[EM] In defence of IRV

Kristofer Munsterhjelm km_elmet at t-online.de
Sun Nov 14 15:59:52 PST 2021

On 11/14/21 10:38 AM, Colin Champion wrote:
> Forrest wrote: "If people interested in voting methods reform would take 
> the time to digest these basic facts .... they would never accept any 
> 'ranked choice voting' method unless it satisfied the Condorcet 
> Criterion." I think that a defence can be offered for people who reject 
> the Condorcet principle.
> Firstly, some published evaluations show no appreciable difference in 
> performance between Condorcet methods and IRV. In Tideman and 
> Plassmann's 2012 paper, Table 1 appears to show that when the number of 
> voters is large, Condorcet methods are 94.46% accurate and AV/IRV is 
> 94.41% accurate. A twentieth of a percent difference! In Table 2 of 
> Green-Armytage et al (2015) you get similar numbers: Minimax is 95.19% 
> accurate and "Hare" 94.45%. If the difference really is that small, then 
> IRV has the advantage of known resistance to tactical voting and has the 
> benefit of having been widely used in practice. There should be no 
> argument that IRV is the way to go.
> In my view there are two weaknesses with this argument. I think (i) that 
> having 3 candidates in a multidimensional space makes the problem 
> unrealistically easy, and (ii) - notwithstanding (i) - that these 
> results could only have been produced by buggy software. I'll say more 
> about this later. But Tideman is probably the most respected worker in 
> the field. You can't argue against IRV if you don't admit that his 
> evaluations have been seriously misleading.
> Secondly, it seems to me that supporters of IRV generally acknowledge 
> the defects of their method (while probably not being aware of their 
> magnitude). They consider that at least IRV has a realistic chance of 
> adoption. They point to the fact that their critics are divided into 
> 1000 factions, that they attach too much importance to theological 
> arguments about logical criteria, and that they often end up advocating 
> unrealistic methods. This allows Condorcet supporters to be portrayed as 
> lacking social responsibilty: see 
> https://rangevoting.org/SchulzeComplic.html.

There are two responses to that, I think.

First (as a proponent of binary criteria) I would make the argument that 
the dynamics can shift the method into a vulnerable area, and that thus, 
failure can become much more severe than what it looks like by a simple 
simulation. Another way to argue this point is to say that we don't know 
the voting distribution, so any statistics gathered about "how often" a 
method fails will be imprecise at best.

For instance, IRV has center squeeze failure with three or more viable 
candidates - the Burlington problem. If IRV is intended to be used in a 
party with only two viable candidates (to make sure that no-hopes can't 
swing the election), then all well and good. But if the point is to 
support multiple parties, then this center squeeze will be a serious 
obstactle to doing so.

If, in the voter distribution that one samples over, three viable 
candidtes is rare, then the problem won't appear on those tests. (So 
it's better to something like Impartial Culture where almost every 
election is an epsilon away from a perfect tie in the limit of many 
voters; or an explicit spatial model that takes multiple viable 
candidates directly into account.)

Of course, if you *want* two party rule, then this is a feature, not a 
bug. See e.g. David L. Wetzell's posts from 2011 and 2012.

The second response is much simpler. It's better to vote for what you 
want and not get it, than vote for what you don't want and get it. 
There's something of an irony that the momentum argument uses the logic 
of the method its proponents want to replace: "choose IRV because it's 
got the following right now". I.e. vote for the lesser evil. And the 
implication isn't even true! In the US, other states are experimenting 
with other methods. Granted, they're usually cardinal ones (Approval or 
Approval-runoff), but it shows that one doesn't have to vote for IRV to 
get results.

I would imagine that the reason that there's no Condorcet in the US is 
because there's no unified advocacy organization around an advanced 
Condorcet method like Ranked Pairs. The closest the US got was Toby 
Nixon's campaign for using Schulze in Washington state: 
which failed. There's also Marquette's use of Nanson: 
but I don't think they specifically chose this method for its Condorcet 

On a side note, when Warren says that any method "significantly more 
complicated than range" is just "mental masturbation", I think that he 
proves too much, because IRV is such a method.

> Finally, voting methods are generally part of larger electoral systems, 
> and decisiveness is often as important as fairness. In the UK, electoral 
> reformers start off thinking they have irresistable logical arguments, 
> and end up getting bogged down in unwinnable debates about the need for 
> 'firm government'. (I can say nothing about the USA, whose institutions 
> I don't understand.) Unless you can argue that a change of voting method 
> will not do more harm through indecisiveness than it does good through 
> fairness, you haven't really got an argument in favour of Condorcet 
> methods.

