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Bias or Balance

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Paul Cohen
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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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2 people are discussing this page, with 5 comments  Post Comment


Paul Cohen

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An election has some similarity with checking references for a job applicant, so let us consider such an analogy. Voters play the role of references, whether they know much about a candidate or not.

One applicant has provided a list of five references. It was impossible to reach two of these references but the other three all gave glowing recommendations. The other candidate has provided a list of fifteen references and all of them were contacted successfully. But while four of them could not remember anything about the applicant, seven of them provided positive recommendations. But the remaining four references expressed negative views of the applicant.

Which applicant would you choose to hire? Would you just ignore the negative responses and base your decision on the number of positive votes? That is essentially the approach used in an AV election. Or might you think it better to take negative responses into account as well as the positive ones?

Submitted on Saturday, Aug 9, 2025 at 4:26:01 PM

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William WAUGH

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A voting system can collect from each voter, a rating of each candidate, using some default for if the voter leaves a candidate's bubbles unmarked.

The tally can start by ranking the candidates according to the total score each candidate receives from the voters.

Systems can be devised that, for their next step, will attempt to pinpoint, using some algorithm, the "worst" candidate of the bunch, and eliminate that candidate from further consideration. The system can iterate this process until only one candidate remains, and declare that candidate the winner.

A "bottom-two runoff" system says, of the bottom two on the list, we will use some rule to determine who is worse. The fact that we are focusing on the bottom two, and not considering eliminating anyone else, is a way of incorporating the notion of seeking _utility_, since the list was originally compiled and ordered by using the total ratings given to the candidates by the voters, a way of approximating utility (it would reflect utility accurately, if we could count on the voters to record the ratings they feel, and not use a tactic that distorts the ratings they give).

The system can compare the bottom two candidates by comparing the count of ballots that prefer Y to Z to the count that prefer Z to Y. Using this basis incorporates _majoritarianism_.

Some students of voting systems say that the best single-winner system would strike an appropriate balance between _utility_ and _majoritarianism_.

Plain Score is wholly utilitarian, and STAR lies somewhere between that and the above bottom-two system, which is quite majoritarian.

Some advocates opine that utilitarianism is best and majoritarianism should not be incorporated at all. Those on the other side could argue that a system that only aims at utility brings minority rule in circumstances where majority rule could be engineered instead, and is therefore unjust.

Submitted on Sunday, Aug 10, 2025 at 11:08:50 AM

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I'm not clear on why this is called "utility" and I'm not particularly impressed with iterative methods of voting. But you may recall that I toyed with asking voters to list the candidates they dislike, starting with the ones they most dislike. Then iteratively eliminate the one that is disliked by the most voters; and as an alternative, I did suggest a balanced but iterative system.

But voting is fundamentally a tool for implementing democracy and I keep my eye on voting that will improve democracy. It should measure voter opinion accurately and strive to evaluate those votes to judge voter opinion accurately. The hope is that this will cause politicians to cater, as best they can to the wishes of the voters.

Submitted on Sunday, Aug 10, 2025 at 11:36:19 AM

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measure voter opinion

The problem is that not all voters have the same opinion. And the question of how fairly to aggregate the different opinions is not settled. Further complicating the problem, voters are not guaranteed to tell us their opinion. Every game we devise will give them some incentive to use tactics in the struggle for power. However, arguably, not all provide equal incentive, and the resulting tactics are not all equally harmful to the goal you stated. Choose-one Plurality voting being an extreme case in both regards.

not particularly impressed with iterative methods of voting

An advantage of these methods is that they are at least one approach toward guaranteeing to elect the Condorcet winner, if there is one. Plain Score (including BAV) does not guarantee this, although it probably often will so elect.

not clear on why this is called "utility"

Maybe I can show the difference between majoritarianism and utilitarianism with an example. I will try that in my next comment.

Submitted on Sunday, Aug 10, 2025 at 4:41:09 PM

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Say we have three candidates A, B, and C for a single seat.

Say we have two factions of voters; call them the Sharks and the Jets.

The honest utilities of the candidates for each Shark are 100, 90, 0. That means a Shark would be wholly unhappy should C win, wholly happy should A win, and 90% satisfied should B win. I'm assuming here that we have a power to read the voters' minds. This doesn't happen in real life, but I want to assume this for the example, to illustrate the concept.

The honest utilities for each Jet are 0, 90, 100.

There are 51 Sharks and 49 Jets.

Let's calculate the aggregate utility for the electorate, giving the voters' valuations equal weight, one voter to another, of each candidate's winning. For A, we have 100 * 51 = 5100 as a total utility score. For C, we have 4900 by a similar calculation. For B, we have (90 * 51) + (90 * 49) =9000.

Since B has the highest utility score by that calculation, she is the utilitarian winner.

However, there are more count of Sharks than Jets, and they are the only two factions. The Sharks constitute a majority of the electorate, all by themselves. And they like A better than they like any other candidate. So, a majoritarian judgment would settle on A, the majoritarian winner.

The example shows that for some selections of candidates and electorates, strict majority rule would produce one outcome and maximizing utility would produce a different one.

Submitted on Sunday, Aug 10, 2025 at 4:46:47 PM

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