[EM] Range > Condorcet (No idea who started this argument, sorry; I am Gregory Nisbet)

[Kristofer Munsterhjelm]

Greg Nisbet wrote:
> 
> 
> On Wed, Oct 15, 2008 at 3:09 PM, Kristofer Munsterhjelm 
> <km-elmet at broadpark.no <mailto:km-elmet at broadpark.no>> wrote:
> 
>     If you like Range, this may be to your advantage, since you could
>     say that instead of there being only one Condorcet method that
>     satisfies FBC, there are none at all, or if there is, that this
>     method must be very obscure indeed.
> 
>  
> Before writing this, I knew there were about five versions of Minmax, 
> all possessing different properties. I think there is one version that 
> satisfies CW but not CLoser and various other weird combinations of 
> properties such as that. On the topic of whether there is a method that 
> satisfies both Condorcet and FBC. 
> http://osdir.com/ml/politics.election-methods/2002-11/msg00020.html claims 
> that any majority method will violate FBC. 

Strong FBC. But that's already been answered. Even so, I don't think 
there's a method that satisfies both weak FBC and Condorcet. If there 
is, I'm unfamiliar with it; but the simulations results given at 
http://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg06443.html 
may show that Schulze, while technically failing FBC, does so rarely.

>         2) How does it make sense to be able to divide a region into two
>         constituencies each electing A if B is the actual winner?
>         Condorcet methods are not additive, this calls into question the
>         actual meaning of being elected by a Condorcet method.
> 
> 
>     I'd consider this problem similar to Simpson's paradox of the means,
>     where one can have trends that go one way for the means of two
>     separate groups, but where this trend reverses if the groups are
>     aggregated. It's unintuitive, but doesn't invalidate the use of
>     means in statistics. 
> 
>  
> ONE CRUCIAL DIFFERENCE: Simpsons paradox relies on comparing fractions 
> with different denominators to mask statistics. (I know it isn't 
> necessarily fractions, it is just different results compared against 
> each other that are weighted differently in the final average, but 
> 'denominator' is easier to say/explain than this sentence.)
>  
> Here is why that analogy fails:
> We are not using different districts for each candidate.
>  
> Let's say I can divide country X two ways. Into Y1 and Y2 and into Z1 and Z2
>  
> The consistency criterion states that if I divide my country into Y1 and 
> Y2 and both of them are a victory for candidate A and B wins this IS a 
> violation of the consistency criterion.
>  
> Now let's say that for candidate A I divide it into Y1 and Y2 and for 
> Candidate B I divide into Z1 and Z2. In addition to this division not 
> making sense, let's say A did manage to win twice (however that work 
> work). B wins. This DOES NOT constitute a violation of the consistency 
> criterion. The regions you are dividing the country into have exactly 
> the same weight for every single candidate.
>  
> The Simpson's paradox is impossible if I am always comparing data of 
> like weights.

It can still happen if the method in question weights raw data 
differently, depending on the circumstances. While thinking about this, 
I found an example for Range with Warren's no opinion feature. Consider 
this case:

There are two candidates: A and B, and also two districts.

Range-10 with the no-opinion option.

For the first district, there are 31 voters. All of them have an opinion 
of A, and only 18 of them about B. The magnitude (total) is 200 for A 
and 108 for B, so that you get mean 6.45 for A and mean 6 for B.

For the second district, there are 30 voters. All of them have an 
opinion of B, but only 13 of them about A. The magnitude for A is 124, 
and for B, 280, so the average for A is 9.54, and for B, 9.33 (both 
candidates are very well liked here).

Now, you may guess what happens next. If we sum this up, there are 44 
voters who had an opinion about A, and 48 about B. The total magnitudes 
are 200+124 = 324 for A, 108+280 = 388 for B. Thus B wins with an 
average score of 8.08 against A's 7.36.

For Condorcet, I'll be more general and say that the reason is that when 
it's using a completion method, some preferences count more than others. 
Because the data is broken down from orderings to pairwise preferences, 
that means that some ballot may have an effect on many preferences (the 
direction of the beatpaths or whatever), while others have an effect on 
relatively fewer. The argument would be weakened if one could find a 
consistency failure example where all three ballot groups (two districts 
and sum) produce a CW.

That doesn't "justify" a Condorcet method, though. For that, I'll say 
that consistency is unnecessarily strict. The only methods that pass it 
are those that are summable with vectors of size equal to or less than 
the number of candidates; meaning Approval, Range (without no-opinion), 
and weighted positional methods.

> Compression is a problem. A makeshift attempt to avoid it might cause 
> more harm than good though. The fact of the matter is that Range at 
> least allows voters to express this.

