[EM] Some chance for consensus revisited: Most simple solution

[Raph Frank]

On Sun, Feb 1, 2009 at 9:02 PM, Jobst Heitzig <heitzig-j at web.de> wrote:
> Dear folks,
>
> I want to describe the most simple solution to the problem of how to
> make sure option C is elected in the following situation:
>
>   a%  having true utilities  A(100) > C(alpha) > B(0),
>   b%  having true utilities  B(100) > C(beta)  > A(0).
>
> with  a+b=100  and  a*alpha + b*beta > max(a,b)*100.
> (The latter condition means C has the largest total utility.)
>
> The ultimately most simple solution to this problem seems to be this method:
>
>
> Simple Efficient Consensus (SEC):
> =================================
>
> 1. Each voter casts two plurality-style ballots:
>   A "consensus ballot" which she puts into the "consensus urn",
>   and a "favourite ballot" put into the "favourites urn".
>
> 2. If all ballots in the "consensus urn" have the same option ticked,
>   that option wins.
>
> 3. Otherwise, a ballot drawn at random from the "favourites urn"
>   decides.

The odds of it actually working are pretty low.  For it to work, all
voters must be aware that C is a valid compromise.

Assuming perfect info, then it would work.

However, if you change the voters to

55: A(100), C(70), B(0)
44: A(0), C(70), B(100)
1: A(0),C(30),B(100)

The votes would likely be of the form

55) A favourite and C compromise
44) B favourite and C compromise
1) B favourite and B compromise

In practice, there needs to be a reasonable threshold.  There is
always going to be a need to balance tyranny of the (N%) majority
against the hold-out problem.