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

[Gervase Lam]

> From: election-methods-bounces at lists.electorama.com
> [mailto:election-methods-bounces at lists.electorama.com] On Behalf Of Jobst
> Heitzig
> Sent: Wednesday, August 22, 2007 1:55 AM
> Subject: [Election-Methods] Challenge: Elect the compromise when
> there'reonly 2 factions

>    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...

One silly method is to use Range Voting except instead of summing the
"utilities", they are multiplied instead.  This results in:

A: 100^55 * 0^45 = 0
B: 100^45 * 0^55 = 0
C: 80^100

However, this similar to Veto Voting!  I had thought of this before as
it is a way of determining "consensus."  What would be nice if there
were a mathematical operator that is mixture of addition and
multiplication.  Or may be some other method to tone down the harshness
of multiplication.

As a compromise, what I thought of doing was to slowly increase the
minimum utilities of each ballot (possibly re-normalising the C
utilities while this happens) until two candidates get (equal) top
scores.  The two candidates then go to the second round of voting.

However, doing this in this scenario, it is inevitable that candidates A
and C will go to the second round...

Thanks,
Gervase.