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Voting like it’s 1938 November 5, 2011

Posted by Ezra Resnick in Democracy, Game theory, Politics.
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It’s Election Day this week in the U.S., and in Cambridge we’ll be electing the City Council (nine members) and the School Committee (six). Cambridge uses a “Proportional Representation” voting method, which allows each voter to rank all of the candidates (instead of just picking a single favorite). The advantage of such a method is that in the event that your top candidate can’t use your vote — either because he got too few votes to be elected or because he has more votes than needed — the rest of your preferences can be taken into account for choosing among the remaining candidates.

For instance, under Cambridge’s system, a City Council candidate needs a tenth of the votes (plus one) to be elected; any votes he receives above that quota are called surplus, and surplus ballots are redistributed among the remaining candidates according to the next preference on each ballot. This is not as straightforward as it sounds, however: we need to decide which of a candidate’s ballots to transfer — and the manner in which we do so can influence the election’s result.

Cambridge uses the “Cincinnati Method” for surplus distribution, wherein the surplus ballots to be transferred from a candidate are drawn at regular intervals from the ordered sequence of all that candidate’s ballots. For example: if some candidate received 500 top-rank votes and only 400 votes are needed for election (i.e. he has a 100-vote surplus), every fifth one of the candidate’s ballots (in the order they were originally counted) — ballots 5, 10, 15, 20, etc. — will be selected for redistribution.

The disturbing aspect of the Cincinnati Method is its somewhat random nature, and the fact that its outcome is dependent on the order in which the ballots happen to be counted: if they’re counted in a different order, the election results could be different!

There are alternative methods for transferring surplus ballots. As explained by mathematician Robert Winters, the method that is generally adopted these days is known as “fractional transfer,” wherein a fraction of all of an elected candidate’s ballots are transferred to the candidates ranked next on those ballots. This method has the virtue of being completely independent of the order in which the ballots are counted, and it is actually the default method built in to the tabulation software used in Cambridge elections — Cambridge explicitly overrides the default option and instructs the software to use the Cincinnati Method instead!

Why does Cambridge insist on using a flawed method instead of switching to a better one? The answer is rather depressing.

Cambridge is […] in the position where we must abide by a 1938 law (Mass. General Laws, Chapter 54A) that restricts our methods for redistributing surplus ballots to systems that were in use somewhere in the United States at that time.

Ah, tradition: things should always be done the way they were done in the past. When will our elected officials get around to repealing this embarrassingly stupid law?

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