[EM] Does anyone know who this person is?

Tue Oct 26 08:24:37 PDT 2021

On 10/25/21 2:35 AM, fdpk69p6uq at snkmail.com wrote:
> Why does their identity matter?  Discuss the facts, not ad hominems.
> 
> Also, I'm surprised and a bit saddened that you haven't come around to 
> cardinal systems yet.  :/
> 
> The goal of democracy is to elect the candidate who best represents the 
> will of the voters.  My near-indifference between two candidates 
> shouldn't arbitrarily be given the same weight as your strong preference 
> between them.

Let me make a ranked voting advocate (ordinalist?) argument here. I'll 
be referring to "simple cardinal methods", by which I mean things like 
Range, and not so much things that I'm fumbling towards in my utility posts.

Cardinal supporters tend to use two arguments to argue for the 
superiority of cardinal methods over ordinal ones.

The first is that cardinal methods support strength of preference; and 
the second is that, because they pass FBC (and IIA), they inherently are 
more robust to strategy.

My response to these are, much abbreviated, that first, the "strength of 
preference" that these methods gather is probably ambiguous, and if it 
weren't, it would come with significant disadvantages.

And second, that the methods' IIA and FBC compliance take a form that 
shoves what used to be tactical voting into a mush that's kind of 
honest, kind of not; and that once that's made clear, it's obvious that 
the methods no longer achieve the impossible. But because it doesn't 
look like ranked voting strategy, cardinal advocates can shift between a 
position that the methods permit everybody to vote "honestly" (an easy 
position) and that the methods are strategy-proof (a hard, incorrect 
position).

-

So for the first point, let's use Range as the standard cardinal method. 
Range asks for a set of ratings that are intended to represent utility, 
so that your rating is proportional to the utility you achieve from 
seeing this candidate elected. That's what's being demonstrated in 
examples like the pizza election: that the meat eaters show that their 
utility from getting mushroom pizza is not that far off from the utility 
of getting pepperoni, so that the method elects the pizza that satisfies 
all.

But here's a problem. I can't know that my scale is calibrated the same 
way as yours. In philosophy, this is known as the problem of 
incommensurability. Suppose I happen to feel more pleasure (and pain) 
than you, but due to growing up in the same society as you, I mistakenly 
appear to use the same scale as you. It's then quite hard to know that 
when I say 6/10 I mean what you would consider twice as good as that.

At first it would seem, though, that Range has dodged a bullet. Because 
if utility were directly comparable on an absolute scale, then there 
might exist "pleasure wizards"[1] who obtain so much utility from a 
choice that they effectively become dictators. By insisting on a 0-1 
scale (in its continuous version), Range limits the power any one voter 
has and so enforces a weak type of one man, one vote. It is what I 
called a type three method - voters might voluntarily decide to forego 
some of their power to make the outcome better for others (again, as in 
the pizza election).

But the problem with this is that Range supposes that there's a common 
scale where there isn't. As a consequence, the concept of just what is a 
honest vote becomes blurred. E.g. suppose that I consider the sure 
election of Y to be equally good as a 50-50 shot of either X or Z 
winning. Do I rate X 1, Y 0.5, and Z 0? Or do I rate X 0.5, Y 0.25, and 
Z 0? Because there's no way to answer that question (unless it somehow 
becomes possible to get at utility information), there's more than one 
honest vote, and a honest voter is faced with the burden of having to 
decide *which one*. (It is assumed that voters will answer the question 
by normalizing[2], but this leads to strategy problems which I'll get to.)

My attempts to generalize STAR came from asking "what if we want to be 
truly honest about what information it makes sense to ask of voters, 
while respecting OMOV?". Well, we could ask the voters about preferences 
over lotteries (as the 50-50 vs certainty example above). Doing so, the 
method acknowledges the ambiguity of comparing utility. Perhaps there's 
more we can do - e.g. by following MJ's reasoning of a common standard, 
or by separating "worse than nothing happening" events from "better than 
nothing happening" ones.

But all of this is better than just saying "it means what you want it to 
mean", and then sweeping the resulting ambiguity in honest voters under 
the carpet.

-

As for the point that e.g. Range is superior to ordinal methods because 
Range passes IIA and the ordinal ones don't, I always feel like that's a 
bit of a sleight of hand. To explain, let's divide the ballot types into 
three:

1. The highest information honest ballot (ranking candidates in order of 
preference, reporting relative utility values in Range).

