## Why Range Voting is Better than Approval Voting

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1. What they are: Range voting: In an N-candidate election, each vote is an N-tuple of numbers each in the range 0 to 99. The Kth number in the tuple is a "score" for candidate K. You take the average of all the Kth entries to find the average score for candidate K. The candidate with the highest average score wins. (Voters are allowed to leave an entry blank to denote "don't know anything about that candidate." Blank entries not incorporated into average.)

Approval voting: Same thing as range voting, except each number, instead of being anywhere from 0 to 99 has to be either 0 ("disapprove") or 1 ("approve"). [Thus, approval voting is really just a special case of range voting.]

2. Simplicity: Approval voting wins this one: it obviously is simpler. (But not by as much as you might think, since Jan Kok showed a simple way to use any voting machine capable of handling multiple plurality contests – i.e. all voting machines in the USA – to perform "single digit" range elections. On lever machines, optical scan machines, and many kinds of punch card machines, the voter finds it extremely easy and straightforward to use any of Plurality, Approval, or single-digit Range Voting, often with no real advantage in simplicity for either.)

In fact, it has been argued that approval voting actually is simpler – both to understand and to count – than plurality voting: since no special caution is necessary to detect "overvotes" and discard them. ("Overvotes," and in fact every possible combination of approval and disapproval votes, are perfectly legal under AV – there is no artificial distinction between "legal" and "illegal" votes that can be used to "justify" massively discriminatory "ballot spoilage" manipulations.)

3. Expressivity and Honesty: Obviously, with range voting, you are free to cast an "approval style" vote by only using 99s and 0s, never using anything in between – if you so desire. (And in fact, "strategic" voters usually would do exactly this.) So range voters clearly can be either equally expressive, or more expressive, than approval voters.

The more information voters can submit in their vote, the better we expect the results of the election (from their point of view) to be.

A real-world example where real voters for the President of France produced a 3-humped score distribution is here. These three humps were genuine ("statistically significant") and prove that at least 7 score-levels are needed, in at least some real-world circumstances, for voters to express their feelings. Some have criticized score voting because of an alleged "lack of meaning" ("what exactly does it mean if I award 5 rather than 6?"). One reason that criticism is wrong because, clearly, the voters of France feel there is a meaning that is clear enough to them that they produce this 3-humped distributiuon. It does not matter what some critic understands or not about his internal meaning. What matters is what the bulk of the population of actual countries feel when they cast actual votes.

So the question is: is approval voting better because it is simpler, or is range voting better because it allows more expressive freedom?

The answer hinges on how many voters will choose to be "honest" and how many will be "strategic" (and how many will adopt some compromise). That is because if all voters are strategic, then range voting will simply degenerate to approval voting and then there would be no reason to adopt RV, since it is more complicated.

However, Doug Greene and W.D.Smith did a range voting election among random voters emerging from polls in the 2004 Presidential election in New York State (#82 here). We found that (with 90% confidence) less than 33% of range voters vote approval-style (central estimate: 25-26%), and, further, that less than 43% even use the full range (i.e. include both a 99 and a 0 in their vote). We told them to vote as they actually would if the real election were being held using range voting, and I know I told my voters things like "the only meaning of the numbers you supply are the numbers themselves; your job is to choose them to make it the most likely the election will turn out in a way you like." Now while I concede that the 25% and 43% would undoubtably rise if our voters were exposed to more information and thought longer than 1 minute (most or all of them had never heard of range voting before they met us), it seems clear there will always be a substantial fraction of range voters who do not want to vote approval-style.

This finding was surprising news to many in the voting research field. There is evidently a large psychological urge to be honest and that urge seems to affect range voters to a far greater degree than plurality voters. (It is known from National Election Study data that fewer than 1 in 10 of year-2000 voters whose favorite was Nader, actually voted for Nader; same thing happened with Buchanan – i.e. plurality voters are very strategic/dishonest. Interesting contrast, eh? Range voting somehow stimulates people's honesty more than plurality does.)

Incidentally, this is not just purely an irrational quirk of human beings. There also is logic behind it. Specifically, if you are going to be strategically dishonest in your vote, then some parts of that vote matter more than others. Namely, the parts which concern the 2 or 3 candidates you think are most likely to win. For them, it makes a good deal of sense to exaggerate and rate them all 0s or 99s. But the "payoffs" for dishonesty about the remaining candidates (whom you think have extremely tiny chance of winning) are extremely small. The typical voter thinks: "why bother? I'll just be honest about them." And he is right to think so.

