[Election-Methods] Elect the Compromise

[Abd ul-Rahman Lomax]

this discussion has developed, for me, a number of interesting ideas, 
it exposes certain aspects of election methods that have been 
otherwise obscured.

At 06:05 PM 8/28/2007, Forest W Simmons wrote:
>Jobst,
>
>so you were thinking of Borda where equal rankings are not allowed. Why
>didn't I think of that?

Now this is certainly interesting. I didn't see the post here where 
Jobst gave that answer, but maybe it was implied and I missed it, 
which could easily happen. The ratings, then, were a serious red 
herring. All that would matter is the ranking.

"Equal rankings are not allowed" requires some conditions that are 
problematic. First of all, this requires that all voters rank all 
candidates on pain of having their ballot tossed. Further, it is 
assumed, for this to work for the stated goal, that write-in 
candidates are also not allowed. This has implications beyond the 
functioning of the method itself, but reaches into how candidates 
make it onto the ballot.

And, of course, it's vulnerable to turkey-raising. I was assuming, in 
my consideration of the problem, what is often assumed in dealing 
with election methods, that the three candidates were merely the top 
three. For example, most studies of election methods, considering a 
candidate set, don't even think about write-ins; they are mostly 
irrelevant, they are only a little noise around the bottom. In 
bottom-elimination, they are gone quickly, leaving us with a smaller 
election set. Unless, of course, a lot of people write them in....

I'd never before taken a close look at Borda Count. It is essentially 
Range with a restriction; in my view it is close to Range, the 
underlying machinery is more like Range than other ranked methods, 
but, of course, it is strictly a ranked method with ranks being 
defined as of equal preference strength.

Let me be explicit about how this could elect C. I will modify the 
way Borda count from how it is usually stated to make it equivalent 
to a Range 2 election (CR 3).

55: A>C>B
45: B>C>A

Counts: A, B, C

55: 3 1 2
45: 1 3 2

totals:

A 210, B 190, C 200. This does not elect C. So I've misunderstood something.

Now, *other things being equal,* C is clearly a good winner, indeed 
the optimal one. But that is actually a strong condition, other 
things may easily not be equal. I gave an example of the *meaning* of 
these rankings -- I was assigning meaning to the ratings, but 
obviously, that meaning was then simply a possible meaning for the 
ratings that Jobst fed us as a distraction. The example was travel 
distance to a public site being chosen by the election, like the 
capital city distances used in Wikipedia election examples.

For 55% of voters, the distances are

A 0, B 100, C 20, thus the voter prefers A>C>B

while the B voter distances are

A 10, B 0, C 2, thus the voter prefers B>C>A

Which, now, is the "just" winner?

total travel distance for the community (assuming 100 voters):

A 450, B 5500, C 2000.

Which of these choices is more just?

The point that I have made, over and over, is that you cannot tell 
from rankings. Borda works, more or less, because *usually* there is 
some preference strength between candidates, and by assuming that 
this preference strength is an average value over the ranked 
candidate set, Borda approximates real preference strengths, and the 
differences will tend to average out.

However, the particular conditions of an election can easily make 
this fail. The travel distance example is one where we have an easily 
understandable, true utility basis for the preferences, the 
preference strengths as indicated in the original ratings (i.e, all 
voters had preferences of the kind 100, 80, 0, but reversed in 
sequence). Jobst claimed to not believe that utilities have any 
meaning, but this is reducing the meaning of elections to something 
quite arbitrary, pure, unexplained preference.

In the example I've given, if A is chosen, the A voters have minimum 
travel distance, 0 as stated, and they are in the majority. The B 
voters have maximum travel distance, but it is only 10 km more than 
the minimum.

If C is chosen, the A voters have a substantially increased travel 
distance, 20 km each, and that impacts a majority of voters, 55%, 
providing a smaller benefit to the B voters, a reduction in distance 
of 8 km over the A choice. In order to provide an 8 km benefit to the 
B voters, the choice of C would cost each A voter 20 km, and there 
are more A voters than B voters.

B, with the given distances, is a preposterous choice. It provides 
maximum benefit to the B voters, but the cost to the A voters is very large.

Jobst wanted to know why I considered the default to be A, when I 
suggested payment by the B voters if they wanted the election to 
choose C. Well, I didn't assign any special meaning to A, beyond the 
obvious one that the A voters were in the majority, so it made sense 
to consider the election from the point of view of the cost of 
shifting preference away from A. However, the situation is quite symmetrical.

Suppose the election is going to be followed by a ratification, and 
the peculiar rules of this community require that the ratification 
vote must be unanimous. How could this be arranged to make sense that 
all voters would prefer the optimal outcome, or be, at least, 
indifferent? And it's pretty obvious. The prevailing voters 
compensate the losing voters in some way, just enough so that they 
become indifferent, at least, but it is even more just if they all 
benefit equally, or, to invert it, that they all have the same 
overall cost, which has been minimized by choosing the optimal 
outcome, in this case, the outcome with the lowest net travel time.

