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

[Abd ul-Rahman Lomax]

At 05:08 PM 9/2/2007, Jobst Heitzig wrote:

>>Yes, it is a synonym for that. However, the implication here is 
>>that not only is one acting in one's own self-interest, it is a 
>>narrow self interest that does not care if nearly half the 
>>electorate ends up with a maximally unsatisfactory outcome, as long 
>>as they personally gain a dime. This is actually sociopathy, 
>>someone who truly thinks like this and who is not afraid of 
>>consequences would slit your throat for pocket change.
>
>And yet you think "they *should* vote in their own interest"?

Yes. Everyone should, and we are free to define our "own interest" 
widely or narrowly. In a Range Vote, in fact, we would want people 
*not* to try to figure out what everyone else wants and then defer to 
that. Such an "altruistic" bias would actually cause the method to 
function less effectively. Rather, the only question is how strong 
one's preferences are. Strong preference is not necessarly a product 
of "selfishness," it could also result from knowledge. By insisting 
that methods consider rank only, and not preference strength, we are 
actually biasing the system against knowledge, for we equate weak 
preference with strong, and, generally, knowledge will improve 
preference strength (but not always, of course, sometimes knowledge 
weakens preference, where the strong knowledge of the ignorant is 
mere prejudice).

In a democratic system, we must trust the people in their judgement, 
knowing that the judgement of some will be corrupt. If the judgement 
of the majority is corrupt, we are in big trouble in any case, no 
matter what election method we use. The majority will, I'm assuming, 
seek and find good advice, and will recognize the special situations 
where some minority will attempt to manipulate Range in an unfair 
way, and they have a very simple option: consider the election 
probabilities and vote -- as they will with all other systems on the 
table -- to correct the imbalance.

This is why I consider Range Voting to be a *voting* method, and the 
marks put on the ballot are *votes,* not sentiments. Votes are only 
sincere in a very primitive way. They are better understood as 
actions, and the doer of the action is responsible for the consequences.


>>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.

>  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.

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.

Essentially, what I'm saying is that if the original utilities are 
arranged to be commensurable and summable, then the summed utility 
measure works. 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. But the choice itself has far 
more than economic or health consequence. It would be seen as unjust, 
and this would properly depress the utilities, even extremely, for 
almost all voters. If you only look at the one narrow issue and 
ignore the others, it seems that a wrong decision would be made, as, 
indeed, it would!

As I've written, Range cannot accurately determine utility such that 
it is always going to choose the S.U. maximizer. But this does not 
mean that S.U. performance cannot be used to judge Range as a method. 
Quite the contrary, it remains just about the only reasonable measure 
we have for election performance.

The problem Jobst raised was a very interesting one, and my 
contribution to it was to point out that the outcome he proposed was 
not necessarily the "fair compromise" it was asserted to be. Only 
under certain conditions would it be so, and those conditions are, 
indeed, common in real elections, but they are certainly not 
universal, and I gave the example of a multiple Ballot Question 
choosing the site of a public facility. These kinds of elections 
actually occur in practice.

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"!

It might still be a good method, compared to some others. That's a 
separate question, and we would want to look at *how often* a method 
fails, and *how seriously* it fails. What is often overlooked with 
Range is that, while it can fail to choose the S.U. winner, under 
real conditions, it strongly tends to choose, if it fails, a close 
second, who is not seriously objectionable to a majority. When Range 
fails, we have a weak preference of a majority vs. a strong 
preference of a minority, as it appears. If the majority had a 
serious objection to a candidate, then we are left with wondering why 
they voted a weak preference.

Only some serious misunderstanding on the part of that majority would 
explain it, a misunderstanding that Range Votes are sentiments 
expressed in a poll to measure sentiment on some absolute scale. That 
is not what they are. Consider, I'd suggest, that they are switches 
connected to lights, each switch controls the brightness of the light 
shining on a candidate. The candidate most illuminated is elected. 
They are actions, and they have no real meaning outside the effect of 
the action, which is to illuminate candidates and thus participate in 
the choice.

Hence, I have written, it would be a political statement to encourage 
voters to vote "sincerely," or to use language on the ballot that 
connects sentiment with votes. To give an example, suppose an 
election official has the option of putting on a ballot, in an 
Approval election, the term "Approve," rather than the much more 
neutral term "Vote," or, more analogously, "Vote For" or "Yes." The 
official knows that the Nader voters often don't "approve" of Gore, 
and that using the language of "Approve" may influence them to not 
mark the Gore position. If the official favors Bush, would it improve 
the election results from the point of view of this official to use 
the language "Approve."

