A recent article, led me to comment that familiarity with score voting is not necessarily an asset. Such familiarity is in no way a prerequisite for understanding balanced approval voting (BAV) and in fact it can be a perverse distraction. But people already schooled in alternative voting systems seem quick to observe that BAV can (and therefore should) be understood as a score voting system. They conclude that BAV must be of no particular interest; it's an old story, just another one of many examples of score voting. One wonders by analogy how many opportunities passed by early humans, dismissing flint as merely a rock, with no consideration that it might be
useful for fashioning tools or for starting fires. Sometimes it does take mustering some attention and even exerting a bit of effort to show how useful an object or concept really is.
This article addresses that line of thinking. This casual dismissal of BAV is a mistake, but also beneath this attitude lies an error in reasoning. When you infer some conclusion based on several assumptions, it is too easy (but a very unfortunate mistake) to hold to that conclusion even when an assumption is violated.
In a Score Voting election, voters are asked to rate, using specified numerical values (possibly just 1 to 3 but often 1 to 5 or even 1 to 100) how strongly they favor each of various alternatives. Score Voting has traditionally postulated, just as a matter of convenience, that every voter explicitly rates every single candidate. The voter-assigned scores are added for each candidate and the candidate with the larges sum of scores wins the election.
So long as the specified scores are equally spaced, what fundamentally distinguishes different score voting systems is merely the number of scores allowed. Using scores 1,2 and 3 is equivalent (in the sense of election outcomes) to the system using scores 3, 6, 9 or in fact 5, 8, 11. In general, you can multiply each of the scores by a positive number or add any number to all of the scores without changing election outcomes. And this is true whether or not the permitted scores are equally spaced.
People often seem prejudiced against negative numbers. Although -9, -6, -3 could equally well be used as the available scores yielding exactly the same election outcomes as with 1, 2, 3 but such choices using negative scores have been rarely even considered. Usually, for a scoring system with three scores 1, 2, 3 will be chosen. By subtracting 1 from each of these scores, zero could be one of he scores. In fact by subtracting other values, it would follow that the score system with scores 1, 2, 3 is equivalent to the one with scores 0, 1, 2 and also with using -1, 0 1. But care is needed here; we will show that you are free to add a constant to the scores without changing the system only on the assumption that voters assign a score for every single candidate.
How convenient it is that within the traditional understanding of score voting, that the handling of an unspecified score can safely just be ignored. This is true (by fiat) because unspecified scores are simply not allowed to happen. But in real-world elections, whether intentionally or not, voters sometimes do ignore a candidate, assigning no score whatever. So in real-world elections using score voting, it is necessary to establish some rule for how to handle those pesky but inevitable unspecified scores.
A workable (though thoroughly distasteful) way to manage this problem would be to throw out those ballots, declaring them to be spoiled. But voters would surely object. Instead, the traditional alternative seems to be to just just ignore those missing scores and add up those scores that voters actually have explicitly specified. In effect a new style of of score voting has come into being. In addition to the the original one which we will call abstract score voting (ASV) there is a new one that we will call reality score voting (RSV). The difference is that ASV does not allow missing scores while RSV permits them.
Notice that skipping over missing scores has exactly the same effect as setting those scores to zero. The RSV approach to tallying the missing scores will (unintentionally) introduce score of zero. The ASV system with scores 1, 2, 3 is transformed into the RSV system with scores [0], 1, 2, 3. In time, no doubt a few attentive voters would realize that by not assigning a score for a disfavored candidate rather than by assigning 1, they could more firmly assert their lack of support for the candidate..
Might RSV behave differently from ASV in other important ways? It surely could be.
Adding 10 to the scores 1, 2, 3 does yield the equivalent ASV system using the scores 11, 12, 13; however, adding 10 to the RSV with scores [0,] 1, 2, 3 produces the fundamentally different RSV system [0,] 11, 12, 13. Because the other scores shift upward, as the amount of upward shifting increases, not assigning a score becomes increasingly more punishing to the candidate in question than assigning the lowest permitted score, 1. Clearly, the claim that you are free to add a fixed value to all scores while preserving the nature of a score voting system (while true for ASV) is not true for RSV.
