A Glitch in Approval

by Devin Ray Freeman

Posted September 08, 2006

The ordinary method of voting is called “Plurality Voting” in voting theory talk. We all know how that works.

Vote

Choose one.

Count

The one on the most ballots wins.

It's the simplest way in the world to vote. What else is great about it is that in elections between two candidates it works perfectly! Seek no further! If, on the other hand, there are more than two candidates in the running, it works poorly.

What works best for elections between more than two candidates, then? For that nothing works splendidly. None is clearly best. Some are demonstrably bad (Instant Runoff comes to mind), and some are variously good depending on what you think matters most. There are probably even some fine methods that have not yet been proposed. One really good method (in my pompous opinion) for voting between more than two is the world's second simplest way to vote - “Approval Voting.” It works like this:

Vote

Choose all tolerable ones.

Count

The one on the most ballots wins.

That one slight difference from what we are all used to seeing in the polling booth, that option to vote for more than one, offers us a get over, a way around that dismal dilemma, the lesser of two evils.

Yes, I'm for Approval, as are many active LRC members. It's the method used here at the Caucus to vote on platform planks and it's been working like buttered corn on the cob. Some of the many benefits of Approval have already been pointed out elsewhere on this site.

Of course, as I said, for elections between more than two candidates, nothing is perfect. Approval in particular, for the purpose of electing officials into office anyway, has one big drawback.

Approval's One Big Drawback

The first choice of a majority should necessarily win.

In voting theory talk, this is called the “majority criterion,” one of many voting criteria isolated by mathematicians. Approval fails it.

To illustrate this shortcoming of Approval I will break it down into the three basic scenarios that an Approval vote can end up in.

Scenario A

None get a majority—no problem.

The one on the most ballots still wins. It can come out this way under Approval just as it does under Plurality (you can win on just a plurality, thus the name). This scenario is very familiar. Since WWII ended, U.S. presidents have been elected on no majority almost as often as not. Under Approval, scenario A is probably a good bit less frequent than it is under Plurality, and it sometimes yields different outcomes. No majority also has a different meaning under Approval.

Some say it's a real problem if nobody crosses the 50% line. They insist that it should require a majority to get voted in, proposing some method that “guarantees a majority” to do it. But let's just suppose there's no candidate that the half of voters think is even OK, as is all too often the reality (and if you're using Approval, that's what scenario A means). Where is a majority to be found in that? Do we beg “Oh please, let us choose between the lesser of two evils?” Voila! We have a majority that finds this candidate either tolerable or intolerable!

I declare the phrase “guarantee a majority” is deceptive. The only majority that can be “guaranteed” is a false one. Sure, where there's no majority, a majority-outcome-designed voting method can wring out an artificial one for you, but if you really want to guarantee a majority, your source for that is Diebold.

scenario B

One candidate gets a majority—no problem.

All will agree that this is the most desirable scenario yielding as it does a clear winner.

scenario C

Two or more candidates get a majority—problem!

It's only in this scenario (a scenario so unfamiliar because, under Plurality, it cannot occur) that Approval just might “fail the majority criterion” (which means “select the wrong candidate” if you think the majority criterion matters much). Mind you, no voting method upholds all criteria. That's impossible. It's just a matter of upholding those criteria that are high priority. Let me state ambivalently that the majority criterion is kind of a high priority. I mean, if most of the voters really think a given candidate is the best one, shouldn't that candidate by all rights win?

For an example of such a failing, let's say Byp's on 59% of ballots, and Thwyp's on 57% (entirely possible under methods that let you give a thumb's up to more than one), and Dyp, Snyp and Ryp all pull in under 30% each. Byp wins.

Now let's suppose that, deep down within the hearts of the voters, Byp was the favorite of only some 40% of voters, while Thwyp was actually the favorite of 51% of them. If that's the case, then Thwyp's the rightful winner (first choice of a majority). Thwyp should win, not Byp.

It's just that we have no way of knowing about favorites because, under Approval, you do not distinguish your first choice, the one you deem best, apart from your other choice(s), the one(s) you deem tolerable. Approval is simpler than that. It's just yea or nay (good enough or not) for each, so it's good in the sense that this simplicity and openess of options does not lend itself much to tactical voting, though there is always some potential for “gaming” any method.

The downside in the trade-off is that if more than one candidate appears on a majority of ballots, there's no way of knowing if there's one candidate among them who is actually preferred by the people (meaning “the first choice of a majority”) or not. If there's no such candidate, then it's certain that the one with the highest percentage deserves to win, but if there is such a majority-preferred candidate, then that candidate deserves to win regardless of how far over the 50% line any other candidate leaps.

What with no recourse for disambiguating between any given majority holder as best or as just generally tolerable, scenario C leaves us with no clear winner. Due to this one glitch in Approval, critics who accuse Approval of selecting not the best, but the mediocre, have got a valid gripe!

Conducive to multi-party democracy though Approval is, proponents of Approval should be mindful of this, Approval's one big drawback.

Approval Majority Runoff

I think it's important for a candidate who is preferred by a majority (if such a candidate exists) to necessarily win. Therefore I've been propounding an extra step for Approval to determine a clear winner where it elsewise fails (namely, scenario C). This new improved (improved because I thought of it?) form of Approval I'm here referring to as “Approval Majority Runoff.”

Vote

Choose all tolerable ones.

Count

The one on the most ballots wins .....

...... except in the event of more than one majority, in which case a runoff is held between all those with a majority.

Runoff Vote

Choose one.

Runoff Count

The one on the most ballots wins.

This method proceeds just as Approval does, except in the odd occurrence of the ambiguous scenario C which calls for a runoff. The method used for the runoff is Plurality.

In the above example then, it would be a runoff between Byp and Thwyp, because they both were on more than half the ballots. Thwyp would go on to win in the runoff, given negligible change in the meantime in voter turn out and popular opinion.

So long as it comes down to two majority holders, the runoff works like a charm yielding one majority. As for the drawback with this, if three cross the 50% line it's the return of the old spoiler effect quandary in the runoff because Plurality works so poorly if it's between more than two. I've proposed the Plurality-style runoff on the supposition that three majority holders would be such a rare outcome that runoffs would almost always be between two.

That is supposing something iffy though, because thus far Approval has been too little tried to know what voter behavior to expect, and mathematicians agree that voter behavior is highly irrational.

The Old is Grim so Try the New

Plurality selects the best . . . ostensibly. If more than two candidates are running, Plurality is sure to encourage negativity. Trial and endless error have proven that voters vote against the more intolerable. Plurality selects one or the other evil (or so minor party supporters and cynics think). Trapped in all this second-guessing and ideas of “electability” only a pure few vote with sincerity. Approval frees us of that because with Approval it's always good to include your favorite on your ballot.

Approval was done even in ancient times, and is the practice for electing U.N. secretaries general, but that's about it these days. Ostensibly, Approval selects something much easier to live up to - the most generally tolerable. Some would say that's all you need (and that Byp should win). Others would say that that just means Approval selects mediocrity.

It's up to us freedom-lovers to use our collective noggin to recognize voting methods with theoretical merit and go on to try them out, because if we don't who will? This website is proof that there exists a caucus in the States that's willing to explore the range of possible ways to vote, and that's an essential initiative in the drive to push aside the lesser-of-two-evils dilemma and wave in multi-party democracy.

As for which ones to try out, I say Approval and permutations thereof have real potential.

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