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Similarities Between Star Voting and Balanced Approval Voting


Paul Cohen
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A practice that resembles Star Voting can be experienced at web sites such as Amazon.com. Customers are asked to rate a product they have purchased, giving it from one to five stars. And Amazon reports the count of customers who have assigned each rating. This gives prospective customers a useful guide for deciding which product to buy while also giving the existing customers a welcome outlet for expressing how they feel about a product they have bought. Since voters know the number of five-star evaluations for each product they have the information to do what much resembles a runoff plurality election between whichever products they are considering.

A practice more resembling BAV can be found in use at other sites such as Pandora. Pandora provides streaming music, but listeners are invited to give individual pieces either a thumbs-up or a thumbs-down rating. Abstentions are not only allowed but quite common and, as you should expect, they are simply ignored; music is in no way rewarded or punished for abstentions. Although Pandora does not provide any direct feedback regarding the net rating of any piece, but it seems likely Pandora computes it for their own purposes. But Pandora does take account of the ratings to adjust what music to play for each account. The point here is that star voting and BAV both find a role at commercial websites. There are other similarities but there are also important differences between these voting systems.

BAV asks voters only easy questions, but still, the answers provide an accurate source of good information for choosing a winner. Though voting this way is easy, this voting system provides voters with substantial freedom of expression. Voters are free to choose to vote support for only their first-choice candidate, but most voters, in a spirit of compromise, will likely mark support for several of them. Likewise, a voter can mark in opposition to just one or even none of the candidates but, more likely voters will mark opposition to most of the candidates that the voter dislikes. But importantly, voters have their say about any or all candidates and in each case they can show support, indifference or opposition.

With respect to allowing voters freedom to express their opinions, BAV is a significant improvement over plurality voting but even over approval voting. Still, some voters might prefer even greater freedom to express details of their opinions. The value of such added detail to election quality is questionable, however, and there is a countervailing imperative to keep the ballots uncomplicated.

In discussion of voting methods, strategic voting often comes up and we might ponder why voters ever resort to strategic voting. Quite often it appears to be an effort by voters to most undermine the election of candidates that a voter opposes. But with BAV the voter has the option of explicitly and effectively voting against such a candidate so there would be no need to resort to any strategic subterfuge. A central feature of balanced voting systems such as BAV is that they provide this important freedom of expression, and the way votes are tallied causes those opposition votes to be as effective as would be a vote of support.

It seems to me now that when I first considered BAV, I was quite fortunate to be unfamiliar with the terminology or the traditions of score voting. This made it easy for me to examine BAV on its own merit, absent the distractions of score voting. But it was not long before I was informed that the right way to think about BAV would be to recognize that it is nothing special, just one of the many examples of range voting (also known as score voting). Exactly the same can be said about approval voting, of course. Since alternative points of view can stimulate a better understanding of a topic, I did welcome this information. Sure, I thought, and how might I take advantage of that? I was soon disappointed to learn that for the most part, score voting contributed only some troubling mistakes and oversights, such as that the characteristics of a score voting systems (with evenly spaced scores) are fully identified by merely the number of score values. But we do learn from mistakes and being motivated to think through how these mistakes happened did help deepen my appreciation of BAV.

The score system that best models BAV asks voters to choose one of three scores; specifically those scores are -1, 0 and 1. The net score for a candidate is then reported as the sum of all scores for that candidate. That net score for this score model is identical to the one obtained by subtracting the number of opposition votes from the number of support votes.

A subtle difference between the alternative formulations is that the score-voting approach avoids recognizing any need for abstentions. In contrast, BAV is quite explicit about allowing abstentions and about how they are interpreted as neutral votes that affect neither the net vote count nor any elections. Another significant difference to contemplate between these two viewpoints regarding BAV is the psychological impact on voters of choosing a numeric score rather than just choosing between support and opposition; the score interpretation introduces a level of abstraction that might well alter some votes and possibly even election outcomes.

A tradition with score voting has been not to use negative scores. Score voting using the scores 1, 2 and 3 is equivalent (with respect to election outcomes) to using the scores -1, 0 and 1 (though the computed net scores would differ, they would remain in the same order). Important, but often overlooked, is that this is true only if one assumes there are no abstentions. But an absence of abstentions can be guaranteed (at least with paper ballots) only in the abstract models of elections. In actual elections with paper ballots, abstentions will occur, accidentally if not intentionally. But the tradition has been to simply ignore this as an obviously insignificant consideration. Critical thinking suggests that we should be especially wary of obviously insignificant considerations.

In tallying a real-world election using score voting there is a temptation to simply skip over abstentions, and this works fine if the scores are -1, 0 and 1. But if the scores are 1, 2 and 3 then to keep the score voting equivalent with BAV, an abstention must not be skipped, but instead be treated by assigning the default score of 2. Briefly considering voter psychology again, since voters cannot abstain, it seems as though the minds of some voters might rebel at the idea of assigning a score of 2 as an expression of indifference to a candidate (the notion of a neutral score will be explored in a comment); that may be an irrational prejudice, but there it is.

