[EM] Orphan method?

[Alex Small]

On the Approval Voting list somebody brought up Rob Legrand's orphaned
voting method.  To recap:

1)  Voters rank the candidates.  (Assume for now, to keep things simple,
that voters don't truncate or rank candidates equal.  I'm sure there are
ways to handle that, but let's keep it simple for now.)  Each person's
vote is given to the top candidate on his/her list.

2)  If somebody has votes from a majority of the voters he/she wins.

3)  Otherwise, the 2 candidates with the fewest first-place votes are
compared pairwise, and the loser of that pairwise contest is eliminated. 
Anybody who had the eliminated candidate as his/her favorite has his/her
vote transferred to the next candidate on his/her list.

4)  Once again, see if anybody has votes from a majority of the voters. 
Continue the process until somebody has a majority.


I thought this is an interesting method.  For starters, it's
Condorcet-compliant (yes, I know, not everybody cares about that
criterion, but many do, and Condorcet methods can be interesting).  And
it's similar to IRV, so some IRV supporters might be interested.  (And, as
Bart Ingles pointed out on either this list or another one, some places
trying IRV in the US have vaguely-worded IRV statutes, so methods other
than standard IRV might be permissible under the law.)  However, as I
think about it I seem some flaws.

It seems to present a perverse phenomenon when there's a cycle.  Say that
there's a cycle A>B>C>A, and assume without loss of generality that A has
the most first-place votes.

There will be a pairwise contest between B and C, and C will be
eliminated.  And since A defeats B pairwise A will win.  This method is
therefore equivalent to plurality-completed Condorcet, at least in the
case of 3 candidates.

I think I prefer IRV-completed Condorcet to this method.  Although from
the description it seems to use information on the voters' full preference
rankings, in the end it's equivalent to a method using far less
information to break cycles.  IRV would break a cycle using 2 pieces of
information:  (1) how many first place votes each candidate has and (2)
the results of a pairwise contest.  This method really only needs the
first piece of information when there's a cycle.  So IRV-completed
Condorcet seems preferable.

Does this method have some virtues that I'm overlooking?



Alex Small