AV/IRO with equal rankings

[Bart Ingles]

There was some discussion a while back about how to handle equal
rankings in IRO.  The two methods discussed were fractional votes, and
treating them as multiple whole votes.  I believe it was decided that it
wouldn't make sense for anyone to use fractional votes, while allowing
multiple votes would cause a rich party problem (and also violate the
spirit of IRO).

It seems to me that the only remaining solution would be to use these
votes conditionally, in effect creating a ranking for them at the time
they are actually used.  You could do this based on the strength of the
candidates in question, so that a vote for (A=B) would be interpreted as
A > B if A had more unconditional votes.  Note that the opposite
wouldn't make any sense, since this could allow a neutral vote to
overturn the decision of others who had definite rankings for A and B.

When all but one of the equal ranked candidates are dropped, the vote
becomes a regular vote for the remaining candidate.  For example, if B
is dropped, the vote for (A=B) is converted to an unequivocal vote for
A.

Since an equal vote would always give highest ranking to the candidate
with the most unequivocal votes, it could never be used to prevent a
candidate from being dropped under IRO.  In practice, this makes
evaluation simple:  just ignore equally ranked votes until only one of
the candidates remains.

Example:

40 A B
25 B
11 (B=C)
24 C B

In the first round B beats C 25:24, so (B=C) is converted to (B>C).  You
now have 40A > 36B > 24C.  C is dropped.
In the second round you have 60B > 40A, so B wins.

Since the equal votes have no influence over which candidate is dropped,
you can ignore them:
In the first round ignore (C=B), so you have 40A > 25B > 24C.  C is
dropped.
In the second round you have 60B > 40A, so B wins.

This seems to conform to the spirit, if not the general definition of
IRO.  It still uses only the top level of choices in a given round, but
probably makes better use of them.

Bart Ingles