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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