Optional preferential dominates approval voting

by John Q on March 9, 2004

I thought I’d said my last word on voting systems, but it’s a topic that’s hard to exhaust. The comments thread to Brian’s latest post raised the notion of Approval voting in which you cast a vote for all candidates of whom you approve, the candidate with the largest number of votes being elected. I suggested that “the appeal of approval voting is mainly to people who can see the inadequacies of plurality (first past the post) but are worried about the supposed complexity of preferential” and the site linked above, with its frequent references to simplicity, supports this view.

I now want to make a stronger point. Approval voting is, for nearly all purposes, dominated by the “optional preferential” system, in which voters can list in order all the candidates whom they wish to give any support, leaving the remaining candidates unranked. In effect, optional preferential is an approval voting version of the single transferable vote system, with the desirable property that voters don’t have to give any support to candidates they dislike. Given the data from on optional preferential ballot, it would always be possible to implement approval voting by disregarding the rankings given by voters, but its hard to see when this could ever be desirable.

The “instant runoff” interpretation of the single transferable vote favors optional preferential voting. In a real runoff, it’s always possible for voters to abstain if all the candidates they support have been eliminated[1], and the optional preferential system mimics this.

As with nearly all voting systems, the optional preferential system has been tried out in Australia. In fact, it prevails in my home state of Queensland. It would be nice to report that this was the result of an extensive study by expert political theorists who came up with the best possible voting system. However, no-one who knows anything about Queensland politics would believe this. In fact, Queensland has two conservative parties, Liberal and National, which often run against each other, and some of whose supporters are mutually antagonistic. Under optional preferential voting, some National supporters will not allocate a second preference to Liberal and vice versaThis is to the benefit of the Labor Party, which was quick to introduce optional preferential voting when it got a majority a decade or so ago, after many years in opposition.

The situation in Australian national politics is truly bizarre. Although the full instant runoff system is in force, it is possible to gain the effect of optional preferential by ranking all the undesired candidates equal last. Should your preferences be counted to this point, the vote will be declared informal and discarded, which is exactly the same outcome as under optional preferential. However it is a criminal offence to advocate such a vote, owing to a disgraceful piece of legislation passed with the intention, and effect, of silencing electoral reform campaigner Albert Langer[2].

Just to cover myself, let me say that whether or not I would cast a “Langer vote” I would never advocate such a vote, at least while current law prevails. On the other hand, I am free to point out that Senator Nick Bolkus, who introduced the relevant legislation is, in this respect at least, an enemy of free speech and democracy.

fn1. in principle, it’s possible to abstain in one round and re-enter in a, but it’s hard to see when this would be sensible.
fn2. In an earlier life, Langer was a famous Maoist agitator. I much prefer his later incarnation.



Alan 03.09.04 at 12:36 pm

Compulsory preferential voting (where you must preference all candidates is exclusively an Australian thing) and STV advocates outside Oz usually scratch their head over it. It’s not integral to the system at all and is not used in Ireland or Malta. The Bolkus legislation is an outrage although I join you ind defintiely not advocating a Langer vote.

IRV and STV with or without compulsory preferences, are in fact the same thing. They have identical methods for determining the quota. The only difference is that if more than one candidate is to be elected STV has mechanics for the fractional transfer of votes from elected candidates as well as the elimination of losing candidates.

Essentally you have a single system that’s equally applicable to electing one or several candidates.


Matt McIrvin 03.09.04 at 2:01 pm

The one election with a proportional voting system in which I ever participated– a Cambridge, Massachusetts city council election– definitely didn’t require ranking all the candidates. There was a huge number of candidates, so it would have been a peculiar situation if this were necessary.


Alan 03.09.04 at 2:14 pm

At the 1999 New South Wales election, voters were presented with an unusual physical challenge in trying to cast their votes for the Legislative Council. A record 264 candidates nominated for 81 groups on a ballot paper measuring one metre by 700mm. Quickly nicknamed the ‘tablecloth’, the ballot paper also created novel administrative problems for polling officials and Electoral Office staff, ranging from the need to increase the width of voting booths and provide larger ballot boxes, to hiring larger forklifts, trucks and planes to cope with the extra weight of paper.

That was a scary election…


Jason 03.09.04 at 3:13 pm

Matt, there is a slight difference between proportional representation (PR) and the preference list methods talked about here. PR is used with a large body of representatives, and gives the share to each party that the party receives as a vote.

