[EM] (Let's try that again) Re: Kristofer: Approval vs Condorcet, 4/28/12

[Kristofer Munsterhjelm]

(It did send, now, but it truncated it early. Again! I'm sending this to 
Mike too, as the original mail I sent to him might have been truncated 
early, too.

If this does work, I've found a bug in Thunderbird.)

--

It appears that your mail program has seriously mangled your reply, 
bunching up all the text into a single block. In addition, it seems to 
have sent multiple versions of your reply in the same message.

Therefore, I couldn't see all of the replies in detail, but I did pick 
out some that I will reply to.

My point about G&S implying every voting method has to hold something 
behind his back is not about FBC in particular. From what I understand, 
you're saying that FBC is much more important than the other criteria 
because US voters are so overcompromising they won't vote honestly if 
they know they could benefit Compromise by ranking him first. (Even 
though, even in Plurality with its very clear punishment of 
non-compromises, US voters sometimes go for their true favorite, e.g. 
Ross Perot in 92.) So you say that Condorcet is at a disadvantage 
because it doesn't pass FBC, and "perhaps it can win even with an arm 
behind its back". What I am saying is that if you take the view that FBC 
is just one desideratum, then all methods have to hold *something* 
behind their backs. It might be FBC, it might be clone independence, it 
might be LIIA or rank expressivity. You just can't have them all.

So if you say "perhaps Condorcet can win even with something behind it's 
back", that's not particular to Condorcet. If what you mean is "perhaps 
Condorcet can win even with FBC behind its back", then okay. That's more 
clear. It doesn't *as such* put Condorcet at a disadvantage, because you 
can't have every criterion. Perhaps Condorcet can win even though it 
doesn't have FBC? Perhaps Approal can win even though it doesn't have 
full ranking. Perhaps Asset can win even though it has an intermediate 
layer between the voters and the representatives. And so on... These are 
all disadvantages. Which are worse disadvantages is another matter, and 
I've given reasoning for why FBC failure might not be so devastating 
after all, even in the United States.

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Next, about "the candidate with most Approvals win". What I see as a 
problem with that definition, or rather, the assumption that this is 
okay, is a subtle switcheroo. If you were to say "the candidate with 
most approvals win", with the standard sense of the word "approval", 
then that might be good. However, we know that in contested elections, 
Approval is very sensitive. It has the defection problem and even when 
people want to be honest, they still have to pick a threshold. So people 
wouldn't just be setting a threshold of who they accept based on some 
internal preference, they'd also look at what others are saying and 
adjusting their thresholds accordingly. Hence, "Approval" starts to 
differ from genuine "approval".

To make it really obvious, consider a similar pitch for Plurality. "In 
Plurality, the candidate who is favorite of the most voters win!". 
Sounds reasonable enough, doesn't it? But in the real world, the 
Plurality "favorite" isn't their real favorite, so the pitch doesn't 
mean what the voters think it means. Now, don't get me wrong. I'm not 
saying Approval is down there with Plurality. I'm just saying that 
there's a subtle equivocation because each method imparts a distortion 
according to the degree to which the voters feel they have to vote 
strategically.

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About Condorcet's strategy resistance: I see a little bit of myself 
here, actually, in the kind of arguments that I would have used against 
IRV. These are arguments of the form: "well, I need to be absolutely 
sure that there won't be any incentive to betray / nonmonotonicity / 
etc". So perhaps this will let me better "stand in their shoes", as it 
were. I still don't think that IRV is a good method, but knowing how 
they think is useful in any argument.

Anyway. Again, as far as I understand, you're saying that because 
Condorcet has the defection problem, it's no better than Approval, and 
because Condorcet doesn't pass FBC, it will be worse off than a method 
that does. But I would argue that situations of partial honesty matter.

If everybody's 100% honest and knows his preference on the level of an 
Olympic judge, then sure, use Range. If everybody's a true game theorist 
of the sort that would give the other guy 1 dollar in the dictator game, 
then use an iterated method because you're only going to get a good 
result if the method has a good game-theoretical equilibrium. But in 
between? That matters, and that's where you'll find most practical 
elections.

 From above, the ranked methods are better than Approval because if 
there's a significant fraction of honest voters, these honest voters 
don't have to ponder where to put their Approval thresholds. They can 
just rank honestly. Ranking may seem easier than rating to me, so that 
may be part of where I'm coming from, but to me, it seems much easier to 
just start ranking than to think about expectation values.

The ranked methods -- at least Condorcet -- are usually quite good at 
rejecting noise, be it unintentional or strategic. The resistance to 
ordinary noise can be formalized in some cases: Kemeny is a maximum 
likelihood estimator under a model where voters get "A vs B" wrong with 
some probability p when voting their ranked ballots, for instance.
As for resistance to uncoordinated strategy, or strategy where a 
significant fraction of the voters is honest, that's most obvious when 
there is no cycle. If there's a sincere CW, like in Burlington, then the 
group that wants to use strategy has to be large enough to induce a 
cycle. If it isn't, nothing happens. Further, if favorite betrayal is to 
pay off, the group doing it have to be large enough that, by voting 
Compromise over Favorite, they reverse the direction of (Favorite > 
Compromise). Thus, that seems to be more the kind of strategy that would 
be directed from party central than something any individual voter would 
come up with, perhaps with the exception of putting the viable opponent 
last.

And this is really where I make my feedback claim. If it takes a lot of 
people to make strategy work, at least in <= 3-major-candidate or u/a 
elections, then the overcompromising voters can kick their habit. You 
seem to consider the voters to be closer to the game theory economist 
position than I do, in that they would compromise "just to be sure" (and 
would similarly min/max rank in MJ "just to be sure").

In short, I say that if people see no change to their overcompromise, 
then they will slowly stop compromising. In matters of probability, 
there are always *some* who don't compromise, and it'll spread from there.

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Finally, I say that I don't dispute that Approval is better than 
Plurality. I am, however, not certain that the change to Approval is as 
simple as you say, and if it isn't and you have to use an IRV-style 
bottom-up approach, then why not get it right the first time?

(If a municipal-to-national approach was the only option, would you 
still prefer Approval, or would you go directly to ICT?)