[Election-Methods] Challenge: Elect the compromise

[Abd ul-Rahman Lomax]

At 09:01 AM 8/25/2007, Jobst Heitzig wrote:
>Dear Steve,
>
> > Although Jobst may not have intended this assumption, I will continue to
> > make the assumption that the B minority's preference intensity for the
> > compromise C over A is much greater than the A majority's preference
> > intensity for A over C.
>
>Sorry, I had just not read carefully the first time. Of course that 
>interpretation is consistent with what I had in mind, although I do 
>not believe that preference "intensities" belonging to different 
>persons can be compared.

Yet by asserting that C is the best winner, the "just" winner was the 
word you used, you are doing just that. The problem is that strong 
preference for one voter may be weak preference for another, 
particularly when ratings (or utilities) have been normalized such 
that, for a specific candidates set, max rating and min rating are 
the same for all voters.

Humans are not necessarily rational, but the only theory we have for 
rational behavior is utility theory, and supposedly irrational 
behavior may be explainable by hidden utilities. That is, if I have a 
strong value, as an example, for being "sincere" and "honest," I 
might vote against my own apparent interests in order to vote 
"sincerely" or "honestly." Some game theory that does not take into 
account the matter of being sincere or honest might judge my behavior 
irrational. Not necessarily.

It is fairly obvious that humans do have some kind of utility 
scaling, it shows in our language about making choices, we "weigh" 
them. And the experience of making choices can feel very much like 
hefting objects to see which is heaviest. Most of us would not sit 
down and calculate, for example, dollar values for various candidates 
winning an election, but we *could*, and if there were a system in 
place where votes were bids, having a cost, we *would*.

And economic return is, by far, not the only consideration that can 
nevertheless be measured in, say, dollars. How much would you pay for 
an election outcome? Suppose you knew that if enough people voted 
like you, and you got what you voted for, you would have to pay the 
cost associated with it. That cost could include actual 
implementation cost plus compensation for losses incurred by others. 
(If we decide to seize land by eminent domain and build a school, the 
costs certainly will include compensation for the seized property.)

Now, utilities are, by custom around here, stated in positive units. 
If we are seeking to maximize individual utility or overall utility, 
that functions well enough. But, in reality, our impression of 
choices is bipolar, we are attracted by a choice -- and thus would be 
willing to pay for it, or we are repelled by it, and thus, to accept 
the choice voluntarily, we would require compensation. Which, for 
some choices, could be a *lot* of compensation (probably, 
collectively, dwarfing the resources of the wealthiest person on the planet).

(If you knew that you could, with the collective compensation 
obtained, save millions of lives by, say, allowing the election of 
Bush at a time like 2000, even though you knew, let's say, that what 
he will do will cost hundreds of thousands of lives, how would you 
choose? If you think the answer is obvious, think again. We make 
choices all the time that involve loss of life for a few, at least. 
How much do we put into neonatal medical care? We use automobiles, 
when it is known that there will be a certain level of accidents, and 
on and on. Actually taking responsibility for the choices we make as 
a society is *difficult*, which is one reason why, I suspect, people 
are averse to realizing how much power they have. If we think it is 
all controlled by *them*, why, we aren't responsible for all the bad 
stuff that comes down. It's *their* fault.)

In any case, a more realistic statement of utilities would be one a 
scale that includes negative numbers; zero then represents a neutral 
point, where one is neither attracted nor averse to an outcome. One 
would not pay for this outcome, nor would one need compensation to 
accept it. (Except by comparison, which is another matter).

This kind of discussion often brings up a huge red herring: that some 
people can afford to pay more than others, and, allegedly, a Clarke 
tax would essentially create a plutocracy. The flaw in this is that, 
almost by definition, the wealthy are few.

The wealthy are wealthy precisely because the stand atop a pyramid of 
people of lesser means. Without that pyramid, their wealth would be 
meaningless. What would a million dollars, or a billion dollars, mean 
if there were not people of lesser means willing to work for you or 
sell you things for that money? Money is a social convention, a means 
whereby we allocate and distribute power and control. If someone has 
obtained money, they can then mobilize, with it, certain resources of 
society as they see fit.

We do not, in general, have any agreement, any social contract, that 
requires us to recognize the value of money, except for debts stated 
in specific currency. If nobody is willing to shave the Barber of 
Seville, he cannot compel it with money, he can only offer it. The 
price someone would charge for that shave is not fixed, in general. 
(It can be in places, and those are places where there is no 
democracy, there is, instead, repression and oligarchy and coercion. 
The actual payment for the shave is in two parts: one, an exchange of 
currency, and, two, we won't put you in jail.)

