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

[Abd ul-Rahman Lomax]

Mr. Kislanko wrote directly to me, which I prefer not be done unless 
there is a specific reason for a personal communication, immediately 
disclosed. I'm responding to the list.

At 12:35 AM 8/31/2007, Paul Kislanko wrote:
>Any question about what method works that is turned into how a question
>about how humans behave is per-force an exercise in navel-gazing.

In a word, nonsense. How humans behave is relevant to election 
methods, or else we'd just do Range and leave it at that. Or 
Plurality, for that matter (if humans simply talk to each other and 
agree on what they want, Plurality is generally adequate as a test).

>No. The question was what method can elect C if all voters vote their
>natural selfishness, which is 55% A 100 C 80, 45 percent B 100 C 80.

I generally consider election methods in the contexts where they are 
used. There is no question about what happens with various methods if 
people vote according to known algorithms. However, they don't, at 
least not according to a single fixed algorithm. People use various 
algorithms to turn preferences into votes, they do it with various 
degrees of knowledge of the election context (i.e., election 
probabilities), etc.

The problem did not describe the "natural selfishness" of the voters 
as those ratings. Rather, it described this as their sincere 
preferences, and that was further clarified using comparison with a 
lottery, i.e., if we assume rational behavior, then those values 
would explain their choices in picking a certainty of an outcome 
against a lottery with those odds.

What "selfish" refers to would be the behavior of any faction of the 
voters in attempting to secure their favorite outcome, by voting 
"selfishly," i.e., strategically, *not* by voting their sincere 
preferences, unless strategy indicates that. Thus the problem boils 
down to selecting a method which would encourage them to vote their 
sincere preferences, or to otherwise respond such as to discover 
those preferences, even in the face of a majority attempting to 
defeat picking the compromise C in order to gain some preferential 
benefit for themselves, in the face of an apparent strong preference 
by a minority.

>If they vote as described in the (highly unlikely) conditions, then any
>method that allows them to split votes 5/9 favorite 4/9 second favorite
>solves the problem.
>
>All of the rest of the discussion related to this problem is noise.

No, though if Mr. Kislanko is correct, it would be error. Error is 
not noise. In fact, if you cannot express an error condition (and 
discover it, of course), you cannot correct your course. When we 
write erroneously to this list, it is not noise, it is *information* 
about our own incorrect understandings, and thus highly useful. It's 
only noise if you don't care about human beings, but only election 
methods. That may be true for Mr. Kislanko, but it's not true for me.

Is he correct? If the A voters know their position, why would they 
give 4/9 of a vote to their second choice?

As I've pointed out, the gap between the A voters' first choice and 
second choice could be quite large, in absolute terms. B would be 
practically suicidal (so to speak), and C is only proportionally 
better. The 20% reduction in preference suffered by the A voters in 
the selection of C might be greater in absolute terms, for each 
member of the A faction, than the 80% gain in utility for each of the B voters.

What this means is that C might *not* be the just outcome, in spite 
of the apparent situation, even if the ratings given are sincere and 
rational. The lottery method of testing the ratings will confirm 
sincere *relative* ratings, not absolute ones.

On the other hand, a Clarke tax, on the one hand, or, on the other, 
free negotiation between the factions for compensation to a faction 
which loses value from an outcome, would determine commensurable 
utilities. If these means, or similar, confirm that the ratings given 
may be treated as commensurable (that is, not absolute, necessarily, 
but covering the same range of absolute utilities for each faction), 
then we could say, indeed, that C would be the just outcome.

Another way to put this is that if the outcome of the method, with 
the given relative preferences, is C, it *could* be unjust, a poor outcome.

Far from being "highly unlikely," the meaning of which is, however, 
unclear, the ratings given would be appropriate and sincere for some 
physical layout of voter locations; perhaps there are two population 
centers in the town, and a layout of roads such that travel distances 
to a proposed public facility explain the ratings. A, B, and C, are, 
of course, locations for the facility.

The A voters have travel distances, in km., of A 0, B 100, C 20
and the B voters have travel distances of A 10, B 0, C 2,
to give an example where the utilities are sincere but the C outcome is unjust.

If we can arrange for the voters to vote absolute utilities in a 
Range election, the outcome will be just; however, it will not be 
*fully* just, all by itself, for it this choice does not distribute 
the benefit of making an optimal choice to all voters. Rather, we can 
say about the Range winner with these sincere absolute utilities is 
that this winner is *efficient*, one possible meaning of which is 
that compensation described to distribute the benefit would be minimized.

In the absolute example I gave, there is no C faction. That, by the 
way, is a rather strong refutation of the IRV proponent's argument 
that Core Support is an important criterion. C, with commensurable 
utilities, is clearly the optimal choice, but has no "core support."

In this example, A is in the majority, and, as it happens, its choice 
is optimal for reducing overall travel distance, assuming equal usage 
of the facility by all voters. Justice, however, would be increased 
if the A voters were to compensate the B faction for their increased 
travel time. Majoritarian systems often ignore this.

But suppose the utilities are not arranged in this way, suppose that 
the travel distances are as implied by the original statement of 
ratings, i.e, 100, 0, 80 and 0, 100, 80, in the same units; i.e., 
these ratings are commensurable as given. In this case C is the best 
choice, so the question then becomes, how do we coerce or induce the 
A voters, as the majority, to given up their preference and suffer a loss?

Since I'd prefer to avoid coercion, there is, then, an obvious 
solution: the B voters offer compensation for the choice of C. Put it 
another way, a set of payments is negotiated such that, for each 
outcome, the voters who benefit from that outcome are compensated by 
the voters who lose value. If we assume that the utilities are 
inverse from travel costs, including the value of time, then we can 
determine a matrix of compensations to be paid for all the outcomes, 
and it will be seen that the choice of C reduces the necessary 
compensation, since it is the most efficient choice.

And I gave an example of how compensation like that is actually 
arranged in a real organization, Alcoholics Anonymous; there is, for 
delegates to the annual Conference, a travel equalization plan, where 
all delegates pay the same travel cost, no matter where they live, 
into a fund, which is then distributed according to distance or other 
measure, I'm not sure of the details. Again, that would not be 
difficult to arrange in a real example as that described, though the 
political practicality might be another matter; it would, in fact, be 
simple: all citizens would be paid a subsidy, perhaps as a credit 
against their taxes, depending on place of residence and the travel 
distance to the facility, calculated to equalize the rational 
utilities. Taxes, of course, would be increased and the increase 
would be borne by all. Thus, other things being equal, such a scheme 
would distribute the maximized benefit of making the optimal choice, 
or, more accurately, the reduced overall cost of making the optimal choice.

However, the problem with the tax plan is that "other things" are 
generally not equal. Different citizens may have different values for 
their time, for example. So a free negotiation, if efficiently done, 
should be better able to balance true utilities, rather than a 
central planning kind of approach, unless the latter could somehow 
deal fairly with the more complex individual utilities. A Clarke tax 
type of scheme may be one means of doing this, but I pointed out how, 
even with Plurality, the citizens could negotiate the equivalent, 
inducing the majority to choose some loss in utility in order to give 
a minority a greater net improvement. After compensation, all 
factions would have the same cost or benefit *within their own 
estimation*, and they would, rationally, sincerely choose the optimal 
outcome, since that would provide them with minimal cost or maximum 
benefit over any of the other outcomes.

Is it necessary to detail the compensation necessary, or is it enough 
to provide the basic principles of how it would be done, i.e., 
equalization of cost or benefit?



The problem with the tax-based equalization