I'd suggest it almost certainly would. Voters are sensitive to small 
details of ballot design; the first position, for example, tends to 
get more votes.

The description of Range Votes as "utilities" or "sincere 
preferences" is thus highly misleading. They are votes. Voters have N 
votes to cast in a Range N election, a Count All the Votes election, 
i.e., Approval. (that's how I define Range N). Now, if you have N 
votes, how should you cast them? It turns out that a very good 
strategy is to use normalized utilities, normalized to the election 
set, the frontrunners only. In an Approval election, indeed, this 
results in standard Approval strategy. In Range, it does well also. 
But are these "sincere utilities"? By the standards used by some 
writers, no. They will equate candidates when a candidate is 
preferred to another. By defining the *meaning* of votes, so that 
this practice becomes "insincere," what should be a practical 
decision is turning into some kind of apparent moral violation.

It's political. It should have no place on a ballot or in any 
official public description of a voting method. It can deceive 
voters. And much of the writing against Range is based on an 
assumption that this is how Range will be described.

>>> > What I ended up suggesting was that the problem is resolved if the
>>> > voters negotiate. It's possible to set up transfers of value (money?)
>>> > such that the utilities are equalized, and that the benefit of
>>> > selecting C is thus distributed such that the A voters do *not* lose
>>> > by voting for C. If they vote for A, they get A but no compensation.
>>> > If they vote for C, they get C plus compensation. If the utilities
>>> > were accurate -- Juho claimed that they were *not* utilities, but
>>> > that then makes the problem incomprehensible in real terms -- then
>>> > overall satisfication is probably optimized by the choice of C with
>>> > compensation to the A voters, coming from the C voters. Certainly the
>>> > reverse is possible, that is, the A voters could pay the C voters
>>> > compensation to elect A, but it would have to be much higher 
>>> compensation!
>>>
>>>I understood this. But I consider it quite absurd that the A 
>>>voters should be "compensated" for anything.
>>
>>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!

>  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.

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.

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. Depending on the original absolute utilities on which each 
voter is basing those ratings (and I'm not assuming that the ratings 
are votes, they are, rather, preferences including relative 
preference strength), the outcome of C could be a good compromise, or not.

>>Indeed, if that is all the information we have, C is the best compromise.
>>
>>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. 
Compensation, properly arranged, actually balances out the loss, so 
that nobody loses, and, indeed, if we accept that some choice *must* 
be made, it causes that choice to become a consensus one. This is 
*clearly* more democratic.

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!

>  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?"

In the real world, the majority generally has power, if it is 
organized. In the real world, if you want to get the majority to 
benefit a minority, to give up some small benefit for themselves in 
order to provide a larger benefit to a minority, you have to get 
their permission *or* you have to coerce them in some way.

Underneath all of what Jobst has proposed is an idea that, somehow, 
the majority must be *coerced* into accepting the supposed 
compromise. I'd say that this is very poor thinking, old thinking, 
and quite antidemocratic. If the choices are arranged properly, not 
only will a majority accept them, without any coercion at all, but 
*nearly all* will accept them. They will be consensus choices.

But it takes deliberative process to accomplish this, a pure election 
method is not going to cut it.

>>Suppose it is realized before the election that B is not a viable 
>>candidate, and we do not consider B at all. What we have left is
>>
>>55: A>C
>>45: C>A
>>
>>What is the optimal outcome? For ranked methods, it is obvious.
>
>You think so? May I assume then that your "obvious" best outcome is 
>the same as mine, namely electing A with 55% probability and C with 
>45%? Because this would make it quite attractive to all of them to 
>search for a compromise that all would like better than this lottery.

But that's not an option. There are two candidates. They just happen 
to be the majority favorite and the good compromise -- from a utility 
point of view -- but we don't get that information from the ranked ballots.

Only if you impose some coercive superstructure *or* negotiation 
takes place, where the minority offers compensation to induce the 
majority to shift its vote, can you get the outcome of C in the 
election shown. Schemes which offer voters a choice by probabilities, 
I'd submit, are only likely to be used if they are forced on the 
voters. However, I'm certainly open to looking at specific, detailed 
proposals that would state exactly how this would be undertaken in a 
real election.