2. Other honest ballots: some monotone transformation of this.

3. Tactical/dishonest ballots (order reversal).

Ranked methods have a very obvious category one, and going for some 
category two ballot instead (e.g. equal rank or truncation) doesn't 
usually produce much harm. Cardinal methods like Range replaces most of 
category three with category two because they pass FBC and IIA.

As I've argued above, there's not really a category one for Range 
because it asks for more than the voter can provide. And we know from 
Gibbard's theorem that no deterministic voting method (cardinal or 
ordinal) is entirely free of strategy. So both categories one and three 
collapse into category two in Range: the former because there's no one 
honest ballot, and the latter because order-reversal isn't necessary 
(the famous FBC compliance, but it's actually stronger than just FBC).

So, in ranked voting methods, voting strategy consists of choosing an 
appropriate category three ballot. In methods like Range, it consists of 
choosing an appropriate category two ballot.

But here's the problem: having a clearly defined category one and a 
narrow category two means that a voter who values honesty *as such* can 
just choose the one honest ballot and then go home without regrets. But 
in Range, because "every ballot is honest", he has to carefully 
deliberate *which* honest vote to choose. And if he chooses wrong (e.g. 
in a Burr dilemma), he'll sure come to regret it.

That kind of peril should only exist, IMHO, for voters who decide to 
play rough by choosing a category three ballot.

And thus the sleight of hand: in a ranked method, "honest" means more or 
less category one[3]. So cardinal voting proponents can say "oh, but our 
category three is empty because of FBC!", but all they're really doing 
is shifting the Gibbard-mandated instrumental voting from category three 
over to category two. This lets them say "you can just vote honestly", 
thus giving the impression there's no risk in Range. But it's actually 
the other way around: it's not only determined strategic voters who may 
regret the strategy they chose, but also honest voters who just want to 
vote honestly and go home.

This also poisons the value of IIA. If IIA is to be practically 
meaningful, it must mean that the outcome doesn't change when a 
candidate who didn't win drops out. But if every voter is deliberating 
which type-two ballot to go for, the ballots may change even if the 
sentiment doesn't.

In other words: if enough voters normalize in Approval, then Approval's 
IIA compliance isn't worth much at all in practice. E.g. first round 
ballots:

25: A>B>>C
40: B>C>>A
35: C>A>>B

The Approval winner is C.

But now let A drop out, and the voters renormalize (as Warren suggests 
everybody would):

25: B>>C
40: B>>C
35: C>>B

and then B wins, so even though Approval passes IIA de jure, it looks 
rather different de facto. Telling the voters to perform a particular 
algorithm on their ballots before submitting them, and then claiming the 
inputs to the method satisfies IIA, doesn't mean the method plus the 
manual algorithm passes IIA!

So the problem, in summing up, is that there's too much vagueness to 
hide subtleties in. Cardinal methods measure utility (but they don't, so 
what do they measure?). Cardinal methods let you vote honestly (but 
honest doesn't mean the same thing anymore). Cardinal methods pass IIA 
and FBC (but it does them much less good than ranked methods). Bayesian 
regret evaluations show Range as superior to ranked methods (but 
questionable assumptions about voter strategy may invalidate the results).

It's better to be honest about the limitations that exist. If we can 
only get lottery information, then the method should reflect that. If we 
can get more, then the method should show how we can get it. That way, 
there won't be anything up its sleeve.

-km

[1] 
https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780195189254.001.0001/oxfordhb-9780195189254-e-020 
or, if you're more in a funny mood, 
https://www.smbc-comics.com/comic/2012-04-03 :-)

[2] E.g. Warren Smith says voters will do so because they're not 
"strategic idiots", and that voters who don't normalize in a 
two-candidate election are simply "idiots". 
http://lists.electorama.com/pipermail/election-methods-electorama.com/2006-December/084357.html 
and 
http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-January/084662.html 
respectively.

[3] There's a caveat here because equal-rank/truncation seem to be in 
category two, and so a response to this reasoning would be "ranked 
ballots have category two too!". But there's very little regret in 
choosing category one instead of two, in practice. However, some ranked 
methods that pass FBC do so by making equal-rank stronger than strict 
ranking, and those reintroduce the problem.