Now. Given that we know this fact about human beings and their observed behavior, it seems clear that range voting is better than approval voting, because it allows more humans to satisfy their urges for honesty, and therefore will produce election results that more honestly reflect voters' true opinions.

This can be a big effect favoring range over approval, and it can lead to dramatically different vote counts.

4. Nursery effect: In particular, a dramatic experimental difference between range and approval voting – which appears to be a consequence of exactly the sort of "weighing the relatively importance of strategy and honesty for different candidates" thinking we just described – is the "nursery effect." That is, small "helpless infant" third parties all receive hugely larger totals under range voting than approval voting. That (we hypothesize) is due to honest range voters who under approval voting feel forced to dishonestly give those parties exactly zero. This effect causes small third parties to be capable of attracting donors and supporters and candidates – and therefore to be capable of growing into big "grown-up" parties with range voting. With approval voting, it may be that third parties will simply never be able to break out of infancy – leaving your country trapped in permanent (and inherently quite undemocratic) 2-party domination.

This is an advantage of range voting over approval voting from the point of view of third parties – all US third parties would have gotten 2% or less under approval voting in 2004 and hence qualify as "helpless infants." But, e.g, Michael Badnarik, the Libertarian party's presidential candidate, who got 0.3% under plurality in 2004, would have gotten 0.6% under approval and 9% under range. Range from his view was 15 times better than approval.

Why do we care about Michael Badnarik's happiness? Several reasons. First, third parties as the ones most victimized by the unfair plurality system, are going to play an essential role in bringing us voting reform. If you ask them to support approval rather than range, then they won't. If you can't even get support from those with the most at stake, forget getting anywhere. So you won't get voting reform. Game over, you lose. This trumps every other argument about range versus approval voting.

Second, it seems to us healthier to have a voting system in which small third parties are capable of growing into big ones. That prevents permanent unhealthy sterile 2-party domination, and more generally prevents parties from getting into power, becoming corrupt, and then staying in power without ever having to fear being supplanted by newcomers.

5. When is the range-favoring approval-disfavoring effect largest? When we have an election with a large number of candidates, and have a lot of honesty in our voters, then range does maximally better than approval voting. (Indeed in this regime, even Borda voting is superior to approval.) But in elections with small numbers of candidates and highly strategic voters, range and approval voting act the same. Note that the Iowa 2008 caucuses are likely to fall exactly in the former, maximally-range-favoring, regime.

Even a small percentage of honest range voters can make a big difference in quality. To illustrate how that can be, consider the following artificial example. Suppose there are 20 candidates, 7 fairly-universally agreed to be good and 13 fairly-universally agreed to be bad. Rational approval voters (or strategic range voters) will approve of all 7 good ones but none of the 13 bad ones. Result: 7-way tie. This tie will then be broken by random chance, or by the effects of a tiny number of irrational or dishonestly biased voters (such as bribed ones, or family members of the candidates) with the result that, on average, the 4th-best candidate will be elected. Now suppose that a fraction (and even only, say, 5% of the population, will work excellently) of the voters are honest range voters, and there is a collectively perceptible quality gradient among the good 7. In that case, the best candidate, not the 4th best, will win.

If we say to the voters: "sorry, we are going to force you all to strategically-exaggeratingly employ approval-style votes (0 and 99 only, intermediate values forbidden)" then we intentionally sacrifice all chance of this enormous quality improvement. What benefit is worth that cost?

6. California 2003: an election with 135 candidates. Suppose most voters knew something about, say, 5 of the 135 candidates, and nothing about the other 130. With approval voting, they would probably "play it safe" by disapproving of all the unknowns, resulting in a huge bias against lesser-known candidates, as opposed to what we want, i.e. a bias against lesser-quality candidates. (That behavior was common in the sample of people I polled. In the version of range and approval I have advocated above they could leave those candidates blank. But it is an experimental fact that many voters prefer zeros to blanks in such cases.)

With range voting, they could give the unknowns all X, where X is a number they choose to fill in everything else with. For many voters quite possibly X would not be zero. This would lessen this bias.

In riposte it was pointed out to me that Approval voters could simulate (a noisier version of) range voting by tossing appropriately biased dice to select whether to approve each candidate. However – be realistic. That is not going to happen in the real world.