The question here is whether the compression would happen often enough 
that there would be less information than is the case for a ranked 
ballot. We won't know that unless we know the degree to which Range and 
Condorcet voters would strategize, and how much the ballots would be 
degraded. I think that Approval-style ballots would have less 
information than strategic ranked ballots for Schulze, but I can't prove 
that. I also think that the competitive nature would make people more 
likely to strategize with time, at least for Range, where strategy is 
obvious.

>     http://en.oreilly.com/oscon2008/public/schedule/detail/3230 mentions
>     that MTV uses Schulze, internally. The French Wikipedia, as well as
>     the Wikimedia Foundation in general, also uses Schulze. The
>     Wikipedia article on the Schulze method also lists some other
>     organizations that, while small, are not communities organized
>     around open source.
> 
>  
> Congratulations, it has some usage. Range Voting is still vastly for 
> familiar to most people.

If people like cardinal ballots, let them have cardinal ballots. Use 
Schulze, CWP, IRNR, or [insert method of choice here] at the back end. I 
think the important part here is to say "with this method, you can vote 
the way you want, and you won't have to mess with your preferences/pick 
the least of two evils". Then show that the method both provides good 
options and is relatively hard to run strategy against (that is, 
requires coordination or has chicken-race dynamics). I'll grant your 
point, though, Range *is* more familiar.

>         Understandability:
>          Range Voting (I dare anyone to challenge me on this)
>          Bayesian Regret:
>          Range Voting (same comment)
> 
> 
>     Granted, though DSV methods based on Range do better (and may help
>     with the compression incentive - I'm not sure, though). If they help
>     sufficiently that one doesn't have to min-max in order to get the
>     most voting power, it would keep Range from degrading to Approval
>     and thus (absent other problems) fix the "Nader-Gore-Bush" problem
>     (where Nader voters don't know whether they should approve Nader and
>     Gore or just Nader).
> 
>  
> Not quite sure what this has to do with the text it is in response to, 
> but whatever. The Nader Gore Bush problem is an issue, Range Voting 
> doesn't use any type of conditional vote (I don't think that Xs count as 
> a conditional vote), so this will, of course influence results. I did 
> admit that Range Voting was susceptible to the Burr Dilemma, but the 
> ability to give subtlely different votes can combat this.

That was a comment on Bayesian Regret. Warren said that his particular 
DSV variant of Range, SARVO-Range, gave better (lower) Bayesian regret 
than unadorned Range. See 
http://listas.apesol.org/pipermail/election-methods-electorama.com/2005-October/017331.html

The rest of that paragraph was me thinking about that if DSV were 
sufficiently powerful to outweigh the advantage of voting 
approval-style, then the Nader-Gore-Bush problem would be fixed for the 
most part. On the other hand, you may lose the elegant properties in the 
process, such as passing participation and consistency, etc.

> Rated rank ballots, eh? That isn't a bad idea. I would recommend an 
> initial score and a tiebreaker value.

What do you mean by initial score, and tiebreaker value?

>     What worries me with regards to RV / cardinal ratings (beyond the
>     majoritarian situation, where I'm not certain if a method failing
>     Majority is a good one) is the dynamics. A reasonable degradation
>     chain might go like this: First range voters find out that they can
>     maximize their power by voting approval-style. Then Range reduces to
>     Approval. At that point, voters basically have to strategize in
>     order to vote effectively. Some basic strategies (frontrunner plus,
>     or the Approval A strategy) might be used, but the point is that
>     voters shouldn't have to do this, and it appears that while approval
>     (and Range) may seem simpler than Condorcet at the "front end", they
>     lose at the "back end" as the voters have to calculate their ballots
>     before voting.
> 
>  
> Approval isn't a particularly bad method, so backsliding might be 
> tolerable, if it occurs at all. Anyway, all voting systems are 
> susceptible to dishonest voters. The Gibbard-Satterthwaite theorem 
> guarantees this. Anyway, this argument mentions nothing of the quality 
> of the post-strategy winners.

I think approval would greatly reward those who had the best strategy, 
so much that the game elements could become a nuisance. But again, I 
can't prove this.

As for Gibbard-Satterthwaite, that's true, but just because all methods 
are susceptible to strategy, that doesn't mean that they're all equally so.

There may even be a tradeoff, where some methods ("optimist") are good 
at honest votes and break down when exposed to strategy, while some 
("pessimist") are very hardy but produce worse results for honest 
voters. One idea I had, though very complex, for an election system 
where lots of strategy is going on, is to have one "optimist" method 
(e.g Schulze) and a "pessimist" method (Smith,IRV, or what I called 
"first preference Copeland"), then do a honest runoff between the two 
(since there's no strategy when there are only two candidates). This was 
considered too complex, and it's probably overkill unless you absolutely 
can't get true information out of the voters.