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

[Abd ul-Rahman Lomax]

At 06:19 PM 9/4/2007, Jobst Heitzig wrote:
>[I wrote:]
>
> > "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?

No, that is not what I mean. Figure it out.

"Commensurable," in this case, means that they may be added. Yes, 
there can be further complications, such as variance across a 
population or utilities of a kind that cannot be summed. But the 
critics don't get this far, generally. They simply say that they 
"don't believe in utilities." Seems to me we heard that recently here....


> > >  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.

The question is meaningless without further information and context. 
Questions exist, for example, not in isolation. A society might make 
a decision a day, and, if so, the 100/0 split would be just if the 
rotation of questions was such that the *average* was 50.

"Commensurable linearly" means that the utilities may be added and 
that the addition has meaning. Again, I gave an example using travel 
distances which has been roundly ignored by Jobst. It's an example 
where we can understand the utilities, they are connected with the 
direct and clear consequences of the election choice with regard to 
the two sets of voters involved.

If every decision was 100 for one faction and 0 for the other, and 
other things being equal (there could be situations where the 
absolute utilities showed no significant harm to the "0" faction), 
and this persisted, and the faction memberships remained the same, we 
could readily agree that it would be unjust.

Note that this is an example which is zero-sum. We are generally 
considering examples which are not zero-sum.

>  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.

What has happened here is that there are unstated utilities. Choices 
have consequences, and the utility of a choice includes *all* the 
consequences, not just a restricted set. By looking, for example, at 
a cash transfer which is going to be created by a choice, and which 
can go as Jobst described, and if this choice is one-time, sure, 
0/100 would seem to have the same sum as 50/50, yet the former may 
seem unjust, but what is happening here is that there is a utility to 
even distribution which has not been considered in the net utilities. 
If we were to include that, the utility of the 0/100 choice would be 
less than 100, and the 50/50 choice would be seen as having the 
maximum net utility.

However, not all would agree that 50/50 is better than 0/100. Some 
would prefer the latter. If not, how would one explain the popularity 
of lotteries? Clearly, there is a value in the uncertainty and 
perhaps excitement of gambling on the 0/100 choice (if one does not 
know which category one is going to be in.)

However, the *theory* of Range Voting is that it is useful to 
maximize what might be called "stated satisfaction" with the outcome 
of the election. I've been arguing that it is misleading to call the 
Range ratings "utilities."

And all the arguments against the summation of utilities, while 
technically correct, serve to obscure the fact that most healthy 
societies would agree, in full deliberative process, with a correct 
"compromise" that is based on utility summation. Note that they will, 
in doing this, consider *all* the utilities, including matters of justice.

Further, it is hard to argue that a solution which includes balancing 
compensation, so that all voters voluntarily accept an outcome as 
being sufficiently in their own self-interest, is "unfair" or 
"unjust" or that the compensation is "unnecessary." Uncoerced 
consensus is the proof of success in democracy.

If we set up a system of compensation that efficiently causes all 
voters to shift their preferences such that there is exactly such a 
consensus -- and we presume that the compensation is net effect zero 
for the society, the compensation is merely distributing utilities to 
equalize utilities -- when then have, in the compensation, a 
commensurable utility for each outcome.

Quite simply, I think that this has received inadequate attention 
from Jobst. It is a method of determining commensurable utilities, 
and I didn't invent it. I'd say he should answer that.

> > 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?

I just mentioned one. An election has two outcomes, which are 
ostensibly equal in utility. However, we consider one of the outcomes 
unjust and the other just. I find it obvious. We have not correctly 
determined the utilities that led us to the conclusion that they were 
equal. They are not equal to *us*!

They might be equal to the voters, in fact. Within certain limits, 
the 0/100 and 50/50 choices *are* equal; in fact, this would be the 
*norm* in most decisions, for most decisions are instances of a 
series of decisions which are going to be made time after time, and 
the faction memberships shift. If you consistently maximize overall 
utility, on average you will maximize *everyone's* utility. But, 
absolutely, the variation can result in injustice. A loss of $100 may 
be quite acceptable. Unless that's all you have and you will starve 
without it. For such a person, the utility of the $100 goes quite 
negative, it is not merely -$100.

To understand utility in considering the value of election outcomes, 
we must consider *all* the effects that an outcome will have on the voter.

Now, in actual Range Voting, the ratings are, most certainly, *not* 
absolute utilities, in general, unless we consider the range of 
satisfaction of each voter to be equal, and make certain other 
assumptions regarding the candidate set and how the voters view it.

>
> > 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".

