[Election-Methods] Challenge: Elect the compromise when there'reonly 2 factions

[Jobst Heitzig]

Dear Abd ul-Rahman,

> >>In a Range poll, social utility is maximized if everyone votes
> >>*absolute* utilities, accurately.
> >
> >Only if "social utility" is defined so that your statement becomes
> >true by definition (and becomes a triviality thus).
>
> "Absolute utilities" means that the utilities are commensurable. Yes,
> it is a tautology. But it still should be said, because a great deal
> is written that ignores this.

You mean, many people "ignore" that you choose to define "social 
utility" as the sum of individual utilities, while others define it 
otherwise?

> >  Welfare economics, however, does not define "social utility" as
> > the sum of individual utility, it rather defines "social welfare"
> > in some more sophisticated ways which we already discussed earlier
> > several times.
>
> That is also true. There can be utilities that combine in a nonlinear
> way. But how complicated do you want to make it? We have enough
> trouble getting a method in place that will optimize, to the degree
> that Range does, linear utilities, and many forms of utility *are*
> commensurable linearly.

What do you mean by "commensurable linearly"? The question is simple, is 
it better for society when one has 100 and the other 0 or when both 
have 50. If the latter is considered better for society, then "social 
utility" is obviously not the sum of individual utilities. That's what 
welfare economics is about.

> Absolutely, there is the problem of extremes, a choice that maximizes
> linearly summed utility may be unacceptable because it causes too
> much harm to some individual, for example, and that harm is
> considered unjust. But all this *really* means is that there is a
> value which was not considered in the original utilities. In other
> words, they were not correctly stated on a truly commensurable scale.

That is really an interesting claim. Could you tell us what value this 
would be?
 
> Essentially, what I'm saying is that if the original utilities are
> arranged to be commensurable and summable, then the summed utility
> measure works. 

What do you mean by "works"? That you can compute it? Of course you can 
compute a sum, but it does not measure the thing you claim it measures, 
namely "social utility".

> For example, the decision to execute some member of 
> the society, chosen at random, and then use the obtained materials
> for research, benefitting all, might with a primitive measure of
> utility, seem to be socially optimal. 

??? I can't follow. Killing a person is perfectly unsocial, of course. 
This is just an extreme example that shows that taking sums is not the 
way to get any meaningful measure of "social utility".

> Jobst's challenge was to find an election method which would
> guarantee a certain outcome. But because the outcome, with the
> "sincere ratings" given, could be seriously unjust, as I think we
> would all agree under one of the possible conditions explaining those
> ratings as accurately sincere, any method which guarantees that
> outcome is set up to fail. I'd suggest that any method which produces
> an outcome which is seriously unacceptable to the majority has earned
> the judgement "Failed"!

Sure. The point of the example was that C was not at all unacceptable to 
the majority but was considered by them quite a good compromise between 
their and the minorities favourite.

> >>This is because you refuse to look at the underlying utilities.
> >>Because you don't believe in utility, in particular in
> >>*commensurable* utilities, you have only preference left, and from
> >>the raw preferences it appears that C is the best compromise.
> >
> >I love to look at utilities. I did just that to infer that C is a
> >good compromise in the example I gave.
>
> Well, sure. But then why object to my analyis, which included
> comments that if, in fact, the ratings were commensurable utilities,
> the choice of C was clearly a good compromise!

How often do I have to repeat that I don't believe in the 
commensurability of utilities and that I therefore gave a reasoning 
that C is a good compromise without assuming that utilities are 
commensurable?

> >  By the same reasoning (which I will not repeat again here) it also
> > follows that C would be *no* good compromise had the ratings been
> >55 voters: A 100, C 20, B 0
> >45 voters: B 100, C 20, A 0
> >Do you still think only the rankings matter? I don't and never did.
>
> The example I gave was quite different, and Jobst has not responded
> to it.

No I haven't. I chose to give another example in order to show you that 
indeed the ratings (and not only the rankings) do matter.

> Commensurable utilities:
>
> 55 voters: A 100, C 80, B 0
> 45 voters: B 10, C 8, A 0
>
> Which, normalized to the candidate set, which is how we expect Range
> Voters to vote, produces the original utilities given. Each voter
> does not have access, generally, to the utilities of the rest of the
> voters, information which is often necessary to even be able to come
> up with commensurable utilities.

Let us assume for the moment that is was really possible to show in a 
convincing way that the given ratings were indeed commensurable in the 
sense that the 55 voters prefer C to B "10 times as much" (whatever 
that means) as the 45 voters prefer C to A, and that the former get 
"zero" utility from B while the latter get "zero" utility from A. Then 
I still claim that C is the best solution in this case, since with C, 
the A voters still get 10 times as much utility as the B voters, but at 
least no-one gets "zero" utility. I still consider this the fairest 
solution, since switching from C to A will take even that little 
utility from the 45 voters, only to give the other 55 still more 
although they already have so much more utility.
 
> The example given, now, by Jobst, *of course* shows C as a poor
> compromise, it would seem. But only if the votes are commensurable
> utilities. 

No, I argued why it is a bad compromise no matter whether utilities are 
commensurable or not: because all voters would prefer a random ballot 
draw to it.

> >>But what has been overlooked, which is precisely what makes the
> >>arguments about compensation mysterious to Jobst, is that
> >>compromise means that all parties lose something, compared to the
> >>ideal for them.
> >
> >Yes, *all* parties, that's exactly the point! So no one of them has
> >to compensate the other,
>
> That is an error. It ignores that different parties lose different
> amounts from the outcome. Once again, Jobst is betraying ranked
> method prejudice. He ignores the *strength* of the loss.

I don't. In comparison to their respective favourite A or B, all voters 
"lose" exactly the same amount when C is chosen, namely 20 rating 
points. No compensation needed, all have the same balance already.

> It's not a matter of one "has to" compensate another. It is that it
> would be just if some compensated others. And if this is arranged
> properly, the outcome, including the compensation scheme, would
> rationally be accepted by *everyone*. How could this not be just? It
> boggles my mind!

Obviously.

> >  since neither can hope to get their will for certain. They have to
> > compromise. After all, that's what societies are about. By the way,
> > compensation is no mystery at all for me, it is simply not
> > justified in the situation at hand.
>
> I gave possibly underlying utilities where it would clearly be
> justified, and even if the utilities are commensurable, I showed how
> compensation would make the outcome a consensus choice. So on what
> basis does Jobst argue that "compensation is not justified?"

On the basis I repeated over and over: Compared to the fairest possible 
benchmark (random ballot), everybody gains when C is chosen, nobody 
loses, so nothing has to be "compensated". Compared to their respective 
favourite A or B, everybody loses the same (20 points), so again no one 
is in a worse or better situation than any other, and nothing has to be 
compensated.

The idea that the A voters should get compensation when C is elected can 
only be justified by claiming A and not the random ballot solution 
should be the benchmark with which outcomes get compared. But this is 
exactly the thing I object to in all vehemence!

> Underneath all of what Jobst has proposed is an idea that, somehow,
> the majority must be *coerced* into accepting the supposed
> compromise. 

No, they need not be coerced more than anybody needs to be coerced who 
has accepted to belong to a certain society with certain rules. If a 
society agrees upon rules which do not always grant majorities their 
will, then nobody has to be "coerced" when these rules are then applied 
in a specific situation.

> I'd say that this is very poor thinking, old thinking, 
> and quite antidemocratic. 

Now that you're getting polemic and unnice, I think it is the time to 
stop this discussion which will lead us nowhere.

Jobst
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