[EM] Why I Prefer IRV to Condorcet

[Kristofer Munsterhjelm]

Greg wrote:
> I have written up my reasons for preferring IRV over Condorcet methods
> in an essay, the current draft of which is available here:
>   http://www.gregdennis.com/voting/irv_vs_condorcet.html
> 
> I welcome any comments you have.

I'll try to do so, then. Note that I support Condorcet.

Regarding reason number one, it is true that if there are minor parties 
that make no difference, IRV will act as if they didn't exist. That is; 
as long as they get a smaller share of the votes than any of those who 
would matter, they are excluded. However, as soon as a former minor 
third party grows large enough, it destabilizes IRV. You can see this in 
  the Yee diagrams for IRV, where the borders near candidates become 
noisy (and this noise some times travels well into the regions of the 
candidates themselves). This may be what you're conceding regarding 
center squeeze, but the problem is not only the third party's, it's all 
the participants', since the destabilization turns IRV a lot more random 
(because of the amplifying nature of the elimination).

IRV may elect Condorcet winners, but if you accept that electing 
Condorcet winners is a good thing, then simple tweaks will make IRV even 
better: one may check for a Condorcet winner (among the remaining 
candidates) after each elimination, or eliminate the one of the two 
bottom rated that loses the pairwise contest between the two. Also, the 
picture may be false: if we were to count Plurality elections as 
Condorcet elections, one of the two major parties would undoubtedly be 
the Condorcet winner according to the ballots, but this is merely 
because of strategy.

Regarding number two, simple Condorcet methods exist. Borda-elimination 
(Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody 
who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll 
partially grant this, though, since the good methods are complex, but 
I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In 
MAM, you take all the pairwise contests, sort by strength, and affirm 
down the list unless you would contradict an earlier affirmed contest. 
This method is cloneproof, monotonic, etc...

Perhaps you could explain it in that "say A won. B's supporters are 
going to say "but some people preferred B to A!". Then you can say, but 
more people preferred C to B and A to C". I'm not sure, there may be 
better explanations.

Even if so, this does provide a hard choice, though. I'll grant that, 
since as far as Condorcet methods have momentum as election methods, 
Schulze has the most. I wonder if there are simpler heuristics for 
Schulze than beatpaths. Schulze's mentioned the Schwartz set heuristic 
(which I think would be hard to explain) and the arborescence heuristic 
(which I don't know what is).

There's also the observation that voters may not need to know the 
method. Some counties in New Zealand use Meek STV, which basically uses 
a convergence algorithm to determine the weights of the ballots after a 
candidate is elected. That's quite complex, yet they still use it.

Regarding the third and fourth, I'll again say that some Condorcet 
methods are more resistant to burial than others. The IRV modifications 
I talked about earlier resists burial - Chris Benham showed that the 
"check for a Condorcet winner" modification passes "mutual dominant 
third burial resistance", meaning that you can't bury a candidate that 
would be in the honest mutual dominant third set. Unfortunately, the 
modification is also nonmonotonic (like IRV is). While I'll have to 
grant this, I'll say that pushover isn't that unintuitive. Imagine a 
runoff; now stack the deck against your opponent by making the method 
elect those who would split your opponent's vote. The randomness or 
chaos of IRV, as mentioned in the first point response, may make this 
more difficult than one would expect, but to the extent that is true, 
IRV suffers from the chaos itself.

Also, you use examples to show that by demanding core support, IRV gets 
rid of unknowns. However, IRV can fail to elect candidates with 
significant core support. Warren has an example of that at 
http://rangevoting.org/CoreSupp.html .

Regarding number five, I would think that IRV would limit Condorcet 
rather than making it feasible. Consider the case where IRV is passed 
but nothing significant happens to the distribution of power. Then we 
say "Hey, IRV is bad, but give us a chance, try Condorcet". The voters 
may readily say "you got your chance, and election methods don't seem to 
matter anyway, we just get two party rule". In addition, if IRV doesn't 
do anything, we're still left with a two party regime, and those parties 
will be very interested in blocking Condorcet. To the extent applicable, 
the Australian House of Representatives election may show whether IRV 
supports multiple parties: in this case, it doesn't seem to do so (the 
House usually being populated by three parties, but the National and 
Liberal parties are usually grouped together as they stay in the same 
coalition). I add he qualifier "to the extent applicable" because one 
could argue that other features of the Australian system, such as 
compulsory full ranking and how-to-vote cards, is the cause of this.

The Australian example can also be used against number six -- if it is 
IRV that's the problem. If IRV supports few parties, it won't really 
help in trying to change a two-party system into a multiparty one. In 
the best case, we have Ireland, where the president has little effective 
power, so that the STV component (which is much better than per-district 
IRV, in my opinion) prevails. In worse cases, we have the Australian 
outcome, with multiple parties in one body (the Senate) but not in the 
other (the House). In the worst case, there would be no STV component at 
all.

I'll grant the point about Condorcet multiwinner elections. This, in my 
opinion, means that we should try to find a good (polytime) multiwinner 
election method that reduces to Condorcet. CPO-STV is too complex, and 
Schulze STV needs a lot of space (to my knowledge). I'll also note that 
it's possible to make multiwinner versions of other non-Condorcet 
methods; I did so with Bucklin, for instance.

The seventh point is good if you agree with the fifth, but not if you 
don't. I don't, so I think this could be a problem. At least we'll get 
STV if your sixth point is true, but even that may not be. As for the 
unintuitive nature of Condorcet, Ranked Pairs seems pretty intuitive to 
me (with the "complaints rebuffed by stronger complaints" nature); even 
if not, everybody knows about tournaments and Copeland, and even if not, 
I think IRV should be strengthened by the simple modifications if 
Condorcet compliance is important (as you have said it is).

-

This reply has not considered the direct advantages of most Condorcet 
methods, like being countable in districts (when using matrices at 
least) or being monotonic. Those should also be acknowledged; Condorcet 
has some weaknesses (like burial problems, except a few methods), but 
IRV has others, and I think they are more serious.