For the rest of us, can you produce a real life instance where an STV election in NZ has produced an outcome you regard as unfair because of the counting system?
In New Zealand? Probably not. As izogi pointed out, the vote data just isn't available. A little effort was made to have more vote data revealed for the first flag referendum, but the Electoral Commission believed it would have been illegal for them to reveal more data. (See http://offsettingbehaviour.blogspot.com/2015/10/flag-cycles.html .)
That's not to say that there aren't perverse STV results in New Zealand; just that it's difficult to identify them, and even if you have your suspicions about a particular result, it would still be very difficult to prove its perverseness beyond doubt, without more data.
However, Burlington in Vermont briefly used to elect its mayors using what they called Instant-runoff voting (IRV, which is basically single-winner STV, like we use for electing Wellington's mayor, for example); they released more complete vote data, so that, in 2009, although the result was "fair" in the sense that the rules announced before the election were, presumably, followed correctly, it was a somewhat perverse result in this way:
The three main candidates were Bob Kiss, Andy Montroll, and Kurt Wright. Of those three, Andy Montroll was the first to be eliminated by IRV; then Bob Kiss beat Kurt Wright and won the election. But according to the preferences they revealed, 4067 voters would have been happier if Andy Montroll had won, compared to only 3477 who would have been less happy with that result; what's more, Andy Montroll would have won a similar preference comparison against Kurt Wright, and against all of the more minor candidates.
Ironically, according to Wikipedia, more of a fuss about this result was made by Kurt Wright's supporters than by Andy Montroll's; apparently they felt that with 33% of first preferences (more than any other candidate) their candidate had been robbed of his legitimate victory, or something, even though, according to the preferences the voters expressed, he would have lost a two-way election against either of his main rivals.
So instead of changing to a system that would have avoided the perverse result, Burlington reverted to a two-round sort of non-instant-runoff system that would have (if voters had expressed the same preferences) delivered exactly the same result, had it been used in 2009, only it would have taken longer, being a two-round system. (However, voter incentives may have been altered if the two-round system had been used.)
the Aussies have completely ruined STV ... The parties also hand out how-to-vote cards which, I understand, most people follow. So, it would not have been too difficult for polling to reveal that a monotonicity violation was in the offing. Such violation could not be revealed in respect of, say, a Wellington mayoral election.
Graeme, is it illegal for candidates to send out how-to-vote cards in New Zealand, or is it just not common practice here yet?
In any case, if the claim is that failure of the monotonicity criterion is acceptable because it would not in practice affect voter incentives in New Zealand (despite Australia's experiences), then any rejection of a system on the basis that it lacks the later-no-harm criterion should be accompanied by evidence that it would in practice affect voter incentives in New Zealand.
there is a trade-off between “refinements” in STV (improved treatment of surpluses, as with NZ STV; improved process of exclusion) and the cost in manageability – for example, very complicated election rules, computer programming, and reporting of results (…).
In the single-winner case, I reckon the Schulze method would actually have simpler rules and simpler computer implementations than single-winner STV. Heck, the Wikipedia article on the Schulze method includes 17 lines of pseudocode implementing what it claims is "The only difficult step".
As for reporting of results, they could publish a table showing how many voters prefer each candidate X over each other candidate Y. Each cell of the table could be colour-coded to indicate whether more people prefer X over Y or vice versa. Then, whenever there's a Condorcet winner, they'll stand out as a complete row of wins, and everyone will know that the Schulze method will elect that person.
Even when there isn't a Condorcet winner, I reckon you could follow along at home, using only a pencil, paper, and the numbers in the table, to confirm that the announced winner is, in fact, correct according to the Schulze method. In comparison, in order to follow along at home with single-winner STV, you'd need to know how many people voted in each different way. With 39 candidates, there will be so many different ways people will have voted (many, many of them with only one voter casting that precise vote), that the amount of data would be overwhelming. Even with all that data, I don't think I could complete the calculations by hand before the next election, 3 years later.
I emphasise that I prefer later-no-harm because it gives ordinary voters the confidence to rank the candidates in their true order of preference.
No matter how many times you say this, it still won't be true — unless, perhaps, by "ordinary voters" you mean people who have heard and believed mistaken analyses of their electoral system.
If they thought their later preferences might harm their earlier preferences, they wouldn’t give them, and we’d be back to FPP again.
Failure of later-no-harm means only that one of your highest-ranked candidates might do better if you refrain from listing remaining candidates; it is by no means automatic, just as the failure of monotonicity doesn't automatically manifest itself in every STV election. But your highest-ranked candidates might also do worse if you refrain from listing remaining candidates. So in practice, why would a well-informed voter want to refrain from listing their remaining candidates?