Tradition poses one more difficulty, however; the tradition with real elections using score voting is to always use the smallest score, in this example, 1, as the default assignment when abstention must be permitted to accommodate an actual election. Unfortunately, this tradition has the effect of penalizing candidates for each abstention. When there are a great many abstentions for a particular candidate, this tradition of converting an abstention to the lowest available score puts a heavy thumb on the scale, preventing the election of a less widely known candidate. Score voting is far from alone in punishing smaller parties and independent candidates.

It seems odd that the most familiar voting systems treat abstention as if it were an expression of opposition. This is unfair because voters often abstain when they are simply indifferent, neither opposed nor in support of the candidate. And a very common reason for indifference is that the voter is not familiar with a candidate. For the major party candidates, abstentions would happen only quite rarely, but for candidates from smaller parties or for independent candidates, unfamiliarity could be quite common, not at all a rare exception. In a score election, treating abstentions by assigning them the lowest available score serves to foster a duopoly.

Comparing BAV with star voting, we might observe that both systems are built on score voting, BAV with three scores (-1, 0 and 1) and Star voting with six (0, 1, 2, 3, 4 and 5). Both BAV and Star voting place the default (assigned in case of abstention) at 0, but for BAV, zero is the neutral middle score while for star voting, 0 is the lowest and most punishing available score. As we have seen, this imposes an unfair penalty on independents and on candidates from small third parties. And because Star voting specifies six scores, voters are even denied any way to specify a neutral score (2.5 is simply not one of the available scores).

In no way should this favoritism be interpreted as anything nefarious. The problem is not likely to derive from intent; it likely is just a failure to recognize the great significance of carefully balancing voter support with voter opposition.

A 2017 article in this series explored the idea of allowing more than the minimum number of scores. For balanced voting systems the minimum would be three, but it is natural to wonder whether it might be better to allow five or seven or perhaps thirty-one? Any odd number of scores would provide a middle score to serve as expressing neutrality or indifference. But the example in that article shows how the added scores would introduce the possibility of a winning voting strategy. It could tempt a conspiracy of voters to mimic BAV by avoiding scores other than the largest, smallest and middle scores. Surely, a guiding principle in the design of a voting system should be to avoid encouraging strategic voting. But it might be argued it would be worth violating that guideline to allow voters the satisfaction of more accurately expressing their opinions. This is a matter of judgement, but as noted earlier, the value of the added scores in terms of improving election outcomes seems doubtful.

While voters do enjoy fully expressing their opinions, they do not much enjoy making tough or seemingly meaningless decisions such as choosing whether to assign a score of 26 or of 27 on a 31-point scale. These feelings are clearly at odds with one another. Keeping voters happy is important of course, but from the standpoint of running an election, the overriding objective should probably be on gathering accurate and reliable information about the aggregate opinions of the entire voter population at large and to make the most suitable selection based on that information. And that does not necessarily require collecting finely defined distinctions of opinion from individual voters. In fact, collecting excessive detail can complicate voting and reduce the reliability of the collected data. For example, adding extra scores for a score election will clutter the ballots with extra rows or columns and that increases the likelihood of mistakes such as mistakenly checking off the wrong box.

For score voting, using an even number of scores seems a particularly poor choice. But a score election using five, or even seven scores, seems less objectionable, so long as the default assigned for resolving abstentions is the middle score. Still, allowing only three scores would be preferable, both for the sake of simplicity and for its reduced susceptibility both to ballot errors and to motivating strategic voting.

But we should remember that star voting is not identical with score voting using six scores. Star voting adds a simulated final runoff using plurality voting. This could provide some emotional appeal for the illusion it creates of ending with a majority decision, but perhaps even more because we are all so habituated to relying on plurality voting. At some deep cultural level, plurality voting now seems to us as the natural and right way to vote. It is quite engrained in our traditions and, in truth, so long as there are only two candidates there is nothing wrong with plurality voting. But many of us would prefer more than just two candidates and making that possible will surely require a clear break with tradition.

The extra runoff step in star voting imposes additional effort on voters and even a bit of gaming. First, the voter must take a gamble regarding who the top two contenders are likely to be. So long as we maintain our duopoly, that is easy, but would it not be great to rid ourselves of the duopoly? Next, the voter must adjust the scores on the ballot to minimize risk in the runoff. This may be

Puzzling and Betting at the Polls
Puzzling and Betting at the Polls
(Image by Paul Cohen)
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likened to solving a puzzle, though it is probably an easy puzzle when more scores are available than there are candidates. But with the duopoly ended, that will not necessarily be the case.

Another issue we should consider is whether voters should be distracted with gambling and puzzles when they likely could easily indicate which of the candidates they find acceptable and which they find unacceptable. Is that not crux of what we should want to learn from election ballots? These are very easy selections that voters can make without strategizing about or even considering the horse races between different candidates. It is hard to imagine why a voter would fail to be honest about voting. The most difficult choices for a voter would be deciding, in borderline cases, whether or not to abstain.

I suspect voters would prefer to end the duopoly so they could have several candidates to choose from. By ending the duopoly, we would ensure additional viable candidates and that would, in turn, reduce at least the most irrational aspects of the intense polarization that now infects our society. When it is adopted, BAV will very likely bring this about.

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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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