We do not generally "measure" social utility, except in simulation, 
where we can *posit* absolute utilities. the simulations so far do 
not include such things as amplified utilities at the limits. I have 
little idea of how these modifications would change the utilities, 
but what is happening here is, in fact, highly offensive. There is a 
means of judging the success of election methods, and it involves 
Bayesian Regret. It uses some simple assumptions which are, in fact, 
oversimplifications if one were to insist. But the fact remains that 
there are elections where absolute utilities can actually be known, 
and I gave an example. Now, I did not include non-linear effects, and 
such effects are certainly possible. But that summation of utilities 
is not perfect does not mean that other far less reasonable measures 
of election success, such as so-called Election Criteria, are better.

How about the Consensus Measure? An election method, including the 
complete context, is successful to the extent that all voters 
voluntarily consent to the outcome.

What I've been pointing to, for some time, is that there are Measures 
and Criteria. Criteria are either satisfied or they are not, and 
there is no specific value to Criteria, which Criteria are most 
important and which are less important are subjects of constant 
debate, and no wonder. There is no standard by which to judge 
Election Criteria. Except, of course, how methods behave with respect 
to posited utility.

It is, for example, easy to come up with election scenarios where the 
Condorcet or Majority Criteria suggest an obviously poor outcome, one 
that would never be accepted, in a healthy society, using full 
standard deliberative process. And certainly this outcome would not 
be accepted by consensus! It *might* be accepted by a majority, in an 
unhealthy society, one where the majority wants its last nickle, it 
does not care what it costs everyone else. (This is a society where 
the majority would consciously and deliberately choose A even though 
the cost to the B voters is heavy and the gain to the A voters small, 
a society that would need some contorted and contrived election 
method to force it to accept broader benefit.)


> > 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".

But I then explained that the utilities imagined were not complete. 
The key words were "a primitive measure of utility," one which 
perhaps assigned some fixed value to a human life, such as the 
average earnings of a person over the remainder of their lifetime, 
then considers the benefit of using the materials for research, which 
might possibly exceed that value. But there is another utility that 
is ignored by this, the value of respecting life and not sacrificing 
it for shallow gain, against the consent of the individual involved.

If the individual consented, it would be another matter, in some 
situations. In others, we would not even accept it with this consent. 
However, we do accept danger of loss of life, which amounts to 
something similar.

"Commensurable utilities" requires that all attached utilities be 
included. The apparent failure of utility analysis in the example 
Jobst gave (0/100 vs 50/50) was a result of failing to include all 
utilities, and specifically a utility coming from the value assigned 
to even distribution. As I pointed out, that the two outcomes are not 
equal in utility is less than clear, some, in some situations, would 
consider them equal; on other situations they would not be considered 
equal, and mostly this has to do with a value assigned to "justice."

If only one election is going to be held, and the outcomes are as 
stated (0/100 vs 50/50), and "100" is the total value of a life 
thoroughly enjoyed, and "0" is a miserable existence, then, quite 
clearly, the 0/100 outcome is unjust, most notably to the segment of 
society that gets the zero. Since we have defined the zero in a way 
that makes it seem a true minimum -- it couldn't get worse, dying 
would be better -- the flaw is in the other end, the presumed 
thorough enjoyment, when half the society (the problem must be 50-50 
split in voters to make sense) is totally miserable, is the 
contradiction. Now, sociopaths might find that quite acceptable. 
Normal members of society, and, fortunately, the vast majority of 
voters, would not. Instead of the outcomes being 0/100 and 50/50, 
they are more like 0/5 and 50/50! Do we then have any trouble seeing 
that 50/50 is better? (The 5 represents the sociopaths, though they 
may be less than 1 in 20.)


> > 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.

Well, no. Remember, they were defined as being "selfish." They will 
vote to get what they want, no matter what the minority needs. This 
was the difficulty of the problem; however, the solution that the 
minority negotiates a distribution of the benefit, such that the 
majority does not lose value by choosing C, does solve it with selfish voters.

If the A voters in fact consider C "quite a good compromise," this 
would be easy. And that is why the B voters are the ones to 
compensate the A voters, rather than the reverse. The A voters need 
less compensation, so it is more efficient. If you do it in reverse, 
where the A voters offer to compensate the B voters for the choice of 
A, it would be expensive, and, in fact, there is no motive for the A 
voters to negotiate, if they can get A by strategic voting or C if 
the plan fails. Of course, if they vote strategically and cause B to 
win, they've got quite a problem!

> > >>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

Didn't I just say that Jobst does not believe in commensurable utilities?

Yet I gave an example where utilities would be commensurable. Didn't 
he notice that? Is his commensurable utility atheism so strong that 
when a utility knocks at his door, he will open it and close it, 
saying there was nobody there? It looks like it!

