Comparison of pro-multipartisan voting systems for single-seat elections

This thread is getting consistently hijacked over the issue, so let’s pick it up here.

At present, the U.S. and most other democracies elect a single officer (“single” must be emphasized – alternative systems for electing multimember policymaking assemblies, such as proportional representation, are a different discussion) by giving the office to whichever candidate won a plurality of the votes cast, i.e., more than any other candidate but not necessarily 50%+1. (Some jurisdictions vary this by requiring a majority and holding a runoff election between the top two finishers – but a second election costs the government more money.) This naturally and strongly discourages third-party candidates – i.e. a third-party (or independent nopartisan) candidate cannot hope even to get the votes of all voters who want him/her to win, because they are afraid of “wasting” their votes. Worse yet, it creates a “spoiler” problem. Suppose it’s 2000 and your favorite presidential candidate in the race is Pat Buchanan (Reform). If so, almost certainly your second choice is George Bush; but you really, really prefer Buchanan; but you really, really, really oppose Al Gore. That means if you vote or, worse yet, volunteer for Buchan, you are “splitting the opposition” to Gore, taking votes away from Bush that he otherwise would have gotten, and making it more likely Gore will win. So, in effect, a vote (or donation of time and/or money) for Buchanan is a vote (or, etc.) for Gore. Likewise, a vote for Ralph Nader (Green) is a vote for Bush. Third-party candidates keep denying this logic – I remember a button from 1980, “A VOTE FOR ANDERSON is a vote for Anderson” – but its practical effect is inescapable. Which means third parties never get a chance to get a chance; if you want to participate meaningfully in politics at all you have to go with one of the two “big tent” parties. In the other thread I argue (at great length) that this is a bad thing; for purposes of this one let’s just assume that, please, and look for alternatives. Several have been proposed:

  1. Instant-runoff voting: You, the voter, rank-order the candidates by order of preference. If your first-choice vote is for Buchanan and he does not get a majority of first-choice votes, your second-choice vote for Bush counts in his column. Whoever gets elected has a real majority mandate, i.e., is demonstrably the choice of a majority of the voters.

Criticism of IRV provided in the other thread by ultrafilter.
2. Approval voting: Without rank-ordering, you simply vote for every candidate acceptable to you. You can vote for Bush and Gore and, what the heck, Harry Browne (Libertarian) too. All your votes count the same and the candidates you don’t like don’t get any of your votes.
3. Range voting: You assign each candidate a score within a specified range, say, 0 to 99 or 1 to 5. Think of measuring a certain amount of sand in a graduated cylinder and pouring it into a cub labeled “Bush,” and at the end every voter’s contribution of Bush-sand gets poured into one big pile and whoever has the biggest pile wins (stop that snickering). Approval voting can be considered a form of range voting with only two levels, 1 (approved) and 2 (dissaproved).

Case for range voting as against IRV provided by ultrafilter.
Which is better? Which is more likely to favor emergence of a multiparty political system? And which is better by any other standard you might propose? (See Criteria in evaluating single-member voting systems.)

It seems to me that Range Voting is the easiest sell politically in the US. You could explain to people that it’s just like the way Olympic judges vote, the ballots should be easier to design, and you could get results much faster than IRV.

Approval voting (since it’s basically simplified range voting) has these benefits, but I think it would seem counterintuitive to people at first, possibly making it difficult to get people to go for.

So, I’d pick Range Voting. I’m ok with IRV, but if we’re going to do that, then I’d prefer Condorcet voting as it removes many of the problems with IRV. But I think either one would be difficult to gain political support for and would make most elections fairly difficult to handle.

In addition to the mathematical properties of voting algorithms, we have to consider how easy it is to implement them in a way that’s secure, but doesn’t make the ballot too confusing for the average voter. The best scheme I know of (Ron Rivest’s Scantegrity II[sup]1[/sup]) wouldn’t be too difficult to adapt to range voting, but it’s incompatible with any rank-based scheme such as IRV or Condorcet. That’s a huge point in the favor of range voting.

I should also mention Arrow’s impossibility theorem, which essentially states that no voting system can be perfect. There will always be some flaw in any system, so it’s necessary to think carefully about which flaws are acceptable and which are not. Non-monotonicity is unacceptable in my view, so IRV is right out.

I’d like to hear a response to the claim that IRV doesn’t support multiple parties. Given that most of the IRV advocates out there say they want a multi-party system, you’d assume they’d be aware of this issue.