Studying utility in elections through utilities does not mean that we 
should actually encourage "sincere voting" by attaching some 
proportional cost to the votes. Rather, I bring up such things as a 
Clarke tax and bidding for votes to point out that there *can* be 
commensurable utilities, and that, indeed, it is these utilities 
which are maximized by fully sincere, non-normalized votes in a Range 
system. It is not necessarily the normalized utilities that Jobst fed 
us. Those are utilities which have been modified to expand the 
preference strengths for a particular candidate set into a single 
vote span, the Range in a Range election.

> > (I am NOT saying there is a way to measure or
> > compare sincere preference intensities or utilities suitable for input
> > into a good vote tallying algorithm.)  Without an assumption like this,
> > we would have no reason to believe C is better than A for the society.

Eppley is almost entirely correct. When you say "no way," it raises 
my hackles a little. There is a way. Not perfect, but a way, and that 
way is to, precisely, assume that the scales are commensurable, 
because, on average, they will be. But that does not mean that they 
are commensurable *in this election*, unless we make the assumption, 
which is what he did.

>I think we have! The reasoning is this: 55% like A best, 45% like B best.

Yes. We have that.

>  Therefore the "democratic benchmark" solution with which we should 
> compare prospective solutions is the lottery that elects A with 55% 
> probability and B with 45% probability.

The algorithm has not been explained. I'm going to guess that its a 
pure preference election, and the percentages are assigned to the 
first preference of that percentage of voters.

>  Now, all voters prefer C to this benchmark, but only 55% prefer A 
> to this benchmark and only 45% prefer B to the benchmark. From this 
> point of view C is a better solution than A is.

Do all voters prefer C to the benchmark? It's true that we can 
neglect the commensurability of utilities here, all that matters is 
that the utilities are internally useful.

The A voters look at this: return for A, 100. Return for B, 0 Return 
for benchmark, 55 average, Return for C, 80.
The B voters look at this: return for A, 0. Return for B, 100. Return 
for benchmark, 45 average. Return for C, 80.

Yes, C is definitely a good bet for all voters. I wouldn't take the 
risk, myself.

"From this point of view," is the kicker, though. The point of view 
is one which assigns the benchmark based on the number of first 
preference votes. The result is, certainly, that C is the best 
choice, *but* we have elsewhere shown that with some real utility 
patterns, i.e, absolute costs or benefits, C is quite unjust. All 
voters prefer C to the benchmark, but that does not mean that the 
outcome is the best outcome.

Only if you can establish that the benchmark is fair would this 
actually work. And clearly it is not, if the normalization of 
utilities has caused a major loss of information. If the utilities 
are equally normalized, that is, the full range of preference is the 
same for all the voters, then the benchmark is indeed fair. But if 
the B voters, for example, really have very little at stake, overall, 
and what we are seeing with their utilities is really a small 
preference range, overall -- as might become visible if there were 
two more candidates that everyone disliked, one the one side, and 
that everyone loved, on the other -- and then the A voters actually 
have a much larger preference range, C could be a very bad choice.

In a previous response, I have the example of a choice of site for 
some public facility. If the votes are distances (inverted Range, 
lowest total wins), and the A voter ratings were A 0, B 100, C 20, 
whereas the B voter ratings were A 10, B 0, C 2, we would have the 
same relative ratings as what Jobst gave us. But the absolute ratings 
would be quite different. And the optimum choice, overall, would be A. Totals:

55 A   0, B 5500, C 1100
45 A 450, B    0, C   90
------------------------
    A 450, B 5500, C 1190.

A is clearly the optimal choice for the community.

Sure, the A voters would prefer C to the benchmark. Because the 
benchmark is quite unfair.


>But I hope that also without this kind of reasoning it should be 
>obvious that a compromise which everybody likes almost as most as 
>her favourite is a better election outcome than one of the polar favourites...

Depends on what "almost" means. Please consider the site choice 
election I described. It just happens to be a way of describing 
utilities that makes them commensurable, and it shows how 
normalization distorts them, making small preferences equal to large 
ones, sometimes.


> > In other words, I believe
> > we should confine ourselves to solving the "Tyranny of the Nearly
> > Indifferent Majority" but not try to solve the "Tyranny of the
> > Passionate Majority."

