[EM] Obvious Elimination

[Forest Simmons]

At each stage, among the remaining candidates let MaxTop and MaxBot,
respectively, be the candidates with the largest Top and Bottom counts ***.

Let COACC be the candidate with the greater of these two max counts.

Eliminate every candidate X  that is outranked by the COACC candidate on a
majority of those ballots that show any preference between them ....
between X and the COACC, that is.

Also eliminate COACC itself if its Bottom Count is greater than its Top
Count ... otherwise keep it.

***[At any stage a candidate's Top count is the number of ballots on which
it is not outranked by any remaining candidate. Similarly, its Bottom count
is the number of ballots on which it outranks no remaining candidate. These
Top and Bottom counts are supposed to be updated (by vote transfers from
eliminated candidates to those remaining) between all elimination stages.]

Example

48 C
28 A>B
24 B

MaxTop and MaxBot are C and A, respectively, with counts of 48 and 72.

Since 72 is larger than 48,  the obvious approval cutoff COACC is A, and
because A's bottom count is greater than its top count, A itself will be
eliminated along with the candidate B, that is disapproved because it is
outranked by A=SOACC on a majority (28 to 24)  of the ballots that show any
preference ... leaving C as the winner.

Note that the cutoff candidate SOACC will always be someone that should
obviously be approved (most Top) or else someone obviously disapproved
(most bottom).  Of these two obvious choices, the more obvious of the two,
the one with the greater max count, is the SOACC cutoff.

This completely resolves the two most difficult approval questions ...
where to place the cutoff between approved and disapproved, and whether or
not to approve candidates ranked exactly on the cutoff boundary. The voters
don't have to worry about it at all unless they want to over-ride the SOACC
cutoff for some personal reason.

Anybody find any significant fault with this method compared to their
previous favorite?

Easy or hard to understand?

Likely or unlikely to elect the "best" candidate?

Easy to sell or hard to sell?

Best selling point?

Biggest drawback?

Thanks!

-Forest
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