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

[Abd ul-Rahman Lomax]

At 02:55 AM 8/22/2007, Jobst Heitzig wrote:
>A common situation: 2 factions & 1 good compromise.
>
>The goal: Make sure the compromise wins.

Simple. I'm in charge. I dictate and sign the election result.

Oh! You want a democratic election method!

>The problem: One of the 2 factions has a majority.
>
>A concrete example: true ratings are
>    55 voters: A 100, C 80, B 0
>    45 voters: B 100, C 80, A 0

"True ratings," I've been pointing out, is not clear in meaning. 
These ratings are obviously normalized, so they are not absolute 
ratings, and therefore we cannot tell what the SU winner would be. 
But if we assume that the "swing" is the same for all voters, and 
that the utilities are such that, say, a tax bid method would show 
those utilities, we do have a clear compromise winner.

>THE CHALLENGE: FIND A METHOD THAT WILL ELECT THE COMPROMISE (C)!
>
>The fine-print: voters are selfish and will vote strategically...

The method, of course, is a Range method. Ranked methods cannot 
detect the compromise winner, who, incidentally, violates the 
Majority and Condorcet Criteria.

However, Range does not convert the Moon into a big green cheese.

Let's assume that this is a full-knowledge election of a certain 
kind. The voters know at the outset the utilities of all the voters.

I have suggested Range with preference-triggered runoff. If the 
voters voted sincerely, there would be a runoff between A and C. The 
fact that a runoff occurs lessens the tendency that the voters would 
bullet vote, a tendency that would be otherwise strong.

(What election method would elect C if the voters decide to bullet 
vote, if they -- or the majority of them -- refuse to acknowledge 
their relatively high opinion of B? Voting with taxes might do it, 
which is an incentive to vote true utilities.)

>Good luck & have fun :-)

Now, suppose this were Range with preference runoff. This pattern, if 
voted, would trigger such a runoff.

The choice is now between A and C. As the conditions have been 
defined, the A voters will simply choose their preference.

But wait a minute! That is a weak preference, whereas the B voters 
now have a very strong preference. Range is no help, because both 
sets of voters would bullet vote, the B voters quite sincerely, and 
the A voters simply expressing their preference, which is normal. 
Unless, of course, there is a cost to voting that way, such as a tax 
you bid and pay if you win.

But this has largely been overlooked. If this is a public election, 
and people are going to the polls for a runoff -- which means that no 
other election is on the ballot -- turnout is normally low. The two 
groups, however, are now quite asymmmetrical in motivation to vote, 
the A supporters are only slightly motivated, whereas the B voters 
have high motivation.

So if there is a runoff, there is a very good chance that C will win.

However, this thinking may cause them to bullet vote in the original 
Range election. I'll point out, however, that if you have a majority 
so selfish as to be willing to take a huge overall hit in the degree 
to which elected officials enjoy broad support, in order to gain a 
small personal benefit, you have a society which is already in deep 
trouble. Frankly, I don't think that under current conditions and any 
that I can imagine, people are *that* selfish. Mostly, I think, in 
Range+PW, if we call it that, they would vote sincerely. The runoff 
would be held, which would test the preference strengths.

(And, contrary to the assumptions, most people will *change* their 
preference if they understand that others have strong preferences 
compared to their own weak ones. We are social animals. So, again, if 
the utilities given were accurate, and the electorate now knows this, 
there is even more force toward C winning. A voters will change their 
vote, and B voters will not, plus many A voters will abstain whereas 
B voters will be highly motivated to turn out and vote. If I lived in 
this society, I certainly would not be betting on A. If I were, I 
would also be buying a ticket out with my winnings. This society 
would be headed for major disaster, on the Ruanda scale. -- and if I 
lost the bet, I'd breathe a huge sigh of relief.)