We just had a contribution to the Range Voting list by an economist 
who detailed some of the history of the controversy over utility. I 
found it fascinating, and I'd suggest reading it. The post was by 
Hillinger, and there are references to papers of his.

>  and that I therefore gave a reasoning
>that C is a good compromise without assuming that utilities are
>commensurable?

However, what if we have a set of absolute utilities that generate 
the ratings given as "sincere" and that will create the choices Jobst 
proposes with regard to lotteries, yet the absolute utilities show 
that the choice of C is far from a "good compromise," it is unjust?

And I did that. C is only clearly a good compromise if we assume 
commensurable utilities. Now, there is another way in which we can 
consider C a good compromise, and it underlies the error, for it is 
an unstated assumption about the preferences of voters and the manner 
in which we amalgamate them. We routinely assume that it is useful to 
amalgamate votes, making all voters equal. Range still does this, but 
it *allows* voters to vote in a manner where all votes are not equal; 
but the maximum range allowed for all voters is still equal. And thus 
the A faction can prevail in a Range election if it chooses to do so. 
If it votes what are called sincere ratings -- which means ratings 
relative to some presumed set of utilities or expected satisfactions, 
normalized to the candidate set --, then C will be chosen. However, 
whether or not this is acceptable to the A faction depends on the 
absolute utilities, and Jobst does not really believe in such, either 
(for absolute utilities are, by definition, commensurable).

Let me put this another way. Jobst did not show that C was a good 
compromise, unless you accept his premise about lotteries, which I do not.

And I do not accept it because it indicates a patently poor outcome 
given certain sets of absolute voter utilities. It is *therefore* not 
a reliable guide to the justice of an outcome.

> > >  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.

Still, Jobst has not responded to the example I gave. I suppose that 
is what he just wrote. "No, I haven't," means, I must assume, "I have 
not responded."

Now, I've never said that the "ratings" don't matter. *On average*, 
the utilities will be commensurable, and this is why Range would work 
even when the range of utilities for each voter varies all over the 
map. *On average,* C is the most just outcome, a "good compromise." 
But Jobst above noted that variation from the average can be 
important; if not, 0/100 and 50/50 would be the same!

*On average*, the ratings will be commensurable, and so we can see 
the justice of the outcome. If we assume that average 
commensurability is acceptable, then the use of the lottery measure 
Jobst proposes becomes acceptable. This is the assumption underneath it!


> > 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.

Jobst is here introducing doubt while pretending to accept a 
scenario. In the original example -- did he notice it? -- the 
utilities were explained as travel distance, from the home of each 
voter to the public facility location under consideration. So a very 
specific meaning was given for the numbers.

I think that my explanation, if read, would have been convincing, so 
to write in the way Jobst has done is to completely disregard the 
example; and this is consistent with a refusal to accept the reality 
of commensurable utilities, even if they are banging on the door. 
What? Some neighbor must be hammering something. Back to my debate:

>  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.

What? In the example given, the choice of C is *preposterous,* and 
that Jobst would baldly assert that C is best shows that he, 
absolutely, is in denial -- or simply error and oversight. Jobst, you 
should look at the example. You have not considered it. The numbers 
are distances. C is not the best choice, C costs the community much 
more than A.

In one post, I think I gave an example of a travel equalization plan, 
used in a real organization to equalize travel expenses to a 
conference site, making it equally possible for delegates to attend 
no matter where they are from. Such a plan applied here would make it 
obvious that the best choice is A.

If everyone in the community, collectively, by a level tax, pays the 
travel costs for everyone to travel to the public facility, then the 
community will rationally choose A, because the costs and therefore 
the tax will be minimized.

On the other hand, if the original ratings were commensurable 
utilities, the tax would be minimized with the choice of C.

It's a bit sad for me to have to explain all this....

>  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.

It's a total misunderstanding of the situation. The A voters have a 
greater range of utilities. The choice has more impact on them. The C 
voters don't lose much no matter what outcome is chosen.

I'm bailing. Quite simply, this is no longer worth the time for me. 
I've learned a great deal, I fear that Jobst has not.

Take what you like and leave the rest.

But one more sally, since I had to look over the rest to delete it:

>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".

(1) I have seen no reason to accept "random ballot" as the fairest 
possible benchmark, and, in fact, I reject it. Jobst has not, to my 
knowledge, even attempted to establish random ballot as a fair 
benchmark, he simply assumed it.

