# Rankled choiceNovember 3, 2010 7:56 PM   Subscribe

I thought instant runoff/ranked choice voting was cool. But now I'm not sure...

Am I missing something? I just participated in my first ranked choice election. In my city, there were 10 candidates for mayor. The way I understand it is this:

If anyone gets 50% of the 1st choice vote, they win.
If no one gets 50%, then the person who got the fewest 1st choice votes has their name taken out of the hat, and the people who voted for her have their second choice votes counted instead.
This process repeats until someone gets 50%.

But what this means is that the people who vote for the most wingnut or unpopular candidate have a meaningful runnoff vote, but the people who voted for say, the third most popular candidate first don't necessarily have their second choice counted, because the 50% point may be reached before their second choice is even looked at!

My question is, am I understanding the system correctly? Is this a criticism others have raised or is it somehow addressed within the system? Bonus question: Is there another voting system that would be more "fair"?
posted by serazin to Law & Government (30 answers total) 3 users marked this as a favorite

Bonus question: No, there's no good way to set up a perfectly "fair" voting system for more than two candidates (and even for two it's difficult, because we assume a binary of opinions when it is really a spectrum). You might be interested in Arrow's Theorem.
posted by muddgirl at 8:08 PM on November 3, 2010 [3 favorites]

But to answer less simplistically: To set up a fair system, you first have to agree on a definition of what's fair.
posted by muddgirl at 8:10 PM on November 3, 2010

Right. So you vote for someone who has a chance to get elected and your vote is counted as it was cast. If you vote for a fringe candidate as a protest vote, your vote gets shifted elsewhere after the wingnut you picked first gets knocked out of the running. Either way, your vote is eventually cast for the candidate with a serious chance of winning.
posted by foodgeek at 8:11 PM on November 3, 2010 [1 favorite]

But I thought part of the point of ranked choice was you get to vote for your real first choice first, without the whole "spoiler" issue.
posted by serazin at 8:14 PM on November 3, 2010

Preferential voting (as we call it in Australia) is explained here. Or of course there's Wikipedia on IRV.

I don't think your concern is a criticism. The majority of votes end up with the least unpopular candidate. If you vote for the third most popular candidate, the fact that some other candidate is already approved by 50% +1 of the eligible voters is not a bad thing (or a good thing, it just is a thing). The winning candidate must have already had substantial support, even if indirectly.
posted by wilful at 8:15 PM on November 3, 2010

Say candidate A is most popular and candidate B is second most popular and candidate C is third most popular.

People who voted for candidate C, the third most popular candidate, mostly chose candidate B as their second choice, but people who voted for candidates D & E mostly voted for candidate A as their second choice.

In the preferential/ranked choice/instant runoff system, the people who voted for D&E first might have their second choices (for A) counted. But the people who voted for C might not. Perhaps if you threw all the 2nd choice votes of people who voted first for C-E, you'd find that B was the winner. But in this system all the votes are not thrown in the pot - only the 2nd choices of those who voted for the least popular candidates. So even if the first choice had "substantial support", did they really have the most support?
posted by serazin at 8:20 PM on November 3, 2010

the third most popular candidate first don't necessarily have their second choice counted, because the 50% point may be reached before their second choice is even looked at!
Exactly. Once you count to 50%+1 votes, by definition all of the other candidates had insufficient support.

Say A receives 49% of the vote, B 30% and C 19%, and D 2%. D is excluded first, and if D's preferences all flow to A, A gets a majority, and the counting stops---but if it continued, there's no way that the outcome would be any different adding B and C. You still don't get to 50%+1.
posted by Fiasco da Gama at 8:46 PM on November 3, 2010 [1 favorite]

If it makes you feel any better, by the way, I count preferential ballots in every election in my country the Party of which I'm a member, and it does rankle to see the preferences of voters for very stupid, very sectarian and/or very racist parties matter so much. Excluding minority voices is the one benefit of first past the post.
posted by Fiasco da Gama at 8:51 PM on November 3, 2010

Serazin, are you maybe thinking that a "score" would be best? Like, your top choice gets a multiplier of 10, your second gets a multiplier of 9, etc., and then everyone's votes are multiplied out and the candidate with the top score wins. That's the only thing I can think of that would be "more fair" under what seem to be your criteria.

