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

Okay, here is my solution. The B voters gain some very substantial 
advantage for the election of C over the favorite of the A voters, 
who have only a substantially smaller preference for A over C.

So the B voters offer something of value to the A voters to 
compensate them for their loss. As an example, they promise to donate 
to the public treasury an amount sufficient to compensate the A 
voters for their loss of value, thus, essentially, paying a 
differential tax in order to get what they want. The payment is 
either irrevocably secured, if C is elected, or on deposit with a trustee.

The original conditions assume commensurability of utilities, so the 
ability to pay is actually equal among the voters. Payment might not 
be in cash, but in terms of some other cooperation. (This is somewhat 
counter-intuitive, but I won't explain it here.)

In deliberative process, this happens all the time. "I'll vote for 
your bill if you will vote for mine." Logrolling, it's called, and it 
is a basic feature of democracy, making majority rule far more 
flexible than it might otherwise be. Sometimes common practices are 
there for a reason, and taking steps to outlaw them or make them 
difficult could actually harm the process far more than allowing it, 
and, perhaps, making it more explicit.