[EM] Better Approval-voting option? Could ABucklin fail FBC?

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Mar 1 13:55:37 PST 2012

Though the options of voting as in AOCBucklin, MTAOC or MCAOC in an Approval election make some sense, when the election is regarded as
that kind of election, with some people (the Approval-ballot voters) rating everyone at top-rank, one can't help noticing that some aspects of those
vote-management options, in an Approval election, seem suboptimal for the voter.

Two conclusions suggest themselves:

1. Maybe MTA, MCA and ABucklin don't often really improve on Approval. Maybe Approval-style voting is often the best strategy
in those methods.

2. Maybe there could be a better vote-management option in an Approval election.

Regarding #2, how about Stepwise-to-Majority?

I'd previously proposed Middle-When-Needed, and Stepwise-When-Needed. Stepwise-When-Needed could be called 
Stepwise-to-Win. The rankings, as in Bucklin, keep simultaneously giving a vote to their next choice, stepwise, by stages,
as in ABucklin, each ballot continuing to do so as long as no candidate it's already given to is the current winner. I acknowledged, at that
time, that it would often turn out to be no different from an Approval count of all the ranked candidates.

Then I noticed that the those 2 methods probably fail FBC. I wondered if there's something somewhat similar that meets FBC.

Maybe, judging candidates by an arbitrary number like majority would avoid the problem, as opposed to judging by whether one of
your higher ranked candidates is winning.

Hence, Stepwise-to-Majority.

During the Buckliln-like vote-giving stages, each ballot keeps giving to its next choice till someone it has given to has a majority.

But could this happen?:

If you rank your favorite, F,  in 1st place, s/he gets a majority, even though s/he doesn't win, because someone else has a higher

A number of people rank F, and, if you help F get a majority, then they won't give a vote to their next choice.

That's regrettable, because their next choice could win with those votes, while F can't win. And when their next choice doesn't win,
someone worse than s/he (as judged by you) wins.

You got a worse result because you didn't favorite-bury.

So maybe, even if that scenario is merely possible, I shouldn't propose Stepwise-to-Majority unless it turns out that the FBC-failure scenario
can't happen.

But more worrying is the fact that one could tell that same story about ABucklin (the ER-Bucklin defined at electowiki).

Of course a vague verbal scenario like the above might not have an actual numerical example that can carry it out. There might
be some reason why such an example couldn't work. Still, it's worrying.

Does anyone know if there's actually a proof that ER-Bucklin meets FBC?  

Can it be shown that the verbal FBC-Failure scenario described above couldn't really happen?

Might ABucklin fail FBC?

Mike Ossipoff

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