There's a sort of duality here. On the one hand, the reason to want to 
replace Plurality with something else is to change the dynamics of the 
system from what Plurality produces to something (considered by the 
reformers to be) better. From that position, you wouldn't expect 
particular features of Plurality SMD to carry over to say, Condorcet 
SMD. On the other, too much of a change may feel too risky, and I guess 
that's where the concern for firm government comes from.

So to this I would respond, again, with two points:

I would expect that single-member Condorcet would produce less 
fragmentation than PR, because parties who enjoy minority support 
everywhere but majority nearly nowhere would still not be elected.

Second, complete proportional representation is not that bad, either, if 
managed properly; and doesn't have to lead to gridlock.

The country where I live (Norway) has a particularly strong legislature 
and weak executive: there are no snap elections, minority or coalition 
governments are the norm, and the way the bill submission process works 
makes it unlikely for the executive to propose bills it knows won't have 
support by a majority of the legislature. Still, there's no paralysis: 
the governmental process works fine.

As I tend to say, the major difference between PR and two-party is that 
in PR countries, the voters show their support for the factions and then 
these factions negotiate. In two-party systems, the factions negotiate 
(within their respective parties), and *then* the voters show their 
support. There's no reason the latter should inherently be better than 
the former. Even two-party democracies can get paralyzed if one of the 
parties decides no longer to play by the rules.

> =====
> On evaluations. The Median Voter Theorem (which I think Forrest was 
> alluding to) predicts that if a large number of voters come from a 
> symmetric distribution (eg Gaussian), then all Condorcet methods will 
> elect the candidate closest to the point in space which minimises the 
> sum of distances to voters (ie. the centre of the distribution). This is 
> not quite the same as electing the candidate who minimises the sum of 
> distances to voters, who will be identified as the rightful winner under 
> standard evaluation procedures. But the difference is tiny, and cannot 
> account for the 5% error rate attributed to Condorcet methods by Tideman 
> and his coworkers.

IIRC, the relevant theorem is a multidimensional extension of Black's 
singlepeakedness theorem. See https://www.rangevoting.org/BlackSingle.html.

> I described an evaluation of my own in a previous post. I used Gaussian 
> mixture models instead of pure Gaussians precisely in order to escape 
> from the Median Voter Theorem; otherwise the Condorcet systems would 
> have been indistinguishable from each other. But it's a trivial change 
> to revert to a single Gaussian. When I do so, the accuracy of Condorcet 
> methods is 99.73% and that of IRV is 95.81% (3 candidates, 30001 voters, 
> a million trials). Similar to Tideman et al for IRV; totally different 
> for Condorcet.
> Now see what happens when we go up to 9 candidates. The accuracy of 
> Condorcet systems drops to 99.43%... and the accuracy of IRV to 56.92% 
> (these figures from 100k trials).

This seems to agree with Brian Olson's results that IRV gets 
comparatively worse the more candidates you add. See 

> To be quite clear: I am not saying that Tideman's evaluations are wrong 
> because they contradict my own; I am saying that they are wrong because 
> they contradict the Median Voter Theorem; that my own evaluation 
> attaches numerical figures to an otherwise qualitative argument; and 
> that the Tideman results are also difficult to reconcile with those in 
> other published evaluations (Chamberlin and Cohen (1978) and Darlington).
> Incidentally there was also a much earlier evaluation by Samuel Merrill 
> III. He defined utility as 'decreasing linearly with (Euclidean) 
> distance' (p26) which brings him under the purview of the Median Voter 
> Theorem, but he nonetheless found the Borda count to outperform 
> Condorcet methods. In his own words (p24) "we will see that this 
> criterion [ie. of maximising utility] and the Condorcet criterion need 
> not agree". I don't trust Merrill's evaluation either, and in this I 
> have some powerful support from Warren D. Smith, who wrote ("Range 
> voting", p24) "That suggests that Merrill's computer program had bugs".

Even though Merrill might be wrong, center-biased methods like Borda and 
Sinkhorn seem to produce better VSE/Bayesian Regret results than 
"neutral" methods. The only full IEVS run I could find published on the 
rangevoting site is this one with a 50-50 mix of strategy and honest: 
https://rangevoting.org/StratHonMix.html. Here, center-biased Borda and 
Sinkhorn both do better than neutral Condorcet

The problem with these methods is that they're not fair, and that, since 
this is a ranked ballot setting, their center bias is exploitable. Borda 
is very vulnerable to teaming - presumably Sinkhorn would also be so.

I've done some calculations on the proportion of elections where the 
most strategy-resistant method fails to strategy, for few candidates and 
voters. It would be interesting to trace the Pareto front for Bayesian 
Regret and manipulability. One more task to add to my queue! I have much 
too little time to do everything I want to do.


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