(2) Without commensurable utilities, it is possible that the A voters 
lose when C is chosen, and they lose more than the B voters gain by 
that choice. This statement is not precise, but I'm not going to 
bother sharpening it, it is enough here to note that what Jobst just 
said, if applied to the example I gave (ABC 100/0/80 vs 0/10/8) is 
absurd. In my original statement of the travel distance example, I 
noted that the utilities stated were inverted travel distances, so 
the distances were

ABC:

55: 0/100/20
45: 10/0/2

These distances, inverted, produce the utilities, i.e., utility is 
inversely proportional to travel distance.

These are commensurable utilities, you can add them to determine 
total utility for the community.

 From this, we can see that what Jobst has stated, quite simply, did 
not understand the situation.

If we choose C, the A voters have to travel 20 km, the B voters 2. If 
we choose A, the A voters have no travel distance at all, and the B 
voters have to travel 10 km. To top it off, there are more A voters 
than B voters. A, in this case, is the most efficient choice, the one 
creating the least burden for the community.

Now, it would, in fact, be just for the A voters to compensate the B voters.

When the optimal choice has been made, compensation to equalize 
benefit is minimized.

If we are not going to compensate, then what we are doing is 
minimizing injustice, not eliminating it. The theory behind this is 
that, on average, it will all even out, over a long series of 
choices, and so the compensation is not worth the effort, the 
overhead to arrange it. To the extent that this is true, compensation 
is not necessary. But that does not mean that it would be unjust or 
inappropriate, if it could be efficiently determined.

>  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.

To claim that for one group to lose "20 points" is the "same" as the 
other group to lose 20 points is to claim commensurable utilities. 
But, remember, Jobst does not believe in commensurable utilities. 
Well, does he or doesn't he? Only his hairdresser knows for sure, a 
comment that might reveal my age.

But the option B was never a realistic option. Generally, democratic 
choices are Yes/No, election methods which attempt to make, in a 
single poll, more complex choices necessarily introduce certain 
difficulties. Here, Jobst's analysis necessarily includes the option 
of B, even though B is clearly the worst option.

I suggested looking at the reduced candidate set, perhaps the product 
of a runoff, the set of A vs. C.

What we have, keeping the original utilities -- which we can do if we 
assume that they are commensurable, but not if they are only relative 
utilities from the candidate set -- is

55: A 100 C 80
45: A 0   C 80

The only reason that Jobst can claim that both groups "lose" the same 
is that he is using a different basis for each group, not a common basis.

If C is chosen, the A voters lose 20 points over the choice of A.
If C is chosen, the B voters gain 80 points over the choice of A.

For symmetry, we could state it in reverse.

If A is chosen, the A voters gain 20 points over the choice of C.
If A is chosen, the B voters lose 80 points over the choice of C.

Compensation to equalize costs or benefits is interesting because, it 
it is freely accepted, it is evidence of commensurable utilities. If 
it is freely accepted and results in consensus regarding the outcome, 
we must consider the outcome just.

>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!

However, it's a straw man argument. I have not claimed that the "A 
voters should get compensation." I have merely noted that if 
compensation is offered, they could be induced to voluntarily shift 
their preference. I'm suggesting exploring this.

And I did go over the situation showing why it was not symmetrical. 
It is not that the A voters are the benchmark. All voters are equal, 
but not all voters benefit equally from a particular outcome. In the 
example given, though, all voters do benefit equally from the choice 
of C, *if the utilities are commensurable.* That is what makes 
Jobst's objection to commensurable utilities so obtuse.

> > 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.

That can be quite a lot.... when the society asserts jurisdiction 
over you by claiming sovereignty over a particular territory, and 
over you because you are within that territory, when membership in 
the society is not voluntary, it is asserted.

In any case, how are the rules of the society determined? Jobst's 
argument is circular. Generally, the majority determines the rules, 
in a democratic society. What Jobst is considering, though, is rule 
of law, not democracy. If, somehow, he can get a rule passed that 
will enforce the election method he's proposing, then we can have 
justice .... but can the majority change the rule? If so, and the 
rule continues, then it is just. If not, it could easily be unjust.

>  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.

Sure. If the majority accepts this! But does it?

What usually happens, in fact, is that a majority *at one time*, 
consisting of different people than the present electorate, decided a 
rule. As things go, in actual practice, the rules set may not even 
have enjoyed true majority support. Rule of law is not democratic. 
Note that I'm not arguing against rule of law, but it is not superior 
to democracy, in general, *if the democracy is properly structured*. 
And, in fact, established rules ("law") does generally give the 
majority the right to change the rules. If it is truly a majority, 
and it persists. Supermajority is generally required for *rapid* 
change, though it is, even there, possible for a majority to set 
aside the rules. There are very strong reasons for majority rule, and 
Jobst does not like them.

> > 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.

Fine with me!