So: range voting handles ignorant voters better than approval voting does – the latter tends to introduce more artificial biases in that situation.

7. Bayesian Regret (For Statistics Nerds): Approval voting does quite badly (measured by Bayesian Regret) compared to many other more expressive voting systems such as Borda and Black, when there are 4 or more candidates and we have honest voters. The more candidates, the worse approval does, with a very big gap developing. This was shown in computer experiments by Merrill, later confirmed by me.

Approval is better than these systems – for strategic voters – but is worse for honest ones.

The joy of range voting is it is better both for honest and for strategic voters. Computer Bayesian regret measurements by me show range voting as good or better than every other voting system tried including Approval, Plurality, IRV, Condorcet, Borda, in a vast number of different kinds of scenarios with either honest or strategic voters, whether there are 5 voters or 200, and either 3,4, or 5 candidates, under different kinds of "utility generators", and with different levels of "voter ignorance". (For W.D.Smith's papers on voting see #56, 59, 76-80 here.)

8. Potential for Ties and Near-tie nightmares: Remember how Bush v Gore, Florida 2000, was officially decided by only 537 votes, and this caused a huge crisis? Ties and near-ties are bad.

Exact and "1-off" ties are much less likely in range voting than approval voting, simply because there is a large range 0-99 rather than 0-1. (Near-ties are probably also less likely, but not tremendously so.)

We reply: if you buy this logic, then it would follow that you also support forcing voters to vote Democrat or Republican in the present plurality system. Since, after all, voting third-party is (while honest) strategically stupid. Those who like third-party candidates and who are stupid enough to honestly say so are placed at an "unfair" disadvantage and we should force them to vote Democratic or Republican to protect them from themselves. Right?

Well, no. Nobody supports that. This is not an "unfair" advantage anyhow, since nobody is forcing any voter to do anything and all voters are treated the same.

Another reply: Any such "advantage" of subset A of voters over subset B of voters, does not exist if A and B both contain equal fractions of strategic members. Our 2004 study of real-world voters found no evidence that, e.g. supporters of Democratic presidential candidate John Kerry were any more or less strategic than supporters of Republican presidential candidate George Bush. Our study did find that "third party" voters (i.e. those who gave a positive score to somebody besides Bush & Kerry) were distinctly less strategic. But this did not mean that third-party candidates got more of an advantage under approval voting – instead, they got far more votes with range voting – and this was due, apparently, to voter honesty, not strategy! So: this feared phenomenon simply did not exist in the 2004 election, in reality!

Third reply: What about candidates who have little chance? By forcing voters to vote all-or-nothing on them (Approval) we get a highly distorted score for them. This all has nothing to do with "unfair strategic advantages" since for these candidates any such "advantage" is very small since they aren't gong to win. So in recompense for this distortion, we gain nothing.

More about this: The worry that strategic range voters could have more relative power than honest ones, is often raised as a criticism of range voting and a reason to prefer approval voting. I think it useful to distinguish strategic voters, who are trying to get a candidate they like elected, but feel that casting an exaggerated vote is a better way to accomplish that goal, versus plain dishonest voters, who are trying to elect a candidate they do not like (e.g. because they have been bribed). Strategic voters are not so bad because strategic voters with different politics tend to cancel out, and even if they do not exactly cancel, a pretty good candidate still tends to win. I find it hard to believe that voters in one political camp will be systematically more strategic (repeatedly, throughout history, without any rapid learning going on?!?) than those in a strong rival camp. Dishonest voters could be serious in some contexts especially, such as judging skating contests. For that purpose I would recommend trimmed-mean range voting which is a variant of range voting designed to be immune to a certain percentage of corrupt voters. But trimmed-mean range voting seems inappropriate for large political elections because of its anti-democratic features (the votes of "extremists" are tossed in the garbage).

10. Mitigation of ignorance/indecisiveness: By not requiring all-or-nothing ratings, Range Voting mitigates the effects of poor strategy and voter misjudgement about the candidates. Better than the misinformed voter not vote his misinformation full-strength, as he must do in Approval.

Another view of the same thing: Sometimes someone doesn't know whether or not to vote for someone in Approval. Approval then forces her to vote a decisiveness that she doesn't feel. Range Voting lets her vote her indecisiveness. If you don't know, why should you have to decisively vote all or nothing?

11. Familiarity: Range Voting is more familiar than Approval Voting, making it easier to "sell" and more adoptable. Who has not been asked to rate something from 0 to 10?