There are pretty much always going to be spoilers. In your scenario in your most recent comment, candidate C is the spoiler because those voters don't get to have their second votes count. That's fine, because if they felt it was important for candidate B to be the winner, that's who their top pick should have been. Doubleplus that if you think about the metapolitical thinking that goes on about elections that make people even think about spoiler candidates.
posted by Night_owl at 8:52 PM on November 3, 2010

No, hold on. In preferential ballots there can't be spoiler candidates in the same way that there are in FPP ballots. A spoiler runs to hinder the chances of a more popular candidate ie. the frequent accusation about Ralph Nader in the American presidential election in 2000. Distribute preferences and you remove the effect.
posted by Fiasco da Gama at 8:57 PM on November 3, 2010

In the scenario you described, assuming I understood it correctly...

If the candidates in order of first preference votes were A, B, C, D & E..

B could only win in the second round if B's first preference votes plus E's second preference votes make up more than 50% of the votes cast. This is mathematically impossible.

Why?

By definition A had more votes than B, and both C and D had more than E. So B + E cannot be more than A + C + D, and therefore can't be more than 50%.

Now A really could win in the second round with the help of E's votes. But, by a similar logic to above, that can happen *only* if A's lead over B was so big that even if all of C and D's second preferences went to B, A would still have won. (Remember, A's over 50% with the help of E, that means all the rest of the candidates haven't got more than 50% first pref voters left between them.)

So if E's very small number of wingnut votes appear to "swing the result", it's only because whoever won was so close to the winning post on their own that a few extra votes are enough to guarantee they can't be overtaken no matter how all the other uncounted second prefs were allocated.

Stopping counting just saves time after the result has become inevitable.

That system's not perfect, but it's one big advantage is that a person must be supported by a majority of the voters in order to get elected.
posted by philipy at 11:10 PM on November 3, 2010

The last explanation was probably way more complicated than necessary.

Think of it like this:

The person that won had more than 50% of the votes, after adding up their own first pref voters and the second pref votes from the last placed wingnut.

That leaves *less* than 50% of the votes left distributed among all the remaining candidates. So whatever all those people's second preferences were, those could never overtake the winner even if they had all voted the same way.
posted by philipy at 11:28 PM on November 3, 2010 [1 favorite]

there are reasonable cases where preferential voting as implemented in Australia (aka IRV) leads to results that are arguably incorrect... that's why other (more complicated) election decision methods like Condorcet exist... so to quote myself from another board, many years ago, in another discussion about IRV and the US electoral system...
how's this for a thought experiment? (please forgive the scene-setting historical inaccuracy)

It's the 1980 presidential election in the Australian Republic (so that we can ignore the senate and house of representatives). The Red ALP keeps on moving further leftwards, and the Tory Liberals are the party of old money and the bosses. Challenging the major parties are the new centrist Democrats, "keeping the bastards honest".

The Democrat candidate gets 25% of the primary vote, with the remainder split evenly between the old major parties. Second preference for Democrat voters goes 50/50 to the ALP and the Liberals. Second preference for ALP and Liberal voters goes 80% to the Democrats and 20% to the other major party.

Under our current preferential voting system the Democrat candidate is the first to go, leaving a close run race between Comrade Hayden and Old Tory Fraser.

However if you asked the electorate "who would you prefer, the Democrats or the Liberals", the Democrats would win 55% to 45%, and likewise with "who would you prefer, the Democrats or the ALP"...

Condorcet vote counting reflects this, giving victory to President Chipp...

The question, then, is which of these outcomes most accurately reflects the Will Of The People?

(overall I reckon in the real world IRV is plenty good enough, but the math geek in me likes the elegance of Condorcet)
posted by russm at 3:00 AM on November 4, 2010

Just searched this thread for "condorcet", and I see Russm has it covered.

The quick answer is that IRV is better than FPP, but possibly not better than condorcet voting - with regard to statistics representing the Will Of The People. Of course, you have to be able to explain why to The People, and I doubt that would work in the US.