The various preference list methods are normally discussed when talk about elections for a single seat (eg., mayor). If a candidate has more than 50% first place votes, they win. If no candidate does, one of the candidates is eliminated, and the process repeats.


Jason 03.09.04 at 3:23 pm

In the comments to Brian’s post, I was a little confused as to why some people prefer STV, which doesn’t cause Condorcet winners to be elected, to a method which does. I guess that the post had slipped into the ether by the time I got around to making my query, as it still stands unresolved.

Why in the following situation, would you want B over A and C?

A field of 50 candidates, a few peoples first and everyone elses second favourite choice is A, but the extremists B and C take up most peoples first (and last) choices.


Jason 03.09.04 at 3:46 pm

Looking at my previous comment, perhaps I didn’t describe the situation as clearly as I would like. Let’s hope this attempt is a little better

There are 50 candidates for the position; one good moderate (A), 3 good polarizers (B,C,D), and 46 minimally competents.

1/3 of the population vote B,A,everyone,C,D
1/3 of the population vote C,A,everyone,D,B
1/3 of the population vote D,A,everyone,B,C

(So you either love or hate the polarizers)

Is there any good reason for not picking A?


humeidayer 03.09.04 at 5:42 pm

As far as voting schemes go, one idea that’s come to my mind (probably not original) would allow one to not only distribute the weight of one’s vote but also the sign of it. In other words, one’s vote would carry a weight of 1.0 but the vote could be for (+1) or against (-1) candidates. In other words, for example, I could vote -1 for Bush; i.e., “100% against Bush.”

Such a system would probably be criticized as too subversive and destructionist, but I think it could be a very effective means of expressing dissent. With the existing American system, one can choose to vote at all, but then one has no influence on the election. With the existing American system, one can also choose to vote for someone other than Bush, but that seems to carry with it implied approval of the chosen candidate.

People often offer up a “protest vote” by voting for candidates they know cannot win (Ralph Nader, Harry Browne, etc.). It would certainly be interesting to see a system in which one could hand a candidate a -1 as a form of protest. One would think it would effect the mandates of those elected. One would hope an elected official with a lot of minus ones would be less apt to practice divisive and highly partisan politics.

Oh well, a crazy thought for the day. Has it ever been done? In a world with +6,000,000,000 souls, I tend to assume it’s all been done, but my laity is in this area is quite admittedly boundless.


Matt Brubeck 03.09.04 at 8:16 pm

humeidayer (“It would certainly be interesting to see a system in which one could hand a candidate a -1 as a form of protest.”):

Ranking candidates from -1 to 1 is mathematically the same as ranking candidates from 1 to 3. Changing the scale just changes the final results by a constant amount. The negative numbers have a purely psychological effect, if any.


Lemma 03.09.04 at 8:55 pm

According to the results of Keith Arrow’s Impossibility Theorem, the set of requirements that must be satisfied to construct social preferences from individual preferences (i.e., by voting) includes the requiment that social preferences should be complete, so that choosing between A and B, either A is preferred over B, B over A, or neither is preferred.

Now, as Matt Brubeck indicated, a scale of -1 to 1 is the same as 1 to 3, but more importantly, the scale is complete in the sense that giving a -1 to a candidate is _not different at all_ from voting for the other candidate. It still indicates that you prefer the other candidate.

The important lesson I think is that voting is about preference, not about perfect choice.

In the case of a protest vote to a third party candidate, that is a preference vote against the other two candidates, which is like giving a -1 to both other candidates. But that is absurd, because given only the choice between one or the other major candidates, you do hold a preference, protest notwithstanding. Therefore, a protest vote is nothing but a preference vote within your voting block, which is precisely what is supposed to happen in the primary season so fix the voting block on one candidate for the real election.

I’m rambling. Nevermind.


John Quiggin 03.09.04 at 9:33 pm

Jason, a major problem with Condorcet proposals is that they are usually discussed without specifying a mechanism to resolve the cases when they don’t work, essentially when A beats B, B beats C and C beats A. Until the rule for this case is specified, Condorcet can’t reasonably be assessed.

As regards the case you mentioned, if the voters for the B,C and D like A and hate the other polarisers, those whose candidate doesn’t have a chance will be well-advised to cast a tactical vote in favor of A, thereby electing her.