In the absence of any examples in which the failure of later-no-harm might plausibly affect voter incentives, insisting on later-no-harm at the expense of monotonicity is like straining out the theoretical possibility of a gnat, while swallowing a known camel: it's one thing to wonder whether one of your favourite candidates might do better if you refrain from listing your less-favoured candidates; it's quite another thing to know in advance that there is a significant possibility that your absolute favourite candidate might do better if you and some like-minded voters give your first preference to another candidate, which is exactly what happened in the Division of Melbourne in 2010.
As I said (implied) to Graeme, general society would need to be far more sophisticated than it currently is, for more intricate versions of STV to be imposed on them. At the moment, you find that greater sophistication / education in private societies, which is why I imagine Shultz-STV is being used in an increasing number of them.
You seem to be suggesting now that the Schulze method might actually be an improvement on STV, but that general society is unlikely to be sufficiently well informed to accept it any time soon. You might be right; it's a much more defensible position than "it’s hard to imagine an informed electorate giving up later-no-harm", given that an informed electorate would probably baulk at the very real examples of non-monotonicity that come with later-no-harm.
But then maybe the Schulze method is more generally acceptable than you might think. It's apparently already used by what was, for a year, consistently the most popular party in Iceland according to opinion polls (and is still neck-and-neck for the lead in more recent opinion polls).
I think you want STV with equality of preference. It can be done. David Hill’s STV program provides for it, but he only allows a maximum of 10 candidates having the same EQP. If you provide for much more than that, certainly 35 or more candidates able to have the same preference number, you get a “combinatorial explosion” that computers, even today, might not be able to cope with.
In contrast, the Schulze method copes perfectly well with giving equal preference to multiple candidates.
I will give you the courtesy of one more, more calmly expressed, response.
Thank you; I have enjoyed thinking about voting systems again, thanks to this conversation.
I have been arguing from the point of view of ordinary people voting in public elections.
Your view of what a vote is is quite a reasonable mental model, given that we're using FPP, STV, and even MMP. But given the choice, would "ordinary people" prefer that votes belong to candidates, or that votes belong to voters? Would they prefer a system that tries to satisfy all of the voters' preferences, or only some of their preferences? These aren't merely rhetorical questions; I'm aware that many people often think differently from me. Are there any ordinary people who've made it this far through the discussion, and want to comment?
I also now realise you were primarily talking about M-PV, whereas I was talking primarily about multi-seat STV.
In that case, your claim that "There is no incentive for a voter to vote in any way other than according to his or her actual preference" is false in many, many more situations, and this is trivial for individual voters to exploit. It's called free-riding . If your favourite candidate is polling very well, then you can safely put them at the bottom of your preference list, knowing that other people's votes will elect them. Instead of your favourite candidate, put at the top of your preference list your favourite among the candidates you think might not win. Then your whole vote goes to trying to help them win, instead of only the fraction of your vote that would have been passed down from your absolute favourite candidate, if you'd put them at the top of your preference list.
how about at least explaining to us why you are “still not persuaded that later-no-harm is more important than having majority support for the winner, wherever possible.” Explain to us why it is worthwhile to give up later-no-harm so that the majority winner – let’s call it the Condorcet winner – is elected 100% of the time, instead of 99.9% of the time.
Well, I thought the whole point of a democracy was to have majority support for the winner, wherever possible. Insisting on later-no-harm, so that reporting truthful lower preferences can't harm the chances of higher preferences, but letting monotonicity slide, so that reporting a truthful highest preference can harm the chances of that most-preferred candidate — that seems to me like straining out a gnat and swallowing a camel.
Then, while you’re at it, explain to us what you mean by this elitist clap-trap, “And in multiple-winner STV elections, later-no-harm seems likely to harm voters’ preferences over the sets of possible winners.”
I think, when I wrote that, I had in mind the example where a voter's preferences are A, then B, then C, all the way to Z. If two winners are to be elected from the 26 candidates, STV assumes that that voter would prefer A and Z to win, rather than B and C; I think this is unlikely to reflect the voter's actual preferences. But I'd forgotten about STV failing the monotonicity criterion; that would have been a much stronger critique to insert at that point.
But, like nonmonotonicity, the no-show paradox, etc., G-S can only be demonstrated with artificial examples. STV’s so-called defects are not properties, if that’s the right word, that ordinary voters in large public elections can in any way take advantage of.
I’m obviously biased, but, although they’re all very interesting, they’re ultimately meaningless when it comes to public elections.
STV does have the following advantages ...
(C) There is no incentive for a voter to vote in any way other than according to his or her actual preference.
These claims are all false, as discussed earlier. (Well, I'm in no position to either confirm or deny the claim that you're biased; I don't know what you might have to gain by promoting STV.)