That can be done in a real example -- and *is* done in one that I 
know of -- by providing all voters with a travel allowance that 
reflects the cost of travel from where they reside to the public 
facility. This travel allowance is assessed as a tax that all pay equally.

Now, I'm assuming here that all voters *are* going to travel to the 
center, the tax would actually be assessed, to be totally fair, per 
trip, and paid per trip.

Where is this actually done? Well, with one of my favorite examples, 
the very paradigm of the Free Association, Alcoholics Anonymous, with 
the national conference. They had exactly this problem: where do they 
hold the conference?

Did they choose the optimum location for minimizing travel distance? 
No. For other reasons, the Conference was set to be in New York, 
where the national office is located. That location predated the 
Conference. However, all delegates attending the Conference pay the 
same amount for travel, no matter where they are from. Yes, this 
means that if you live in New York, you are paying for travel about 
the same as if you lived in California. Is this fair?

Of course it is. The other common solution to this problem, done in 
another 12-step program, is to rotate the Conference, local areas 
around the country volunteering to host it. If AA did this, sure, 
were the conference to be held in New York, New York delegates would 
not pay anything for travel. But come next year, when it is held in 
Anchorage, Alaska ....

And, of course, every year a new set of people have to reinvent the 
wheel, reserve space, handle the thousand and one things involved in 
arranging a meeting for a substantial number of people. It's highly 
inefficient. While a more central site could have been chosen, New 
York is also a transportation hub, and because the national office is 
there, paid staff can be involved, and the same people do the work 
each year, and it's all documented, I'm sure, so a new employee can 
take over easily.

So, would the B voters pay compensation to the A voters in order to 
induce them to consent to the choice of C? They *could* pay them to 
induce them to choose B, but it's pretty unlikely that they would 
want to pay them enough.

And that option, that the B voters pay, I suggested only as one 
possibility. It would be more efficient, other things being equal, 
for the A voters to compensate the B voters. Reducing the total 
travel distance reduces the total cost to the community, and so, if 
it's going to be equalized, everyone's cost goes down, whereas 
settling on a less efficient choice raises the overall cost and 
therefore the equalized cost to everyone.

It's a bit shocking to me that this seems not to be obvious!

Conclusions:

Ranked ballots cannot collect sufficient information to optimize 
outcome to the most just result.
Range ballots can, but normalization and strategic voting causes the 
information to be distorted such that the optimal outcome is not 
necessarily selected.
Compensation or cost distribution can equalize utilities. Zero is 
commensurable! With the exact compensation, a voter is indifferent; 
the travel time will be inconvenient, but the compensation makes it 
not a burden.

Now, exact compensation is *defined* as that which makes the voter 
indifferent. Naturally, a greedy voter may pretend to need more to 
become indifferent, particularly if armed with good information about 
the position of the others and their ability to pay. However, this is 
where negotiation comes in, and where it is better for communities to 
negotiate, through representatives, than individuals. And we 
routinely solve this problem, it is solved every day by the market. 
Not perfectly, but, generally, adequately. Greed is restrained by a 
number of mechanisms, including preserving the freedom of choice of 
the participants, general knowledge of fair pricing, and so forth. 
And, the point I have been making, *in addition to that restraint*, 
there is shame, or the inverse of that, pride in serving the community well.

Serving the community well is the actual operating motivation of most 
small businesspeople that I see regularly. There are others, to be 
sure, but I don't see them very often! Why should I go into a small 
grocery where I think the owner is out to get as much as he can at my 
expense, and he'll take every opportunity to cheat me, when I can go 
into one where I walk in, the owner knows me and smiles at me, and I 
can tell that his goal is to do well by serving me well. The fact is 
that I'm willing to pay higher prices at that store! Not a *lot* 
higher, and, in fact, the one I have in mind is, for some things, 
very inexpensive, they have gone out of their way to find certain 
products that they can sell at lower than prevailing prices, they 
actually beat the big chain supermarkets *for those things*. Other 
things I buy at this market are for convenience, I don't want to 
drive the extra five minutes to get to a place where I can save a few 
cents or even a few dollars. But doing a big shop, I go to the big 
market, usually.

Am I suggesting that we should depend on people to make the best 
choice for the community? Of course not! But I do think we should 
give people the *option* to optimize their votes, which would mean 
voting in a more sincere manner than the exaggeration that would be 
involved if, in the distance example, a voter exaggerated votes to 
that they were distorted from the distances.

Suppose that the ballot actually has a means for marking the real 
travel distance. In this case, exaggeration would, in fact, be lying, 
and it could have a strategic advantage. Is this what would happen?

It depends. Any practical system is going to have to accommodate the 
possibility and continue to function reasonably well in the face of 
it. We have evidence that Range Voting does just this, and I see *no* 
evidence for the reverse.

(Ah, yes: utilities are commonly stated as positive values. But real 
voter preferences, and the underlying states, are more realistically 
arrayed over a spectrum of aversion/attraction. While this makes no 
difference to the relative sums, it explains voter behavior better.)