[sup]1[/sup]: As an interesting aside, one of the most essential parts of modern e-commerce is the RSA algorithm. Ron Rivest is the R in RSA, so his credentials on security are pretty impressive.

OK, here’s the thing:

For multi-member districts, I think approval voting is seriously inferior to single-vote systems. It either amplifies a plurality to majority or wipes it out through, “Anyone but the Nazis,” voting.

But for single-seat elections, I think it’s better than single-vote systems. And maybe this Range Voting idea, which is a more complex version of approval voting, is even finer. I don’t know.

multi-seat: single-vote
single-seat: multi-vote

Here’s an argument for IRV, from 2002, on the occasion of San Francisco voters approving a referendum to adopt IRV for city elections. (Does anybody know what actual effect that has had on SF politics and government?)

My primary criticism of approval voting is that it’s not clear where to set the threshold between “approve” and “disapprove”, since it can’t be the same in all elections.

As an example, suppose that A, B, and C are all running for city dogcatcher. I think they’d all do an OK job, but that A would be even better than B and C (whom I consider equally good). Now, I could choose to vote “approve” on all of them, since I think they’d all do OK, but that would just be throwing my vote away: An across-the-board approve vote can have no effect whatsoever on the outcome. Since I think that A is a little better than B or C, my best strategic vote is to approve A, but disapprove B and C.

Now, though, suppose that instead my ballot consists of A, B, C, D, E, and F. The first three are as described above, but I think that D or E would be terrible, and that F fellow is the worst of the bunch. It seems pretty clear, in this case, that I ought to vote “Approve” for A, B, and C, and “Disapprove” of D, E, and F. So, suddenly, without any change in B or C, I’ve gone from disapproving of them to approving of them-- Why?

Or suppose instead that there isn’t a clear divide between the acceptable and unacceptable candidates: Let’s say that I think that T is a little better than U, U is a little better than V, V is a little better than W, W is a little better than X, X is a little better than Y, and Y is a little better than Z. Clearly, in this case, I’m going to approve of T and disapprove of Z, but ought I to draw the line in between?

A similar issue shows up, incidentally, in range voting, though to a lesser degree, in that the rating I give to a candidate is going to depend on what other candidates are in the race. If I’m rating them on a scale of 1 to 100, for instance, it is always in my best interest to rate the candidate I like best as a 100 and the one I like least as a 1, regardless of how I feel about the candidates in absolute terms.

I have a slightly different take to Wiki.

Any voting system must be usable, easy, and fast at the voting booth. This rules out range voting and any system where the voter has to rank the candidates (e.g. IRV). Do you really want someone taking half an hour or more in the voting booth? Further, the more complex the form, the more likely it is to contain an error or be spoiled. Or require examination afterwards.

Any system must also be able to easily deal with recounts. Suppose you’re 10 rounds into a tightly-fought IRV election and you discover a bunch of votes that have been miscounted and favour a candidate who was eliminated 5 rounds ago but should not have been?

Just as ‘justice must be seen to be done’, so voting must be easily understandable. Not just because of corruption, but because of the suspicion of corruption. People tend to be suspicious of what they don’t understand.

Both First Past The Post and Approval Voting meet all these clearly and unambiguously. Further, Approval Voting extends itself well to multi-member constituencies. And if you get a tie, there’s always the coin toss.

I don’t see how range voting is unduly complex. I also don’t see why you think people wouldn’t understand it, when they are exposed to it at every Olympics.

Yeah, but with Approval Voting, a disciplined 40% plurality in the electorate can gain an overwhelming majority of seats. A disciplined 51% majority can gain all seats. Is that a feature, or a bug?

Of the ones that you have put out for us, I would chose instant run-off.

And the people giving the ranged score at the Olympics are experts. And you’l always get someone who accidentally inverts their score and has to redo it, creating even more delay.

A disciplined 51% majority can gain 100% of the seats in a FPTP election too.

What do you mean inverts their scores? Range voting isn’t a ranking system.

Simple: on a range of 1 to 10, is 1 good or bad? Some people will get it wrong.

I guess, but in US culture we tend to pick 10 as the best, so I would think that this sort of confusion should be rare and could be handled through educational programs.

Wait, I thought the chant goes USA! USA! We’re number one! Are you saying it should go ‘we’re number 192’?

Stop being pedantic. You know what I mean. On a fixed scale of 1 to 10, ten is usually the best.

Yes, and in a field of 10 candidates, #1 is best. Hence the problem.