If your real concern is what will happen in practice, rather than the theoretical niceties of the various systems, then why are you so concerned that a system should satisfy the theoretical later-no-harm criterion? I've mentioned examples where non-monotonicity came into play in real-world elections, including one in which the possibility was real enough before the election that people were talking about tactically down-voting one candidate in order to hand them the victory. Can you give an example in which the failure of later-no-harm would have come into play in a real-world election, and in which the voters would have had sufficient information before the election to reasonably come to the conclusion that their best strategy did not involve voting according to their true preferences? You can analyze a real-world preferential election that was conducted using another preferential voting system, if you like, or search the electoral archives of any of the numerous organizations that use the Schulze method, or construct your own scenario that you think might plausibly come up in a real-world election. Good luck; I'll be genuinely interested to see your results.
I think I'm starting to understand at least part of the reason for our difference of opinion. Please correct me if I'm wrong, but I think you're thinking of a "vote" as something that a voter gives to a particular candidate, as in FPP. But unlike FPP, you're allowing the vote to be re-allocated to another candidate if the first one doesn't need it any more (because they've either been elected or eliminated). With this understanding of what a vote is, you quite reasonably want the candidate or candidates who end up with the most votes to win; STV is a reasonable way of achieving this.
But I'm thinking of a "vote" as the voter's entire list of preferences. It doesn't belong to any of the candidates; it belongs to the voter. With this understanding of what a vote is, I want the winner of the election to be the one that best satisfies all of the preferences of the voters. Arrow's theorem shows that it isn't always possible to do this in an unambiguous way, but I want a system that, wherever possible, chooses a winner who, over every other candidate, has the support of a majority of voters. STV doesn't do that. Other systems do.
People like you (e.g. Doron and Kronick, et al) argue your case, using carefully constructed artificial voting patterns.
I was careful to use your artificially constructed voting pattern to argue against your case.
It astonishes me that you continue to pick away at a perceived fault of STV (which is used in public elections in many places around the world), which can only be remedied by accepting another fault, but you don’t argue for *your* preferred system (which, whatever it might be, we know is not used in public elections anywhere), explaining why it is better than STV. How about you do so.
For single-winner elections (and multiple-winner elections if you don't care about proportionality), I prefer the Schulze method. It always selects the winner from a minimal non-empty set of candidates none of whom are beaten by any candidates outside the set. This is a stronger requirement than the Condorcet criterion, so if there is a candidate who has, over every other candidate, majority support, then that candidate will be elected. STV does not have this property, which is the main reason that the Schulze method is, according to my preferences, better than STV. Other people may reasonably disagree, if they don't care about the winner having majority support (wherever possible), but they have other (peculiar, to my mind) preferences about what kinds of tactical voting should be ruled out. The Schulze method also satisfies the monotonicity criterion, so it rules out the kind of tactical voting in which a voter's most-preferred candidate can be helped by that voter not giving their first preference to that candidate; STV does not have this property, in theory or in practice, as I mentioned earlier.
For multiple-winner elections in which proportionality is desired, I'm less settled about my preferences, and I'm aware that better systems may be developed over time. For now, I'm somewhat attracted by Schulze STV, but the computational complexity of its counting process puts me off. (Incidentally, the computational complexity of ordinary STV is another minor point against it, from my point of view, but it may well be better than Schulze STV on that score.)
I may not be as opposed to STV as you may think I am. I just think that, at least in the single-winner case, we could do better.
Later-no-harm insists that a particular kind of tactical voting is unnecessary and impossible.
Does it. Why not explain how?
I worded that badly. It would have been better for me to say "Later-no-harm insists that a particular kind of tactical voting should be unnecessary and impossible". The kind of tactical voting later-no-harm insists on ruling out is the kind where you can help (or avoid harming) one candidate by refraining from expressing your true preferences among less-preferred candidates. It ignores the kind of tactical voting where you have to give a favoured candidate a lower ranking in order to give them a better chance of winning. Why is ruling out the first kind of tactical voting more important than ruling out the second?
And is it worth it if it means that a voter’s preference between their two favourite candidates is always treated as more important than their preference for their second-favourite candidate over their least-favourite candidate?
Yes it is. Why would it not be?
Because if there are dozens of candidates, then it seems very likely that many voters will have a relatively weak preference between their two favourite candidates, compared to their preference that their least-favourite candidate doesn't beat their second-favourite candidate. If the system assumes that the strengths of voters' preferences are significantly different from the actual strengths of those preferences, then those are ideal conditions for encouraging voters to cast tactical votes, in order to better achieve their actual preferences.
That is exactly what STV does. As there is no incentive for voters not to vote their true preferences, ...
