[EM] Recursive Elimination Supervisor

[Tony Simmons]

Forest,

I found your scheme fascinating, and it worked with an
example or two I tried it with.

For three candidates, we first select one who wins
conventional IRV, and who we can figure is unlikely to be the
CL.  We're not sure, but that isn't necessary, since the
principal purpose of this step is just to cut the number of
candidates in the next step to two.

Then we compare the two "lower" candidates.  The one who
loses this comparison is definitely not the CW, and is
eliminated from counting.

Next, we compare the two remaining candidates.  Since the
candidate already completely eliminated is not CW, one of the
remaining two must be the CW, if there is one, and that is
the one that wins.

You have invented a Ranked Pairs method!

What's interesting is the way the method deals with a
situation in which there is no CW.  I haven't thought through
the complications sufficiently to know, but with three
candidates, is there a likelihood that your method would pick
a different winner than straight IRV?

Some other interesting things:  The first step is to find a
temporary IRV winner in order to find the first loser.  How
about just using IRV inverted to elect a first loser
directly?  Then eliminate him/her/it, transfer votes and
proceed as usual.

Or suppose:

    1.  Use IRV to select a temporary winner, say, A.

    2.  Select a loser from between B and C, say it's C.
        That leaves A and B.

    3.  Select a winner from between A and B, say it's B.
        That leaves A and C.

    4.  Select a loser from between A and C.  Suppose it's A.
        That leaves B and C.

    5.  Select a winner from B and C.  Suppose it's C.  Stop
        here and call C the winner.

You could keep iterating.  Does it converge to a single
winner every iteration?  If so, is it a better winner in some
sense than you'd get straight from IRV?

How much of a difference does it make if you use something
other than IRV?

Just some interesting possibilities.  I think.  Certainly an
interesting scheme.

    Tony