Of course. But the solution is already with us. It is full 
deliberative process, undertaken in a small group that represents the 
whole society. Because of various flaws in the system, it does not 
always work under current conditions, but it *does* work much more 
often than simple preference analysis would indicate. In a 
functioning legislature, members *do* work out compromises that bring 
broad support. This doesn't make for such entertaining news as the 
issues where they duke it out, eking out a small victory for one side 
or the other, which is sometimes a pyrrhic victory. But its normal 
business for most legislatures, most of the time. Recent years have 
been bad for the U.S. Congress in this respect, though.

No election method is going to take the place of this; however, 
deliberative process can choose and use *any* election method it 
considers helpful. I've seen polling used to quite good effect, 
bringing a result where the clear preference of a majority was passed 
over to select an option that enjoyed, in the end, unanimous consent. 
It's even possible, here, that the final choice was not the S.U. 
optimizer, in a simple sense, this was an organization where group 
unity was highly valued. That is, making a choice that had universal 
acceptance had *extra* value. So what happened was that the majority 
shifted its preference when impacted by the knowledge of preference 
strengths (and the reasons behind the preferences).

>You suggest not to solve the problem of the "Tyranny of the 
>Passionate Majority"? Why? Shouldn't problems be solved?

The solution to that problem is education of the majority, and good 
leadership, not substituting some hidden higher authority, which is 
the bottom line if election method trumps the consent of the majority.

> > In the real world, it is much easier to elect a compromise than Mr.
> > Lomax seems to be saying below, because in the real world the set of
> > alternatives is not fixed to {A,B,C} by nature (nor by Jobst).

"Seems to be" was a correct hedge. It is *often* true that the 
problems I note with election methods are ameliorated in the "real 
world" by various factors, typically ones that introduce elements of 
deliberation. For example, we do not spring elections on voters with 
no preparation. There is, first of all, the nomination process, which 
is part of the *real* election system (one which some want to 
eliminate, thus moving toward pure aggregation, a bad move on 
principle). And then there is the campaign and public debate. All of 
this means that there is more than meets the eye, there is no just 
the final poll to analyze. And then, of course, many voters do vote 
strategically. They take into account poll information as well as 
their general sense of how their friends and acquaintances feel.

>   Most
> > procedures allow a very small minority to add an alternative to the set
> > being voted on. (Under Robert's Rules of Order, for instance, only two
> > people are required: one to propose alternative D and the other to
> > "second" the proposal.)

Of course, I've noted similar many times. Eppley is referring to the 
standard process for nomination, in some peer organizations. In 
others, petitions are required, and it gets dicier, sometimes the 
"small minorith" is too large, or the process too cumbersome.

More often, I mention that standard deliberative process for election 
by ordinary motion not only allows the equivalent of nomination as 
mentioned (it just takes two to insert a candidate into the process), 
but it is also Condorcet compliant.

If not for problems of scale, we would not need election methods at 
all, beyond being able to participate in deliberative process and 
vote Yes or No on the motions as they appear and are modified to 
their final form. Since I'm proposing that representation does not 
require elections, indeed, elections for representation, in the sense 
of contests where there are winners and losers, guarantee loss of 
representation; under the current system, it is a reasonable 
assertion that most people are not represented in our legislatures, 
other than by representatives chosen by someone other than them.

So, if I had my druthers, and I think ultimately I will, though not 
necessarily in my lifetime, which is getting fairly short, I would 
make almost all of what we call "election methods" footnotes in 
history, what people did when they didn't know better. What would 
remain are two things: pure and full chosen representation in 
process, where only the most intransigent and isolated of individuals 
are not represented, *and* direct voting for those who are willing to 
vote in public (Asset Voting for the rest). Because of the direct 
voting option, even highly isolated voters are not deprived of their 
right to consent or not consent to any public action.

The other thing that would remain is voting on issues, and among the 
issues is the election of officers. While election methods can be 
used to create a nomination, in the end any election must be ratified 
-- i.e., accepted -- by a majority, as a minimum. Healthy societies 
would strive to see them accepted by much more than that.

>It seems you and Adb ul-Rahman try to convince us that the problem I 
>posed does not exist in the real world. Well, if you really think 
>so, I can't help it.

No, I think we are pointing out to Jobst some things that he has 
overlooked, some assumptions that he has made which are distorting.

Further, the comment about the real world problems not being so bad 
was not intended, I'm sure, to say that there was no problem, only 
that the real situation is not as bad as we might think just from the 
analysis that has been presented so far. The "tyranny of the 
majority" is ameliorated by many factors, in actual practice. 
Logrolling is only part of this.

>Anyway, it would be nice if you could still give a hint what kind of 
>method you would suggest to solve the stated problem *assuming* that 
>the problem exists :-)

Certainly I think I have done that.