## Monday, July 6, 2009

### How Should Election Results Be Determined?

So, finally the election in Minnesota, that started in November of last year, is over, with the declaration of Al Franken as the winner in the senate race. The ballots went through multiple recounts, and the candidates went through multiple rounds of lawsuits before the state supreme court got tired of it and ruled for one of the candidates. The funny thing is, they could have ruled for either, and it would have made no difference to the correctness of the result.

Let me explain what I am trying to say. Al Franken won by 312 votes. Al Franken was finally certified to have received 1,212,629 votes, while his opponent, Norm Coleman was certified to have received 1,212,317 votes. The total number of votes cast in the race was 2,887,646 (including all the votes for the Libertarian party candidate, Independent candidates, write-ins, etc.). So, Al Franken won by a 0.0108% margin with respect to the total votes cast.

Why is that important? Let me answer by making some basic assumptions and setting up my premises. I will then make my arguments based on these premises. I assume that in a democracy, the person who is most popular among the electorate should be declared the winner. I also assume that in a democracy, the way to decide who is the most popular is by casting ballots in an election.

So, the election serves as a kind of sampling of the population to determine who is most popular. Now, as all statisticians know, all samples have what is called sampling error. When Gallup calls up 1,500 random people from the phone book before the election to gauge trends, they publish the results and then say that the results have a margin of error of some percentage points. If the two opposing points of view in the poll are within that margin of error apart, then it is fair to consider the poll a dead heat.

I see the election in Minnesota as nothing but an extension of the same concept. Instead of 1,500 likely voters, the sample included 2,887,646 actual voters. But that is not 100% of the electorate, it is still only a sample. So, the same statistical principles that are used to determine the margin of error for a sample of 1,500 people can be used on this sample also to find the margin of error of this sample.

Wait a minute, you might say. Just because only 2,887,646 people voted does not mean that only those many people were sampled. Everybody was given an opportunity to vote, but only these many people took advantage of it. Therefore, it is not really a sample of the electorate, but is the entire electorate. That argument certainly has its merits, and I might be inclined to agree with that argument. After all, I vote religiously in every primary and election, and so should everyone else.

The problem is that, unlike in most other countries, elections in this country seem to be specifically held to discourage people from voting. Most polls are open only during a working day during working hours, so unless you take the time to vote early (before election day), vote absentee, or are willing to spend some time away from work on election day, it becomes very difficult to cast a ballot in any election. Moreover, this presumed low turnout is actually baked into the planning for the election itself, with most polling places not being able to handle more than about a 50 to 60% turnout without melting down completely. This was evident in various precincts in the country which saw more than the normal turnout because of the enthusiasm for Barack Obama in last year's election.

So, even though technically everyone has the chance to cast a vote in a given election, for all practical intents and purposes, the polling process is only designed to function as a sampling mechanism. But for now, let us assume that polls were not sampling mechanisms. Let us assume that every election has a 100% turnout. Let us assume that the number 2,887,646 represents the entire electorate that was eligible to make its choice known in the Minnesota senate election.

That still does not get rid of a fundamental problem. Any technology set up to count that number of opinions will always have some error associated with it. It does not matter whether the election is on paper ballots, electronic ballots or some other technology. Some technologies have a higher rate of error than others, but all of them have errors. What do I mean by errors? Let me explain this way: let us assume that all 2,887,646 people went to the polls twice and cast the exact same votes in both elections. The counts of votes for the candidates in the two elections will almost certainly not match (except by chance and coincidence). I am willing to guarantee this result.

The errors need not be inherent to the technology itself. For instance, in the case of electronic balloting, the computer that is keeping track of results, in most cases, will not have a problem with its CPU or software such that it would lose track of results. However, people, however careful they are, make mistakes entering their choices into the computer. In the case of paper ballots, the errors come not only from people entering the wrong choices on the ballot sheet, but also from the counters making mistakes when counting the ballot sheets. So, a fully electronic poll (assuming that there was no hacking or other shennanigans going on) would have a lower margin of error than a poll conducted on paper ballots, but the margin of error would not be zero in either case.

My argument is that, once the margin of error is known for the given election technology (electronic, paper ballot, etc.), if the final results fall within this margin of error, the election should be declared essentially a dead heat. The winner, after such a determination, should simply be declared on the basis of a coin toss at this point. Many states already recognize and acknowledge the presence of this margin of error. That is why they have rules saying that if the preliminary counts put the candidates within a certain percentage of each other, the ballots should undergo more scrutiny and a thorough recount. In the case of Minnesota, that margin is one half of one percent (0.5%).

People may argue that the 0.5% does not actually represent the margin of error. And I agree. It is probably an arbitrary number pulled out of some legislator's hat that seemed nice and round enough to pass into law. But the existence of these statutes is proof that people do believe in the fallibility of election methods, counting methods, etc. But the fact that a margin of error does exist is beyond argument. I am sure statisticians can conduct experiments to establish the exact margin of error for any given polling and/or counting mechanism. Such a scientifically established margin of error should be used to decide whether an election is a dead heat.

Once an election does result in a dead heat, it means that the people did not have a clear preference in terms of a candidate to represent them in office. So, it becomes perfectly valid to toss a coin and choose any one of the candidates in the dead heat to represent the people.

This would have many advantages over the current system. Chief among them would be the immense savings of time and money for the election jurisdiction so that they don't have to conduct recount after recount of the ballots. It would save a lot of time for the court system so that they don't have to go through lengthy litigation to come up with a winner. It is also completely scientifically justifiable (though, in this country, that might be considered a disadvantage rather than as an advantage!). Most importantly, the people will have a representative on a timely basis rather than what happened in this case: Al Franken missed out on 8 months of senate business because his election was tied up in knots unnecessarily.

In this particular election, I am pretty sure the margin of error was at least a couple of orders of magnitude higher than the actual margin of 0.0108%. Hence my assertion at the bottom of the first paragraph that the supreme court would have been right regardless of who they had ruled in favor of. Perhaps, I am missing something that I should have considered that would make my arguments invalid. If so, I am hard-pressed to identify it. So, I am going to throw this out there and see what the rest of the world thinks about it. Have at it, and enjoy!

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