Basically, there's no true right answer, except that FPP is stupid unless there are always only going to be two candidates.

So, my ballot goes:

1) IRV
2) Condorcet
3) anything else
4) FPP.
posted by pompomtom at 5:17 AM on November 4, 2010

But I thought part of the point of ranked choice was you get to vote for your real first choice first, without the whole "spoiler" issue.

Per Arrow's Theorem, there is no voting system (not just no known voting system, no voting system as in it's been proved impossible) which completely eliminates the issue of "strategic voting" when a ballot includes three or more candidates, that is, makes it impossible that it would sometimes make sense for a voter to rank a less preferred candidate above a more preferred candidate, in order to elect the less preferred candidate over the least preferred candidate. There are only systems which make the possibility of strategic voting being a rational choice somewhat less likely, in practice.

This only needs a three-person race to demonstrate; examples with four or more work too but are overly complicated for illustrative purposes.

Suppose you have three candidates, A, B, and C. A and B are the two "major party" candidates, and C is a "fringe" candidate. Let's also, as a means of illustration, say that the three candidates lie roughly along a one-dimensional political spectrum, such that all voters who rank A first rank B second, all those who rank C first also rank B second, and those who rank B first are split 50-50 between ranking A or C second.

As long as C remains a fringe candidate and garners less support than B, the system works as intended. If 45% vote A first, 40% vote B first, and 15% vote C first, C's votes are transferred to B and B wins. All well and good.

When you run into trouble is when C becomes so popular that he garners more support than B. If 45% vote A first, 20% vote B first, and 35% vote C first, then B's votes are split between A and C, and A wins. If the C voters had voted "strategically" and voted for B as their first choice, B would have won, which C's supporters would have preferred over the actual outcome.

I'm not saying that plurality voting is better than IRV, just that no system can ever completely eliminate the possibility that strategic voting will sometimes be the rational choice in an election among three or more candidates. And as a practical matter, it's probably an issue much less frequently in IRV than it is in plurality voting. But it's impossible to eliminate entirely.
posted by DevilsAdvocate at 5:39 AM on November 4, 2010 [2 favorites]

Per Arrow's Theorem, there is no voting system (not just no known voting system, no voting system as in it's been proved impossible) which completely eliminates the issue of "strategic voting" when a ballot includes three or more candidates

That's actually the Gibbard-Satterthwaite theorem.

The Arrow theorem actually goes beyond voting; there is no method of generating collective preference orderings, whether by voting or some other way, that is not demonstrably terrible.
posted by ROU_Xenophobe at 5:54 AM on November 4, 2010 [1 favorite]

pompomtom: So, my ballot goes:

let me guess... you actually prefer Condorcet, but you're tactical voting for IRV to keep FPP out?

DevilsAdvocate: Per Arrow's Theorem, there is no voting system (not just no known voting system, no voting system as in it's been proved impossible) which completely eliminates the issue of "strategic voting" when a ballot includes three or more candidates

assuming you accept Arrow's criteria... throw out the universality criterion and you can run a random ballot, where there is absolutely no incentive for strategic voting...
posted by russm at 5:55 AM on November 4, 2010 [1 favorite]

Thanks, ROU_X and russm, I stand corrected on both points.
posted by DevilsAdvocate at 6:36 AM on November 4, 2010

Range Voting and Approval Voting are the far superior choices. I wrote an article briefly describing why. They both bypass the pitfalls of ranked voting. Range is slightly more complex (give each candidate a number from 0-99) but is almost perfect in choosing the best candidate. Approval is extremely simple (vote for as many as you wish) and is nearly as good.

There is a quantity called "Bayesian Regret" that measures how far the actual winner is from the theoretical best candidate. In a series of simulations, it has been shown that range is not only far superior to every other method, but the gain from switching from the American sysem (plurality) to range voting is larger than the gain from switching from "random winner" to plurality!
posted by Earl the Polliwog at 1:06 PM on November 4, 2010 [1 favorite]

let me guess... you actually prefer Condorcet, but you're tactical voting for IRV to keep FPP out?

Heh. Cute.

