[EM] Democratic Fair Choice

[Jobst Heitzig]

Dear Folks!

Under the working title "Democratic Fair Choice", I described on our
Wiki a detailed voting procedure composed from ideas by Forest (most)
and me (some):
http://wiki.electorama.com/wiki/Imagine_Democratic_Fair_Choice
I tried to make it more interesting by writing it as a fictitious
television show reporting on an actual election -- hope you have some
fun reading it.

In short, this is what I suggest:
0. Each candidate simultaneously publishes a ranking of all candidates.
1. Each voter marks one candidate as "directly supported" and
arbitrarily many additional ones as "approved".
2. This is transformed automatically into an individual ranking by
placing the approved over the unapproved ones and completing the ranking
by means of the directly supported candidate's published ranking.
3. After booths have closed, direct support, approval, and pairwise
comparisons are counted.
4. A numbered list of voters grouped by directly supported candidates in
order of decreasing direct support is constructed like this:
   0000001-0821461: supporters of C
   0821462-1318964: supporters of F
   ...
Then each candidate submits in a sealed envelope a number between 1 and
the number of voters. The envelopes are opened in public, and the
numbers are added modulo the number of voters, giving the number of the
"proposing voter".
5. The published ranking of the proposing voter's directly supported
candidate becomes the "proposing order".
6. Only now the approval values and the matrix of pairwise defeats are
published, and the winner is the topmost candidate in the proposing
order who pairwise defeats all more approved candidates.

Essentially, this is "Random Ballot from Forest's set P", but without
the need to specify individual rankings, and with no "real"
randomization but instead with a sophisticated pseudo-random procedure
which is under complete deterministic control by the candidates...

I'm quite curious about your thoughts!

Yours, Jobst