OTOH, in a three-candidate situation where A is the first preference of only a few voters, and the partisans of B and C each regard her as only marginally preferable to the main opposing candidate (so are unwilling to cast tactical votes in her favor), I don’t think it’s at all clear that A should be elected. In this case, under STV she won’t be, but her voters’ preferences will decide between B and C, assuming neither has an outright majority.


John Quiggin 03.09.04 at 9:40 pm

Alan, an earlier NSW Senate election (1974?) was even scarier, since there was no option of voting for a list. There were about 100 candidates, and a valid vote at the time required that all candidates be numbered, with no numbers omitted or repeated. It was suggested at the time that bogus candidates had been run in the hope of making the voting task too difficult for less-educated voters and non-English-speaking migrants (assumed likely to vote Labor).

But the result demolished claims that STV and so on are too complicated for ordinary mortals. Despite the complexity of the task, only about 10 per cent of votes were informal – this in a system of compulsory voting. Since there are usually a fair number of deliberate informal votes (blank ballots and so on) the outcome was apparently unaffected by the ploy.


humeidayer 03.09.04 at 11:43 pm

Now, as Matt Brubeck indicated, a scale of -1 to 1 is the same as 1 to 3, but more importantly, the scale is complete in the sense that giving a -1 to a candidate is not different at all from voting for the other candidate. It still indicates that you prefer the other candidate.

The outcome might be the same, but consider two different scenarios.

Scenario #1
Kerry 51%
Bush 49%

Scenario #2
Kerry 26%
Bush +49% -24% = 25%

Kerry wins by 1% in both cases, but in the second case, a high degree of dissent is apparent. A candidate winning under Scenario #2 might claim some sort of mandate, but it would certainly be questionable.


novalis 03.10.04 at 12:16 am

John, IRV with optional preferences still has the problem that adding votes for a candidate can cause them to lose. The problem with IRV is that it’s non-monotonic, not that it requires supporting candidates low on priority lists.


John Quiggin 03.10.04 at 12:24 am

novalis, I can’t see how your claim of nonmonotonicity can work. Adding votes to candidate A can’t change the order in which other candidates are eliminated, so it’s only relevant if A is in danger of elimination, or in the final two-way vote. Either way, more votes make A more likely to win.

But this is a tricky topic and maybe you can point to a flaw in the reasoning above.


Brian Weatherson 03.10.04 at 1:37 am

I don’t __think__ it’s true that adding votes to a candidate can cause them to lose, but *transferring* votes to a candidate (i.e. getting people to change from A to B) can cause that candidate (i.e. B) to lose. Here’s a scenario in which it happens.

45 votes for DBAC
20 votes for BCAD
18 votes for ACBD
17 votes for CBDA

In this case B wins relatively comfortably. But if 2 of A’s voters change their mind and suddenly vote BCAD, A is eliminated first, all her votes go to C, then B is eliminated and C wins. In principle, B doing better among the electorate can make her not win.

Opponents of STV try to find cases of this actually happening, but I haven’t seen them come up with a convincing case.


humeidayer 03.10.04 at 1:48 pm

Ranking candidates from -1 to 1 is mathematically the same as ranking candidates from 1 to 3. Changing the scale just changes the final results by a constant amount. The negative numbers have a purely psychological effect, if any.

To comment a little more, I see an enormous difference between being “AGAINST X” and being “FOR Y.” Part of the problem is that a vote for a candidate tends to imply support when in fact the vote may have been made primarily to avoid a greater evil. Many economists, I’m sure, will be uninterested in the distinction and say all that matters is that a preference exists, but I think the meaning of a vote is very important and giving the voter more power to indicate that meaning of his or her vote could change election outcomes.

Suppose the polls project Extremely Bad Man 45%, Very Bad Man 43% and Very Good Man 12%. Voting for Very Bad Man implies support for Very Bad Man. There’s a range from idealism to pragmatism. Some voters will vote their conscience for Very Good Man regardless of the situation. Other voters will take a pragmatic approach and vote for Very Bad Man to avoid Extremely Bad Man.

The ability to explicitly vote against candidates might create some middle ground, because it would give people the freedom to exert the power of the vote without offering any implied support for candidates they consider little more than lesser evils. If rather than voting for Very Bad Man to avoid Extremely Bad Man one could simply vote against Extremely Bad man, then one could then avoid a lot of the guilt associated with feeling morally responsible for the actions of Very Bad Man and the guilt stemming from one’s part in contributing to the perceived legitimacy of Very Bad Man.