The probabilistic approach does *not* maximize utility because it 
assumes normalization, and the present situation is drastically 
distorted by normalization.


>(This is how far I got into your post.)
>
>Yours, Jobst
>
>>For Range and selfish voters, it is also obvious. Only the 
>>introduction of the irrelevent candidate makes it appear not obvious.
>>
>>But we do have more information than the ranks. *If* we assume 
>>commensurable utilities in the original votes, then we can say much 
>>more. There is a relative preference strength, commensurable, of 
>>100:80 for the A voters and 80:0 for the original B voters.
>>
>>The majority has a weak preference and the minority a strong one. 
>>There is a complication, if this is a real election. The majority 
>>will have reduced motivation to turn out, so if we actually get a 
>>55:45 preference in the  final poll, the *real* preference would be 
>>greater than that, generally. Forcing all voters to turn out warps 
>>elections unnaturally, causing true weak preference to become equal 
>>to strong preference.
>>
>>The common argument that strong preference is somehow selfish is 
>>seriously flawed, because true knowledge will cause strong 
>>preference. The *knowledgeable* may have a weak preference when 
>>they understand the complexity of a situation, but they will have 
>>have a strong preference when they see clearly. Forcing complete 
>>voter turnout *seems* like it will make results more "democratic," 
>>but, in fact, it amplifies the effect of media manipulation of 
>>voters, since this manipulation is more effective with those who 
>>care less, who are not motivated to research and reflect deeply.
>>
>>In any case, consider the result shown above. Why should we choose C?
>>
>>Well, what if there were a free negotiation between the A voters 
>>and the C voters. At an appropriate transfer of value (*no 
>>presumption exists that it is from C to A, it could be the 
>>reverse*), and if the two factions were uniform, the vote would be 
>>come unanimous, and, because the S.U. winner will optimize overall 
>>value to society, it is highly likely that the transfer would be 
>>from the C voters to the A voters.
>>
>>But it could be in the other direction; however, that would make 
>>sense only if the commensurable utilities were different than 
>>stated. This is why I wrote about a transfer from the B voters to the A voters.
>>
>>Consider the possibility that the B voters are rich and the A 
>>voters are poor. The A voters need that extra value more than the B 
>>voters. The transfer suggested by the commensurable utilities does 
>>not consider this, it simply equalizes the benefit from the result 
>>of choosing C, spreading it uniformly acrcoss society instead of 
>>selectively benefiting one faction.
>>
>>The theory of this, that allows such unequal benefit, is justified 
>>by the assumption that over many elections, the value is spread. 
>>But that assumption is clearly accepting an unsatisfactory 
>>solution, perhaps because the negotiations are considered too 
>>complicated or difficult. It is *not* because they would be unjust, 
>>no, they would be *accurately* just.
>>
>>This has become, from this discussion, crystal clear to me. 
>>"Tyranny of the majority" applies, really, to any decision made by 
>>less than consensus. A truly just system would equalize benefit 
>>from all decisions -- or, more accurately, it would link decisions 
>>such that benefit is equalized. The decision to build the public 
>>facility at C is a separate one from the decision that the 
>>residents of neighborhood B would be taxed more to compensate for 
>>the increased convenience to them, but a negotiation would link the 
>>two decisions -- and perhaps would substitute a voluntary offer in 
>>compromise, made in escrow, for a tax.
>>
>>It makes sense for the C voters to offer to compensate the A voters 
>>for their relinquishment of their preference; and the most just 
>>compensation is one which equalizes benefit, such that all equally 
>>benefit from the result of the election.
>>
>>The beautiful thing about the negotiation is that it equalizes 
>>utilities *without* having to use commensurable utilities in a 
>>Range election. The negotiation shifts utilities until all votes 
>>will vote, in their own self-interest, for the best compromise.
>>
>>That C is even called the "compromise" candidate shows that Jobst 
>>recognizes that there is a loss. Is the loss shared equally? This 
>>could also be stated in term of differential gain, but, in fact, 
>>the term for this is "utility."
>>
>>It is fashionable to state, "I don't believe in utilities," but if 
>>we look at what this could rationally mean, it must mean, not that 
>>there are no utilities, but that it is impossible to measure them 
>>in a way that makes them useful. Opponents of Range Voting are 
>>claiming that the distortions of strategy (including the necessary 
