[EM] The "Turkey" problem and limited ranks

[Gervase Lam]

> Date: Sun, 25 May 2003 10:10:12 +0200 (CEST)
> From: =?iso-8859-1?q?Kevin=20Venzke?= <stepjak at yahoo.fr>
> Subject: Re: [EM] The "Turkey" problem and limited ranks

> 48: A>B>C  (A worth 100, B worth 15, C worth 0)
> 2: B (B worth 100, A and C worth 0)
> 48: C>B>A  (C worth 100, B worth 15, A worth 0)

> In Approval, unless A or C look hopeless, only the 2 voters will
> approve B.  The other 96 voters are better off trying to break a
> 100-15 tie than a 15-0 one.  Thus the average utility of the winner
> is improved by collecting information on preference priorities.

Interesting to see how things look with the "one step up" improved 
Approval (i.e. MCA).

At first, I thought that if MCA were used, B would be the winner.  But 
now, I'm not 100% sure.  It depends on how anxious 96 voters are at 
showing on their ballots that B is better than their worst enemy by 
putting B in the middle slot.  I think the voters most probably would.

Thinking about this a little more, the 96 voters might even put B in the 
top slot because their worst enemy is very close to the 50% mark.  Would 
the voters use Approval strategy if normal Approval were used?  If so, 
they might do the same thing and vote for B as well as their favorite.  It 
really depends on what type of "Approval" strategy the voters in MCA and 
normal Approval use.

May be Forrest is right in saying that the number of slots should be 
square_root(Number of Candidates).

Thanks,
Gervase.