Nah, I'm just stuck in my ways (lights pipe, rocks on chair), and am used to voting against people rather than having to learn how to vote for people.
posted by pompomtom at 2:27 PM on November 4, 2010

The approval method seems pretty ideal: it's the easiest to understand and would allow you to vote your conscience and strategically at the same time. Hmm.
posted by serazin at 7:43 PM on November 4, 2010

I'm still confused about the math though with RCV.

Folks have been saying that you may go over 50% for candidate A with the second choice votes before you work your way up to the 3rd choice candidate. But I'm confused because the size of the pool keeps changing as you add more second-choice votes. So maybe you have 50% when you get to candidate D, but if you were to move on to candidate C second choice votes, is it not possible that that percent (of a larger overall pool) would shift to give candidate A fewer than 50% of the vote?
posted by serazin at 7:46 PM on November 4, 2010

Night Owl, my city currently has (well, might have) more or less the situation you describe. I'm in Oakland. Our 3rd most popular candidate (of the 1st choice votes), Rebecca Kaplan, seems to be a spoiler for Jean Quan, the second choice and most politically similar to Kaplan, if the 4th choice candidate, Joe Tuman's votes end up mostly going to the first place candidate, Don Perata, as I suspect they might. Unless I'm misunderstanding the math.

But it's probably irrelevant because likely most second choice votes overall will go to the first place candidate, which, I'm reading, is what generally occurs in RCV here.

We'll find out tomorrow when they release the results.
posted by serazin at 7:50 PM on November 4, 2010

DevilsAdvocate - though I suspect that Random Ballot and the other hypothetical methods are the kind of thing that ROU_Xenephobe was talking about when he said "demonstrably terrible"...
posted by russm at 4:17 AM on November 5, 2010

No, "demonstrably terrible" just means "violates one of Arrow's conditions."

I'm not sure that a random ballot violates universal admissibility; the preferences of almost everyone are being discounted, but not on the basis of the content of those preferences. There are lots of proofs of Arrow out there, but in the ones I'm most familiar with the whole point of the universality criterion is to prevent the disallowing of the peculiar sets of preferences that allow the contagion of dictatorship from preferences over one pair of alternatives to preferences over all possible pairs of alternatives.

It sort of obviously violates nondictatorship, since the polity's preference ordering is then the preference ordering of the selected individual.

And I think of all the Arrow conditions, you'd have the hardest time getting people to give up nondictatorship.
posted by ROU_Xenophobe at 2:21 PM on November 5, 2010

my (layman's) understanding is that universality includes determinism - the result must be universal across the domain of elections with a particular set of ballots cast. random ballot obviously fails this. also, wrt dictatorship, doesn't that also apply across the set of all elections? (and hence be fulfilled by random ballot since there's no single voter whose preference is *always* reflected by the output ranking).
posted by russm at 2:55 PM on November 5, 2010

Oh, and range voting is not Condorcet but I consider it a strength in this case, a testament to its ability to incorporate peoples' opinions that are at varying levels of like and dislike.
posted by Earl the Polliwog at 7:09 PM on November 5, 2010

I just came in to point out (to others, not you, serazin, as I'm guessing you're tracking it anyway) that the specific case that prompted serazin's question is having unexpected results. Initially in the Oakland mayor's race, Perata had 35% of 1st-place votes, Quan 24%, Kaplan 21%, Tuman 12%; after Tuman and those who got less than him were eliminated, Perata was still in first, then Quan, then Kaplan; but after Kaplan was eliminated, Quan got about 75% of Kaplan's votes, pushing her (unofficially) to 51% of the vote, ahead of Perata (see here and here).

Apparently the Anybody but Perata movement was successful.

Again, these aren't final results, as a number of ballots still need to be counted. But the trend is interesting.
posted by mistersix at 6:18 PM on November 6, 2010

Yeah, the worries I had when I posted this have certainly been answered by these preliminary results. But I really learned from this thread! Thanks everyone for helping me understand voting systems!
posted by serazin at 8:16 PM on November 6, 2010

In case anyone's interested, I thought this was an interesting piece about how ranked choice went down here last week.
posted by serazin at 12:18 PM on November 8, 2010

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