>>"strategy" or algorithm used to convert utilities to votes) make 
>>utilities useless.
>>
>>But, in fact, that is an assertion that I have never seen proven. 
>>Rather, we can study election methods by positing utilities and 
>>seeing how they behave with various distributions of utilities 
>>among voters. Essentially, there is a Utility Measure that 
>>evaluates election methods based on how often they choose the S.U. 
>>maximizer, and, properly, when they do not, how great the loss of 
>>utility is. This is the work that Warren Smith has done.
>>
>>It does *not* mean that utilities are actually used by the method. 
>>Rather, posited absolute utilities are used to create voting 
>>patterns, based on various strategies, and the method deals only 
>>with the voting patterns.
>>
>>However, there can be circumstances with elections where the 
>>utilities become known. And free negotiations to compensate voters 
>>for voting a certain way, can discover absolute utilities. If there 
>>is no secret ballot, it becomes relatively simple, but various 
>>devices can be used when there is secret ballot, and vote buying -- 
>>which, as it has existed, is a form of corruption -- should become a nonissue.
>>
>>(What is offensive about vote buying is when it is secret and used 
>>to shift an election result, with compensation only to a few 
>>voters; such buying does *not* equalize benefits, rather it 
>>distorts them even further. Suppose the B voters get together to 
>>make an offer to a selected subset of the A voters, just 6% of the 
>>electorate. This would cost them less than compensating all the A 
>>voters. Even if they paid these voters double the fair 
>>equalization, they would be ahead. A subset of the A voters, about 
>>10%, gains all the benefit of the compensation, and the rest of 
>>them are uncompensated. In practical terms, however, it would be 
>>difficult to keep such an offer secret with such a large group, and 
>>so such a secret manipulation would only make sense if the gap 
>>between the A and B factions was smaller. There remain implications 
>>unexplored here.)
>>
>>>  This would be only justified if something was taken from them 
>>> which in a sense belonged to them rightfully.
>>
>>That is correct. And something is is taken which is legitimately 
>>theirs, which is an equal share of the benefits of social 
>>decision-making. other things being equal. We routinely accept 
>>inequality in this, but that does not mean that it is just to do so.
>>
>>(Other things being equal means that, for example, all are paying 
>>the same taxes. Note that I gave a real-world example of 
>>equalization, it seems that all this has been wasted on Jobst. 
>>Equalization works and is recognized as just by those participating 
>>in it, including those who pay, effectively, to the others.)
>>
>>>  What my arguing is all about is that I don't think the A voters 
>>> have such a right to the certain election of A, at most one could 
>>> perhaps say the have a right to A getting at least 55% winning probability.
>>
>>Jobst gets here by assuming that it is a given that the A voters 
>>are going to participate in this society, that they are not going 
>>to walk, presumably because they will not be allowed to.
>>
>>What he is doing is presuming fixed election outcomes, that cannot 
>>be modified to make them agreeable to all. He is assuming that 
>>consensus is impossible to obtain. The kind of negotiations I 
>>mentioned are free ones, and the negotiation is deliberative 
>>process. Election methods are dangerous because they bypass 
>>deliberative process, and this must be understood to understand the 
>>theory of elections. The problem of deliberation, the difficulty of 
>>it, appears when the scale is large, and because we have not 
>>developed the mechanisms which would make large-scale negotiations 
>>practical. But even if we accept that they are impractical -- and I 
>>believe that they *are* practical, and I believe I understand how 
>>it could be done, FA/DP -- this would not make them and their 
>>results unjust. His argument is that it would be unjust; what he 
>>wishes to do is to impose some system on this electorate that would 
>>*force* the A voters to accept the loss of their preference.
>>
>>But if we look at a small group with similar underlying utilities, 
>>even two people with A>C and C>A preferences, and we insist upon 
>>consensus in order to make any decision at all -- which becomes 
>>much more necessary when there are two people! -- the matter 
>>becomes clear. Would we think that these people should make the 
>>choice by lottery?
>>
>>Sure, if there is no better way. If they cannot, for some reason, 
>>negotiate with each other. If the utilities are not equal, one side 
>>or the other is going to, relatively speaking, lose. What is 
>>*normal* in social interaction, however is that some negotiation 