Could we somehow patch this mess up? A way to make ASV and RSV relate more to each-other as we might wish would be to insist that in both systems zero must be included as one of the available scores. That way, at least the real-world adaptation of a score voting system, there would be no danger of adding 0 as an extra score when relaxing the ASV rule against unspecified scores. But notice that with this reformulation, adding a constant to all of the scores could cause another problem by eliminating zero from the allowed score, something that now is disallowed. And this would be the case for ASV just as it is for RSV.
By making 0 necessarily one of the scores, it becomes apparent that, there are three different score voting systems using three scores. 0, 1, 2 is one possibility but another is -1, 0, 1 and a third is -2, -1, 0. Traditionalists (habituated to never voting in opposition) as well as people who simply harbor a distaste for negative numbers will no doubt prefer the first alternative, but nonetheless there really are three distinct possibilities. Selecting which particular form to use in an election should not be guided only on whim, habit or intuition. In real-world elections, each of these three systems can result in different outcomes and such consequences should guide that selection. Further discussion on this topic appears in this earlier article where the three different alternatives are provided names.
With an odd number of scores there will be one that is positioned in the middle. Provided the scores are equally spaced, choosing that middle value to be zero is what characterizes a balanced score voting system. We have demonstrated in other articles that the balanced score voting system with three scores, will quite certainly make it very unlikely to form or to maintain a two-party duopoly. And this is the only one of the three systems for which this is true. Should we want to put an end to the two-party duopoly, that should be reason enough to choose the scores -1, 0, 1 with 0 in the middle.
We can now elaborate on how all of this relates to BAV, a system that I have written about at some length. BAV, it is a quite simple system to describe, particularly when the larger but not truly relevant topic of score voting fails to intrude. A BAV ballot lists all of the candidates, each with one check box for support and another for opposition. For each candidate, the voter checks some (even none) of the support boxes to show support for the candidate. Likewise that voter checks some (or none) of the opposition boxes. And a voter may skip over yet other candidates, possibly because of unfamiliarity, indecision or indifference, checking neither box.
Once voters have finished, the net vote for each candidate is determined by subtracting the count of opposition check-marks for the candidate from the count of supporting check-marks. The candidate with the largest net vote wins election. As with other voting systems, some method must be established to deal with the rare but remotely possible tie votes, but in establishing this method it is helpful to keep in mind that voters have shown, in aggregate, that they consider all of the candidates with the same largest net vote to be equally satisfactory choices.
It is worth taking note of how very different from score voting BAV appears to be. With BAV there are no numeric scores mentioned on the ballot. There is no reason for the issue of a default assignment to even arise.
It may be unfortunate, but BAV actually can be understood as the score voting system with three scores, -1, 0 and 1. We can pretend that when a voter checks the opposition box for a candidate, the voter is thinking of this as the way to specify a score of -1. Similarly we might imagine the voter thinking that checking the support box is more properly understood as specifying a score of 1 in a score voting election. The voter might even think of passing over a candidate without checking either box to be assigning a score of 0. The voter is perfectly free to think in these ways because BAV fits perfectly as an example of even the abstract score voting system. This is because every ballot really is assigned one of the scores either explicitly or implicitly. But how many voters would actually go through such mental gymnastics? Perhaps there would be a few, at least until voters are accustomed to using BAV for voting.
The important point is that there is really no real need to even mention the superfluous and (as we have seen) confusing superstructure of score voting. BAV can be described on its own and still stand quite comfortably on its own, with no help or (more likely) hindrance from the score voting formalism.
Out of a distaste for negative numbers, some people might still object to BAV even though no negative scores are mentioned. Nevertheless, the computed net vote for a candidate can turn negative, in which case considerations of courtesy might raise an objection to advertising such a fact. A negative net vote would reveal how widely opposed a candidate to be. And a candidate with a negative net vote might even win election and that would reveal that all of the candidates to be, on balance, opposed by the voters. How embarrassing it would be to openly admit such a failure of democracy.
My personal view is that it actually is foolish to cover up such unpleasant truths when they happen; exposure may be just what needed to encourage there to be more suitable candidates in future elections.
But with BAV such a cover-up would not be difficult and as a demonstration, In fact, Latvia has adopted a version of BAV that does exactly that. Instead of computing the net vote as I described above, Latvia computes what we might call the election score as the sum of the net vote and the number of voters. The election outcome remains unchanged, but unlike the net vote, the election score will always be nicely positive (and possibly no one will even notice how unpopular the candidates are).