That is, at least in voting theory, not true. And since you've already mentioned non-monotonicity, I assume you already know that. So you must mean that in practice there will never be such an incentive. But that isn't true, either. Wikipedia's article on the monotonicity criterion has a section on real-life monotonicity violations that mentions two elections in Australia: one in which it was shown after the election that monotonicity was violated (in that if somewhere between 31 and 321 Liberal supporters had switched their votes to Labor, then the Liberal candidate would have won), and one in which it was identified before the election that monotonicity might be violated, and that Labor supporters might be better off if a few of them put the Liberal candidate first on their preference list instead.
What proof do have that STV “certainly doesn’t have that property?”
I already explained how, in your own example, supporters of B, C, and D could be better off if they said their first preference was E, instead of voting according to their true preferences.
If more than three-quarters of voters preferred E to win, then why didn’t they vote for E.
Perhaps I should have been clearer. I meant that "more than three quarters of all the voters would have preferred E to win rather than A ". I didn't mean that more than three quarters of the voters had E's victory as their absolute highest preference.
I put up that voting pattern to show that, even though E is the Condorcet candidate, s/he cannot realistically, in a public election, be regarded as the correct winner.
Earlier, you said:
E is certainly the Condorcet candidate and, in spite of a poor showing on first preferences, really a very strong candidate in that if any one of A, B, C, or D were to withdraw before the count (for a single seat), E would win without question.
Why does the choice between A and E of the "correct winner" depend on whether or not D chooses to stand as a candidate?
Tactical voting is possible in all fair electoral systems with more than two candidates.
This is true, but it only makes the later-no-harm criterion seem even more peculiar. Later-no-harm insists that a particular kind of tactical voting is unnecessary and impossible. But why is it more important to rule out that kind of tactical voting, while ignoring all the other possible kinds? And is it worth it if it means that a voter's preference between their two favourite candidates is always treated as more important than their preference for their second-favourite candidate over their least-favourite candidate? Why not insist instead that the system should ensure that a voter's best strategy (or at least one of their best-equal strategies) always involves ranking their favourite candidate first? STV certainly doesn't have that property, and I wouldn't be surprised if it was incompatible with later-no-harm.
consider the following highly artificial example where there are five candidates and votes—
101 AE.. 100 BE.. 99 CE.. 98 DE.. 10 E..
I really don't think this example helps your case. Under STV, one of A, B, C, or D will win (depending on whether, and which, subsequent preferences are expressed). Without much loss of generality, suppose A is the winner. Do you really want to insist that this would be the correct result, even though more than three quarters of all the voters would have preferred E to win? Would B's supporters really be saying to themselves "Oh, well; at least my preference for E over A didn't harm B's chances of winning"? If pre-election polls indicated that this was likely to happen, would the supporters of B, C, and D really have had "the confidence to rank-order the candidates in their true and genuine order of preference", or would they have decided to tactically give their first preferences to E, in order to deny A the unpopular victory over E?
it’s quite possible that tiny little bits of your single vote will get distributed all the way down your preference list
Only if the eventual first runner-up is your lowest preference (or you didn't give them a ranking at all). Because the eventual first runner-up is neither elected nor excluded, preferences for them are never passed on to other candidates. Once, back when I was more enthusiastic about casting as much of a vote as possible, I ranked all two-dozen or so candidates in a health board election. My first preference was, in the end, the first runner-up, so all my work of deciding how to rank the remaining candidates was wasted. (And then, from memory, she was appointed to join the board anyway.)
Slightly too late to edit my post:
I've just noticed that, according to Wikipedia, The Condorcet criterion is incompatible with later-no-harm. If that's right, then I guess we can't both be satisfied, but I'm still not persuaded that later-no-harm is more important than having majority support for the winner, wherever possible. And in multiple-winner STV elections, later-no-harm seems likely to harm voters' preferences over the sets of possible winners.
I quite like STV because it meets the later no harm criterion (where you cannot harm the election prospects of a candidate by ranking additional candidates lower than them).
As opposed to ranking additional candidates above them? I'm being a bit cheeky there; I assume that what you meant is that your preference among your less-preferred candidates (including whether or not you even have and express such a preference) doesn't affect the chances of your more-preferred candidates. But STV places unnecessarily heavy weight on your higher preferences.
Suppose your first preference is A, your second is B, then C, etc., all the way to Z. STV seems to presume that you care more about A beating B than you care about B beating Z, which is highly dubious if it's a multiple-winner election, and you want both A and B to win, and you really don't want Z to win, even if it means you have to settle for B and C instead of having A as one of the winners.
(If we're still talking only about single-winner elections, then I'm pretty sure that any situation in which a Condorcet-satisfying system fails to satisfy the later-no-harm criterion will be a situation in which there is no Condorcet winner, in which case the tie among the Smith set can be broken by STV, which would presumably satisfy both of us.)
But yes, it is impossible to satisfy all reasonable desiderata for any election system in which there are three or more candidates.