[EM] Simple Acceptable Ranked Choice Voting

[Forest Simmons]

It is well known that not all nice properties are compatible with each
other in a common single winner voting method. However, we shall see by
example that the following nice features are mutually compatible in a
simple RCV voting method (MGCB defined below). Therefore, excluding any of
them can only be justified by trading in the excluded ones for equally
important ones in an equally simple method.

1. The method should be clone independent like IRV ... therefore not
plagued by the spoiler problem like First Past The Post Plurality or by
"teaming" like the Borda Count.

2. The method should pass the majority Criterion... a majority of first
place votes should always vouchsafe the win.

3. The method should be monotone: if a recount reveals more votes for X
than the initial count, it should not change X from winner to loser.

4. The method should be decisive: ties should be extremely rare under usual
conditions.

5. The method should be computationally efficient with a one pass precinct
summable tally.

6. The method should not elect covered candidates: a covered winner is an
embarrassment ... if X defeats the winner W head to head, and the winner
cannot defend itself in a short beatpath, then X covers W.  That's one way
of describing (without mentioning Condorcet) the recent failure of IRV in
Alaska, as well as a previous notable failure of IRV in Burlington, VT.

This sixth feature can be tacked onto any RCV method as a kluge ... but
it's nice when it follows seamlessly from the simple basic tally.

IRV satisfies features 1, 2, and 4.

If you can think of any simple method (besides the one below) that has all
six features (or better ones), please let us know; it will probably be a
significant improvement over every extant public method.

Max Gradient Chain Building (MGCB):

Initialize a pairwise defeat chain with the strongest over-all defeat A>B.
Then ...

... as long as possible, accommodate into the chain (from among the
candidates that defeat all current chain members) the candidate that has
the strongest defeat against the current chain head

Elect the head of the completed chain.

It was a comment of Kristofer that inspired this method. He mentioned that
according to his recent simulations electing the winner of the over-all
strongest defeat A>B is a surprisingly burial resistant stand-alone
method.  It seems to me that the burial resistance should carry over to
this MGCB completion of his discovery.

Furthermore, it appears that if defeat strength is gauged by margins, then
the method is Chicken resistant.

A fairly simple modification ... where the chain is built up from both ends
... always giving priority to the end where the new defeat is stronger ....
preserves all six of the nice features in our list while adding a Strong
Reverse Symmetry feature ... reversing all of the ballot rankings precisely
reverses the output chain .... swapping the head and tail of the completed
chain.

So this MGCB method seems pretty promising .... but the proof will be in
its acual performance when it is put through its paces.

Please try it on your favorite test profiles, and report your observations.

Thanks!

Forest
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