12. A failure of approval voting in the real world: The IEEE (Institute of Electrical and Electronic Engineers world's largest professional organization, comparable in clout, money, and membership to some small countries) adopted approval voting in 1987, but then backslid by restoring plurality voting in 2002. Why? Their claimed reason was the large percentage (80%) of IEEE members who voted plurality-style. In contrast, our studies show with range voting, only a small percentage vote in plurality style (about 19%). So: that excuse for backsliding will not be available with range.

13. Burr's dilemma: Approval voting is subject to a problem which Nagel dubbed Burr's dilemma. Range voting is less subject to that problem.

14. Saari's attacks on approval voting: Mathematician Don Saari raises two criticisms of Approval Voting. The first is what might be called "indecisiveness." The trouble is, voters who feel A>B>C are forced to vote as though A=B>C or as though A>B=C. They have to decide which way to score B – approve or not. They may, depending on whim, rumors, or whatever – some rather random and arbitrary-seeming cause – decide to go predominantly one way or the other, causing a big swing.

That prospect makes Saari uncomfortable.

Now actually, in Bayesian Regret measurements, approval still works quite well despite this effect. So it is not immediately clear there is any real ground for discomfort. Remember, it does not matter whether "Saari is uncomfortable." What matters is "the Bayesian Regret for all of society."

Saari's second criticism [raised with J.Van Newenhizen: "The Problem of Indeterminacy in Approval, Multiple and Truncated Voting Systems," Public Choice 59,2 (1988) 101-120; responses & rejoinders 59,2 (1988) 121-131, 133-147, 149], which is related and is intended to make the first criticism maximally dramatic, is this.

#voters Their Vote
9999 A>B>C
1 nut C>B>A

"Obviously" A should be the winner here. But with approval voting it is possible that the 9999 voters will all approve both the excellent A and the mediocre B – perhaps because of a rumor that the horrible C might win, and they are determined to prevent that. Although this is possible, it seems highly unlikely; and indeed Saari himself on other occasions, including in email to me, claimed approval voters would have no reason to do anything other than always approving just one candidate (!) – Saari was also wrong about that, but he's right that in small (e.g. 10 or fewer voters) approval elections with 3 candidates, vote-for-one is a pretty good strategy. Anyway, to return to Saari's line of thought: if all the red candidates get approved, the mediocre B would win with unanimous approval, even though he also is unanimously agreed to be mediocre and A is agreed by 9999-to-1 margin to be excellent.

The problem here is all of B's votes are really second-place votes, but approval "rounds them off" to count as full-approval just like for A.

Both of these Saari-problems are cured, either partially or totally, by range voting: range voters are not forced to "round off" B to full equality with A. (If even a few percent rated B slightly below A, this pathology could not happen.) And wild swings caused by rumors driving biased roundoffs, would diminish. (A different cure for wild rumor-driven swings is Simmons' DYN modification of approval.)

To repeat ourselves: Dana Mackenzie (SIAM News Oct 2000) describess it thus:

Saari called approval voting a "cure worse than the disease," on the grounds that it divorces the results of an election from the voters' preferences. That is, the same voter profile can produce many different results, depending on where each voter decides to draw the line between approved and non-approved candidates. Brams, however, viewed this as an advantage, because it gives each voter "sovereignty" over the way she expresses her preferences.
Well, note that range voting does not perform such a "divorce," although it is true that the same preferences with strength information removed can produce many different results with range voting (depending what preference strengths are used). Borda voting divorces the results of the election from this strength information. Range voting does not.

Saari in his book "Chaotic Elections" notes that in, e.g. a perfectly symmetric 3-way cyclic tie, with approval voting "anybody could win." Saari regards that as a disadvantage of approval voting. With (continuum) range voting, such ties will generically not happen at all, which I would regard as an advantage for range voting.

15. Summary: Isn't the purpose of voting to provide information about your opinions? Why would you want to have a system (Approval) that forces you to express less information, when you can have one (Range) that permits you to express more?

Range is better than approval for honest voters and the same as approval for strategic voters, and in practice there are a lot of both kinds of voter. Consequently there is a big quality advantage for range voting, especially if there are a lot of candidates, and this advantage is well worth the slight extra complexity of range. And thanks to the nursery effect, unified third party support for range can happen – but unified third party support for approval cannot happen. That is a huge tactical advantage for range in the fight to get voting reform.

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