Rather than saying that Rick Scott got 4,099,805 votes and Bill Nelson got 4,089,472 votes, it might make more sense just to say that each got approximately 4.1 million votes. There are errors due to mishandled ballots, natural wear and tear, machine failures, honest mistakes, and even local small-scale cheating. Once you admit there is a margin of error, then the silliness of recounts becomes apparent: a recount is just a roll of the dice, introducing a different error into the count, with no real claim to be more precise or correct. So under the current system, if you lose a close election, it would be foolish not to pour all the resources you have into forcing a recount.

But if we agree that the voting process has a margin of error, this leads to a natural solution, suggested by Seife: if the votes are close enough, let’s just agree to forsake all the legal battles, recounts, and bitter accusations, and flip a coin. It would be just as accurate— just as likely to reflect the true will of the people— and a much cheaper, faster, and amicable method of resolution. But if you think carefully, you will realize that this solution alone doesn’t totally solve the issue. Now we will repeat the previous battles wherever the vote is just over the margin that would trigger a coin flip. For example, if we said that the victory margin had to be 51% or greater in a 1000-vote race to avoid a coin flip, and the initial count gave the victor precisely 510 votes, there would be a huge legal battle by the loser to try to shave off just one vote and trigger his random shot.

This leads to my variant of Seife’s proposal: let’s modify the system so that there is *always* a random element added to the election, with odds that vary according to the initial vote count. We will use a continuous bell curve, with its peak in the middle, to determine the probability of overturning the initial result. In the middle, it would be a 50% probability, or a simple coin flip. In our 1000-vote election, at the 510 vote mark the probability would be very close to 50-50, but a smidgen higher, depending on how we configure the curve, something like 51%. Now the difference between a 50% chance of winning and a 49%, or 51%, will probably not seem very significant to either candidate: rather than fighting a legal battle over the margin, they will probably want to go ahead, generate the random number, and be done with it. Of course we will agree that once the random die is cast, with the agreement of all parties to the election, both winners and losers accept the result without future accusations or legal battles. Due to the continuity of the curve, there will never be a case where a tiny vote margin will seem to create life-or-death stakes. The probability of overturning the election will fall smoothly as the margin increases, until it gets down to approximately zero as the vote results approach 100%. So Kim Jong Un would still be safe.

You can probably see the natural objection to this scheme: as you move further out from the center of the curve, having *any* possibility of overriding the result starts to seem rather undemocratic. Do we really want to have a small chance of overturning the election of a victor who got 60% of the vote? If this system is implemented widely, such a low-probability result probably will happen somewhere at some point. But think about all the other random factors that can affect an election: a sudden terrorist attack, mass layoff at a local company, random arrest of a peripheral campaign figure, a lurid tabloid story from a prostitute, a sudden revelation of Math Mutation’s endorsement—- the truth is, due to arbitrarily timed world events, there is always a random factor in elections to some degree. This is just a slightly more explicit case. Is it really that much less fair? And again, think of the benefits: in addition to saving the millions of dollars spent on legal battles and recounts, the reduction in the need for bitter partisan battles in every local precinct on close elections has got to be better for our body politic.

So, what do you think? Is it time for our politicians to consider truly out-of-the-box solutions to heal our system? Maybe if all the Math Mutation listeners got together, we could convince a secretary of state somewhere to try this system out. Of course, I know I’m probably just dreaming, outright nuclear war in Broward County, Florida is a much more likely solution to this issue. At least I’m located pretty far outside the fallout zone for that one.

And this has been your math mutation for today.

References:

- https://www.hackmath.net/en/calculator/normal-distribution?mean=500&sd=300&area=above&above=510&below=&ll=&ul=&outsideLL=&outsideUL=&draw=Calculate
- http://books.google.com/books?id=ghJaYi3FELMC&printsec=frontcover
- http://news.rice.edu/2012/02/02/hand-counts-of-votes-may-cause-errors-says-new-rice-u-study

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