(Sorry for the digression.)


Kerim Friedman 03.10.04 at 3:21 pm

Given the data from on optional preferential ballot, it would always be possible to implement approval voting by disregarding the rankings given by voters, but its hard to see when this could ever be desirable.

As I wrote in my comment on the last post, my understanding of what the Approval Voting system is advocating is not that it is “simpler” as much as that it is less open to strategic manipulation. I haven’t see anyone address this claim. I would be interested in knowing if it holds up to scrutiny.


Brian Weatherson 03.10.04 at 3:48 pm

Kerim, I’ve never seen any good evidence that any real-life STV ballot has been seriously open to strategic manipulation. Since there have been tens of thousands of STV ballots run in Australia alone, this is good evidence I think that it just isn’t a serious problem.

On the other hand, in very common situations (e.g. when there are three candidates and one prefers one of the non-moderates) there is a really hard strategic choice facing one in an approval voting system – do you vote for the moderate or not? It seems to me that to make that choice you need lots of information about how other people will vote, which is just the alleged problem with STV. (‘Alleged’ only because there’s no evidence that it ever arises in practice, and the theoretical situations in which it could arise, like the one I mentioned just above, are quite complex.)


Jason 03.10.04 at 8:16 pm


I know Condorcet is a little unclear on what to do when there is no clear winner, but it seems that there are plenty of elimination rules that would let Condorcet winners win, if there happens to be 1.

For example (not really putting much thought into it), you could take the 2 people with the least number of first place votes, and do a pairwise runoff to see who is eliminated.

It seems to me that you’d like a system that would vote in a Condorcet winner if there did happen to be one.

FYI, My roommate is an intelligent, politically active australian (I’m a kiwi, so take the first adjective with a grain of salt). I asked him how STV worked (before searching online), and he didn’t know how the candidates were eliminated. I think you can have fairly complicated elimination rules, and people will just trust expert opinions that the eliminations are reasonable, and vote their preferences.


Kerim Friedman 03.10.04 at 8:33 pm

Thanks Brian. FYI: This is the article referred to on the Approval Voting page regarding IRV. But from what you are saying, it seems that these concerns are unfounded, or at least highly unlikely?


Brian Weatherson 03.10.04 at 11:26 pm

I think it would be a serious problem if it happened at all regularly, but I don’t think it will (or has). In practice, just voting your preferences will maximise the probability of results you want in every plausible circumstance. (I note the absence of real life examples on the approval voting page.)

I don’t think that’s true for approval voting – I think in all sorts of actual seats in the UK if approval voting was brought in there would be no way for a voter like me to tell how they should vote without knowing who other people are going to vote for. And that I thought is what is meant to be wrong with ‘strategic voting’.


novalis 03.11.04 at 7:35 pm

Brian, looking for real-life examples will be hard, because voting systems shape the political reality.

It looks to me that the most recent election in Australia (disclaimer: I know nothing about Australian politics) was quite close between Liberal and Labor, with the difference being provided by non-first-choices. I don’t know how the non-major parties are politically, but I suspect that a difference in elimination order could have made a difference (which, I’m aware, is a weaker claim than nonmonotonicity). Still, it’s not any more strategy free than approval voting.


Alan 03.11.04 at 11:54 pm

The two-party preferred vote (counting the election as if only Labor and Coalition candidates had stood) in 2001 was Labor 49% to Liberal 51%. The first preference figures were Labor 37.8% and Coalition 43%.

Thre’s a good description at http://www.aph.gov.au/library/pubs/rn/2001-02/02rn39.htm


Brian Weatherson 03.12.04 at 2:11 am

Novalis, to get a case where elimination order matters, you have to have a case where fewer than 2 candidates get 33.3% of the vote. Otherwise those two candidates will be the two remaining whatever else happens. And that’s normally the case in Australian seats. (Sometimes one of the majors gets less than 33% because the other tops 50%. Elimination order doesn’t matter then either.)

The standard way to count an election in Australia is to count the primary votes then assume the top 2 primary vote getters will be the last 2 and distribute preferences straight to them. This doesn’t always work (especially when there are strong independent candidates) but it’s pretty reliable in my experience.

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