[EM] Re: Total Approval Ranked Pairs (Was "Re: Ted's Total Approval Beatpath")

[Forest Simmons]

Here's the original recursive procedure that I gave for Approval Seeded 
Bubble Sort:

1. List the candidates in order of approval, from top to bottom.

2. Percolate the bottom candidate as far as possible up the recursively 
sorted list of the other candidates.

How's that for concise?

Jobst is right: the winner is the lowest approval score candidate that 
beats all of the candidates with greater approval, which turns out to be 
the same as the first CW that eventually appears as low approval 
candidates are eliminated successively.

Furthermore, the set P of all candidates none of which is beaten by any 
candidate with greater approval turns out to be the set of candidates that 
are as high or higher than the approval winner in the sorted order.



> As others (Kevin?  Gervase?  Alex?) have mentioned during the last
> couple of days, it could be easier to simply have two sets of
> rankings, some approved and some disapproved.  I think any even number
> of options from 6 to 10 would be adequate, with the approval cutoff in
> the middle.  Perhaps 6 would be a good starting point for a public
> proposal.
>

Using powers of two for the number of ranks makes the most efficient use 
of bits. Eight would be just right, requiring just three bits to rank or 
rate zero through seven:


Before marking:

   John Doe  (4) (2) (1)


After marking:

   John Doe  (*) (2) (*)

[John Doe's rating is five, the sum of the shaded bits.]



Forest