[EM] Maximum Consent

[Forest Simmons]

On 6 Aug 2001, Buddha Buck wrote in part:

> 
> Given four candidates for President: Al Gore, Pat Buchanan, Yog
> Shuggoth, or Cthulhu.
> 
> If my friend Barb and I were given plurality ballots, Our ballots would
> probably look like so:
> 
>   Buddha                 Barb
>    [Y]     Al Gore       [Y]
>    [ ]   Pat Buchanan    [ ]
>    [ ]   Yog Shuggoth    [ ]
>    [ ]     Cthulhu       [ ]
> 
> If we were given ranked ballots, we'd end up with
> 
>    [1]     Al Gore       [1]
>    [3]   Pat Buchanan    [2]
>    [2]   Yog Shuggoth    [3]
>    [4]     Cthulhu       [4]
> 
> If we were given approval ballots, we'd get
> 
>    [Y]     Al Gore       [N]
>    [N]   Pat Buchanan    [N]
>    [N]   Yog Shuggoth    [N]
>    [N]     Cthulhu       [N]
> 
> Only on the approval ballot does Barb get to indicate that she doesn't
> consent to be governed by Al Gore.

Knowing nothing about Yog or Cthulhu, I would duplicate Barb's approval
vote.

Nevertheless, Blake makes a good point [hitting my devil's advocate
argument in the jugular vein]; most real Approval votes are more or less
relative to the available choices. 

That's why Dyadic Approval and other refinements have potential to give
superior results to simple Approval. 

Note that dyadic ballots make explicit use of relative approval:

A > B >> C > D

Among A, B, C, and D this voter approves A and B.

But if C and D were out of the picture, this voter would only approve A.

Furthermore, if A and B were both out of the picture, this voter would
approve C relative to D.

Forest