>>takes place. It may be a very informal one, based on something like 
>>"Well see your favorite movie this time and mine next time," or it 
>>may be quite formal, a contract that states, "You will do this and 
>>I will pay you that." It is *routine*. But Jobst, looking it 
>>through some very narrow slits, sees only the decision-making 
>>process, with restricted options, and no possibility of any 
>>compensation or negotiation that would make the result equally 
>>satisfactory to everyone.
>>
>>This way of thinking is common, it is a major obstacle to true 
>>reform. There are probably hundreds of held concepts that interfere 
>>with clear thinking about our situation, and it takes time to dismantle them.
>>
>>But we are doing it. I see great progress over the last few years, 
>>and it is accelerating. The necessary insights are becoming more common.
>>
>>http://www.bobdylan.com/songs/times.html
>>
>>
>>>  So, if they would prefer to have A with 55% and B with 45% over 
>>> having C with 100%, only then one could perhaps argue that they 
>>> should be compensated if C was to be elected with certainty.
>>
>>But that is exactly what is being proposed. The A voters are 
>>compensated in order to make the election of C certain. It's 
>>certain if they all agree!
>>
>>The lottery analysis is one which tests normalized utilities, not 
>>absolute ones. That's its defect. It works if the range of the A 
>>voters and the B voters is equal, such that the preferences stated 
>>are commensurable.
>>
>>I'm not sure I've seen a precise description of how the lottery 
>>would work, though, and perhaps I don't understand it. What I see, 
>>however, is that an election run in this way, with real utilities 
>>underneath, leaves part of the electorate with a different benefit 
>>than another part. Only one outcome can be chosen, we assume, so 
>>what we are trying to do is choose the one which does the least 
>>damage -- or produces the most *overall* benefit, without caring 
>>how this is distributed. This can fail rather badly if it creates 
>>even a small minority which is highly dissatisfied, they can start 
>>to sabotage the society. Even tiny minorities, highly motivated, 
>>can do a lot of damage! Think Shining Path.
>>
>>Spreading out the benefits of social organization such that all 
>>benefit from it equally -- at least roughly -- actually should benefit all.
>>
>>It is in our common interest to avoid the tragedy of the commons, a 
>>tragedy which results from isolation and anomie. When significant 
>>numbers of us stop caring about our neighbors and only seek our own 
>>personal benefit, we all lose, on average and typically 
>>individually as well. The oligarch who lives high off the fat of 
>>the land might be sacrificing his entire family, ultimately, for 
>>his momentary pleasures. Landlords did not do well in China after 
>>the revolution. There was great injustice to many, to be sure, but 
>>this took place because the society did not take care to distribute 
>>wealth fairly.
>>
>>I'm *not* proposing communism, it's certainly not clear that it's 
>>fair to *equally* distribute wealth, precisely because effort is 
>>not equal, nor is the benefit to society of that effort on the part 
>>of individuals. However, social organization should benefit all, it 
>>should always be a positive return for individuals to participate 
>>rather than rebel or subvert the system.
>>
>>And voluntary participation is always preferable to coerced 
>>participation, when that is possible. Indeed, coercion should be 
>>reserved for protection, where possible. I'm not settled, myself, 
>>on the issues of matters like solving the tragedy of the commons 
>>by, say, legal control, punishment, and taxes for maintenance. My 
>>sense is that better solutions exist, but, until we have them, I'd 
>>also prefer to leave the status quo. Destroying the protective 
>>mechanisms that have been built up over centuries, before having 
>>alternatives in place, proven to work, strikes me as foolish, an 
>>error that was made many times in the last century, with disastrous 
>>consequences. Perhaps I'm becoming a conservative in my old age, 
>>but not really. I'm just recognizing the true instinct underlying 
>>conservatism, a fear of premature change, a fear that has often 
>>been quite justified.
>>
>>Fortunately, we can reform the system without such premature, 
>>abrupt change. And we can start today. Subscribe to 
>>fa-dp at yahoogroups.com ( fa-dp-subscribe at yahoogroups.com )if you'd 
>>like to be part of the solution, or at least to watch it unfold. 
>>This is about far more than election methods, so I'll be shifting 
>>most of the discussion, for my part, away from the EM list; this 
>>post is going there as well as EM because there are FA/DP related 
>>issues that have come up. And there are other initiatives under 
>>way, I'll be pointing to them on the fa-dp list.
>>
>