[EM] Another statement of a very slight variation of Chris Benham's IBIFA (Forest Simmons)

[Forest Simmons]

My previous post gave the following slight variation of Chris Benham's
IBIFA:

Range style ballots are used.

While the equal top winner X has greater pairwise opposition than her equal
top score, modify the ballots by decrementing the old equal top ratings so
that the new equal top candidates include the old next-to-top candidates.

Upon exiting the While loop, elect the candidate X with the current
greatest equal top score.

However, I prefer the following similar method:

While

   for every candidate X there exists a candidate Y such that the number of
(potentially revised)
   ballots on which Y is rated greater than X exceeds the number of
(potentially revised) ballots on
   which X is rated equal top,

Do

    revise the ballots by decrementing the old equal top ratings so that
the old next-to-top
   candidates are included among the new equal top candidates on the
revised ballots.

EndWhile

Elect the candidate X with the greatest difference between the number of
(potentially revised) ballots that top rate her and her Max Pairwise
Opposition based on the current (potentially revised) ballots.

A third variant would just change this last paragraph to ...

Elect the candidate X with the smallest Max Pairwise Opposition based on
the current (potentially revised) ballots.

The following Participation Criterion holds for all three:

Suppose that an additional ballot is thrown into the mix and the winner is
re-calculated.

If the winner changes and the new ballot rates the old winner at a level
that became "top" at some stage of the old calculation, then the new winner
will be determined at an earlier stage than the old winner was, and will
come from among the "equal top" candidates of that earlier stage.
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