[EM] Method X, bummer

[Kristofer Munsterhjelm]

On 8/8/23 01:17, Forest Simmons wrote:

>> I think it depends on the person. Myself, I find ranking easier
>> than rating, because I'm always trying (and failing) to find some
>> natural calibrated scale when rating, but ranking is easy: just "do
>> I prefer a world with X to one with Y?". And then if it's below my
>> JND,  equal-rank.
> 
> 
> To me "Below my JND" is the same as "infinitely close." And "I strongly 
> approve X" means I consider X to be infinitely close to my favorite.  "I 
> strongly disapprove Z" means I consider Z to be infinitely close to my 
> anti-favorite.

Yes, that's an intuitive idea. But after further consideration, I think 
it also depends on the effort, which brings a sort of "paradox of 
voting" logic to it.

Suppose that I'm an agrarian leftist voter. Suppose that candidate X has 
a strong agrarian position while candidate Y has a strong leftist 
position. On intial examination, I find that they're about equally good, 
so I would rank X and Y equally.

So far so good, "very close".

But let's say I were instead part of a deliberative body (something like 
a citizens' assembly) writing a reference on the different candidates' 
policies for voters to consult. Then I might investigate the candidates' 
past records, the results of policies they supported, and so on, because 
the assembly is smaller and the effect of getting it wrong is more 
serious (assuming the guide would be used by the voters). And after 
careful investigation, I might find out that, in my opinion, X is better 
than Y.

Because the stakes are higher, I would make an additional effort to 
distinguish X from Y. While complete instrumental rationality is 
completely unrealistic for elections (or nobody would vote), there's 
*some* part of it to ranking otherwise very close, or very hard to tell 
apart, candidates.

These candidates may not even be an epsilon apart in the limit of time 
spent scrutinizing them going to infinity. I just can't determine what 
the actual distance is at a glance. So my equal-rank is an expression 
that I trust the rest of the electorate enough, and that it would not be 
worth it to spend excessive effort trying to determine if X is really 
better than Y.

I'm kind of mixing "personal preference" (i.e. what I like the most) and
"best for society" (what candidate would be best for society), but it's 
the best I can do at getting at what my intuition says.

>> Perhaps I would disapprove of the other end of the scale from where
>> my preferences lie, but if you were to add a (hypothetical)
>> Stalinist party and a Norwegian NSDAP (to mirror the Stalin and
>> Hitler example above), then my disapproval thresholds would
>> probably change so that I would disapprove of those two and approve
>> of all the democratic parties. >
>> And what that suggests to me is that when multiparty rule happens 
>> and there's more of a gradual scale, then it gets harder to place
>> dividing lines [...]
> 
> 
> You seem to be forgetting that strong approval and strong disapproval 
> are optional designations. If you do not feel strongly about approving 
> or disapproving a candidate, then you cannot honestly use those 
> designations.
> 
> In infinitesimal calculus, you are not required to classify every number 
> you use as infinitely large, infinitesimal, or neither ...  but it is 
> nice to have those options.

I think what I was trying to say is that it seems on principle very hard 
for a method to infer anything consistent from the approval cutoffs, due 
to the voters' differences in idea about where they should lie. Like I 
said in my quick and dirty STAR post, even if we assume consistent 
utilities in a vNM sense, the voter-dependent affine scaling values 
makes it very difficult to compare my expression of a cutoff to someone 
else's.

With ranking, there's no problem, because the affine transformations are 
all monotone.

The relative difficulty in a gradual setting (like multiparty democracy) 
also makes sense in that context. Suppose U(v, x) is voter v's utility 
if x is elected, and suppose that we have two voters with rating functions:

R(v1, x) = a_1 * U(v1, x) + b_1
R(v2, x) = a_2 * U(v2, x) + b_2

and some very large threshold values A >> B so that a voter v strongly 
approves of every candidate for which if R(v, x) >= A, and strongly 
disapproves of every candidate for which R(v, x) <= B.

Then if we suppose that the values of a and b are bounded in magnitude, 
something kinda like Balinski and Laraki's "common language" idea, then 
as long as candidates are easy to tell apart, then you *can* compare 
different voters' below-B/above-A statements. In addition, the voters 
can more easily classify them, particularly if the difference between 
the sides are clear; if U(v, "my side") >> U(v, "their side"), then the 
distinction is natural.

On the other hand, if U is a sliding scale, then either it's very 
difficult to say just where the cutoffs should be, or the meaning won't 
be preserved.

I have a kind of vague feeling that to the degree the meaning isn't 
clear, honest voters will be incentivized to strategize because there 
are multiple honest ballots. So the harder it is to understand, the 
harder it is to "just stay honest".

Or in the terms of the above: if I'm only willing to disapprove of 
totalitarian dictators, and I see that nobody on the ballot is a 
totalitarian dictator, then I may start thinking "what other use could I 
put this cutoff to?". Which seems to go against the purpose of elections 
as information gathering.

I'm repeating myself, but maybe it'll give a better idea of the hard to 
express intuitive feeling I have that approval cutoffs are hard and have 
very unclear interpretations. Maybe it'll give both of us a better idea, 
even!

-km