Who's Counting: Alternative Voting Methods and Mitt Romney's Mathematical/Political Gaffes

The large number of candidates running for president in both parties splinters voter support. Two unfortunate consequences of this are that good second-tier candidates often quickly fall by the wayside and that not so impressive first-tier candidates are anointed early by the prevailing poobahs and pundits.

Alternative Voting Methods

A partial solution to the first problem of losing good second-tier candidates prematurely is to use a method different than the standard plurality way of determining winners in the various primaries and caucuses. There are many.

Voters might, for example, rank their favorite candidates, giving, say, three points to their first choice, two to their second, and one to their third, and the one with the highest point total would be the winner. In this way voters could give support to both Obama and Clinton, say, or indulge their secret liking for Ron Paul.

Alternatively, voters might vote for as many of the candidates as they wish and the one with the highest approval percentage would be the winner. The principle of "one person, one vote" might be replaced with "one candidate, one vote." Scenarios in which, for example, two liberal candidates split the liberal vote, say 32 percent to 28 percent, and allow a conservative candidate to win with 40 percent of the vote would not develop. This method might favor consensus candidates and work against polarizing ones.

Yet another method would have the voters rank the candidates -- their first, second, third, fourth choices, etc. -- and if none of the candidates received a majority of the voters' first-place votes, the candidate with the fewest first-place votes would be eliminated and the votes adjusted upward according to the original rankings. This would be repeated until a candidate obtains a majority of the adjusted first-place votes. The method provides, in effect, an instant runoff election and is used in various municipalities from Minneapolis to San Francisco.

All methods have their flaws (in fact, a mathematical result known as Arrow's theorem says so), but some are usually better than others, especially in multicandidate races.

The Null Set, Non Sequiturs and Mitt Romney

A partial solution to the second problem of the early anointing of front-runners is radical. It is to focus on the actual content of the candidates' pronouncements and not on their hair, posture, jaw lines or rankings in the polls.

Let me step back and first note the definition of two elementary terms from formal logic.

The null set is a notion common in mathematics and is generally taken to be a collection having no members, an empty set. The set of humans who are over 12 feet in height is a null set as is the set of square circles as is the set of even prime numbers bigger than 2. Occasionally, it is used to indicate a set that is sparse in some other way. But, in any case, the empty set is not a difficult notion and is employed widely in mathematics and formal logic.

A non sequitur is an argument in which the conclusion does not follow from the assumptions. A simple example is 1. If I'm in Bangkok, then I'm in Thailand. 2. I'm in Thailand. 3. Therefore, I'm in Bangkok. Conclusion 3 does not follow from assumptions 1 and 2. Occasionally a statement lacking any relation at all to statements preceding it is deemed a non sequitur, but, as with the null set, it is not a difficult notion and is widely used in mathematics, formal logic and informal discourse.

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