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Bias or Balance

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Paul Cohen
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I'm Special! I'm FAMOUS.
I'm Special! I'm FAMOUS.
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If you are lucky enough to be born into a famous family, then you have a special advantage going into politics. But even if someone's fame stems purely from their own accomplishments, and possibly even from public failures, they still have a special advantage. Famous people often are rich, but in addition, their fame is apt to provide them with a network of contacts and supporters. And if those advantages were not enough, most elections credit what amounts to some extra votes just for being famous.

On the other side of the tracks, if you do not happen to be famous this means that the deck is well stacked against you.

The issue here comes down to a lack of balance in how we vote; voters are allowed to support a candidate, but they have no way to balance the electoral scales by explicitly opposing another candidate. In the special case of there being only two candidates (an unfortunate condition we are thoroughly conditioned to assume) they can vote for the other candidate and that has the same effect on the election outcome as a vote of opposition should have (while making it more difficult to interpret election results). But when there are more than two candidates, you cannot vote for more than one of them. And a vote for just one of the other candidates is quite different than a genuine vote of opposition would have.

At times, voters do fail to form an opinion about a candidate. In fact, this happens often. In a plurality election or in an approval election, these voters would not likely support such a candidate. And even if given the opportunity, they would not vote against her either. They simply have formed no opinion whatever. But for famous candidates, such indifference will be rare. For a famous candidate, most voters generally will have formulated an opinion, and likely a strong one. In effect, the famous candidate can draw support from a larger pool of voters. A concrete example will illustrate how perverse this could be.

Consider a plurality election in which one of the candidates, F, is quite famous and another, L, is less so; and suppose there are three other candidates for voters to choose from. Specifically, let us say that there are 100,000 voters who show up to vote in the election. 80,000 of these voters are familiar with and have strong opinions about F but only 40,000 are familiar with L. In this election, 32,000 (40% of F's voter pool) do vote for the famous candidate, F, while the other 60% vote for some other candidate. And 24,000 voters (60% of L's voter pool) vote for L.

In comparison with F, the less-famous L appears to be much more popular with voters who have formed an opinion of her. In contrast, F seems not very popular at all, getting support from less than half of the voters who have formed any opinion of him. But in a plurality election it is only the number of supporting votes that matters.

Between them, these two candidates account for 56% of the votes, and the other three candidates split the remaining votes fairly evenly with none of them receiving even 15,000 votes. F wins the election with a plurality of 32,000 votes over the 24,000 votes for L.

Looking carefully at this election, we would seem fully justified in crediting F's win to fame, and not to his overwhelming popularity with the voters.

Approval voting (AV) illustrates a very similar bias problem. With AV, voters are allowed to vote for each candidate they support so there will be many more votes of support. It is likely that both F and L will collect more supporting votes as a result, and it is likely that with Fs larger pool of voters, the increase in support for F, using AV, could easily exceed that increase for L.

Balanced Approval Voting (BAV) has much in common with AV; even the names are similar. Using either system, for each candidate the voter can vote either support or abstain; but the BAV voter has the added option of voting opposition. Using BAV, each candidate will likely get votes of opposition along with votes of support; so famous candidates will get more support but also more opposition than less famous candidates. Just as F's larger pool of voters is apt to provide an increase in support, however, it is also apt to bring a larger increase in opposition votes. In the example, F could get as many as 40,000 votes of opposition to balance his 40,000 votes of support. Of course, L will likely get votes of opposition as well, so she is in no way guaranteed a win. Neither is there any guarantee that the other three candidates will necessarily still lose. There is, using BAV, a possibility for any of the five candidates to win. With BAV, they are all viable candidates.

Finally, we consider ranked-choice voting (IRV). IRV can be understood as a simulation of a series of plurality elections; for this reason, IRV is likely to inherit many of the problems of plurality voting. Surely, the problems related to invalid data can only become more severe as they are applied iteratively, multiple times. And each iteration of the vote tally is just like the tally of a plurality election, favoring the famous candidates over the less famous. Any one of the iterations could depend on arbitrary choices between candidates among several that some voters regard as equals.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)
 

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