[EM] Election-Methods Digest, Vol 235, Issue 30

[Kristofer Munsterhjelm]

On 2024-02-19 22:07, Closed Limelike Curves wrote:
>>     Suppose now that someone adds, to the Wikipedia article about this
>>     theorem, that it doesn't apply to ranked voting because some ranked
>>     voting methods pass the FBC and therefore allow voters to honestly state
>>     who their favorite is.
> 
> I suppose this is where we'd disagree; I'd say that adding this line to 
> the article is more likely to clear up confusion than create it. Every 
> time I bring up score voting's sincerity in the 3-candidate (or perfect 
> information, or zero-information) cases, I get people claiming that's 
> obviously impossible, because Gibbard-Satterthwaite says so.
> 
> The problem is if someone says "Here's Gibbard-Satterthwaite; by the 
> way, it doesn't apply to cardinal methods, but Gibbard does," it gives 
> the mistaken impression that Gibbard-Satterthwaite and Gibbard's theorem 
> are proving the same result, just in two different domains. (Thus why 
> there was a lot of confusion about merging the two articles in earlier 
> discussions, and people mistaking the two.) In reality the concept of 
> honesty in Gibbard is different (and stricter) than the concept of 
> honesty in Gibbard-Satterthwaite.

 From one perspective, they *are* giving the same result, mainly that 
you sometimes need to pick a different member of the set of allowed 
expressions based on what other voters are doing, if you're optimizing. 
For ranked methods that's ranked ballots, for rated methods that's rated 
ones.

But I won't harp on that. What I would like to do, however, is point at 
the reddit conversation I linked to in my "rank consistency" post:

https://old.reddit.com/r/EndFPTP/comments/1arr7bc/utah_lawmakers_advance_bill_to_drop_ranked_choice/kr28m85/

Here the user Llamas115 responds to rb-j (hi Robert)'s claim:

"Cardinal methods demand too much tactical thinking from voters"

by saying

"Cardinal systems [...] don’t require insincere voting with 3 candidates"

Llamas115 is presumably using Warren's (and Brams and Fishburn)'s 
definition of sincerity as being rank-consistent. But rb-j is talking 
about being strategyproof, or more generally, there not being too much 
of a consequence to not thinking about tactics.

(As a side note: a method can be rank-consistent yet there can be higher 
penalties for voting in a straightforward way than in a method that 
isn't. That a method is consistent/incentive-free in parts of the data 
that makes up a ballot does not mean that the voter necessarily has an 
easier time, because the method could be more sensitive to the remaining 
bits of the data.)

Then in the thread I linked, ant-arctica gets GS and Gibbard confused. 
And Llamas describes the distinction between the two, after which 
ant-arctica says "okay, now I'm underwhelmed, and by the way, this feels 
a bit like a motte and bailey".

So there, at least, is someone who didn't understand the precise 
definitions of sincerity according to Brams et al., and who thinks the 
cardinal proponent is (kinda) using a sincerity definition that casts 
cardinal voting in a good light.

>>     It doesn't imply IIA as such. But it is related to what I called "de
>>     facto IIA" in my other post.
> 
> A counterexample would be nice instead, then, since I'd conjectured any 
> system that isn't strategyproof would have a "de facto IIA" failure.

I must have been a bit unclear or misunderstood what you were saying.

When you said

>>> By the way, I'd be very interested in a source on strategy implying
>>> IIA violations, so I can add it to the article!

I read that as "I think that a method that is vulnerable to strategy 
will always fail IIA, I would be interested in a source corroborating 
that". And by IIA, I thought you meant the traditional sense: if you 
have the same ballots and then remove some candidate who didn't win, the 
winner shouldn't change.

Thus I said, or meant to say: you can easily find a method that's 
vulnerable to strategy but passes IIA, so strategy vulnerable ==> IIA 
failure is incorrect. (Just pick a cardinal method).

Then I said, again rephrasing: But it's very possible that being 
vulnerable to strategy leads to "de facto IIA" failure, because the 
voters may change their strategies when a non-winner drops out.

If that's your conjecture, then we agree!

Formalizing it would require shoring up the may in "voters may change 
their strategies".

-km