[EM] RE: Better-worded definition of ERBucklin(whole)

[Simmons, Forest]

Adam wrote:

I haven't been following this line of threads terribly closely, so I just
want to be clear that I understand. The way I think about Bucklin is an
approval election where the approval cutoff bar on everyone's ballot keeps
getting lowered until we have a majority approved winner. It seems like
there are three choices for the "speed" of the lowering of the cutoff in
ERBucklin(whole):

1) Move down one slot on the ballot each round of the election, skipping
empty slots
2) Move down one slot on the ballot each round of the election, NOT skipping
empty slots
3) Move down one candidate each round of the election (cutoff is just below
that candidate, whatever rank they are at)

I have no emotional attachment to any of these (although the second one is
especially easy to explain, I think). I have no trouble believing the third
is the best. I'd just like a quick explanation as to what the third approach
offers that the others do not.


I reply:

Alternative (1) makes the method fail the FBC, because raising Compromise makes third choice appear on the scene too soon, which discourages raising Compromise without lowering Favorite to delay the counting of third choice.

Alternatives (2) and (3) avoid this problem, but alternative (3) is designed for rankings where there are no fixed slots.

Personally, I prefer fixed slots A,B,C,D, and F standing for Excellent, Above Average, Average, Below Average, and Lousy, respectively.

I think that only rarely would it be necessary to lower the approval cutoff bar more than twice to get a 50% plus approval winner, so why have more than five levels?

Here's my proposal:

Each voter rates each candidate with an A, B, C, D, or F.  

Also, a voter may mark a "plus" next to his favorite candidate.

The candidate with the highest median rating (ignoring plusses) wins.

If two candidates have the same median rating, then the one rated by the most voters at that grade or above is the winner.

Note that a candidate's median rating is the highest grade G (ignoring plusses) such that fewer than half of the ballots rate him below G.

In case of a tie, a random ballot is drawn.  The candidate marked plus on that ballot picks the winner from among the tied candidates.

Why not just break the tie by choosing the tied candidate with the most plusses?  Because that would violate the FBC.  If you thought that your Compromise had a much greater chance of being one of the tied candidates than Favorite, then you would be tempted to assign your plus to Compromise rather than waste it on Favorite.  This would be a clear betrayal of Favorite.

For those who don't think the plus is important, consider these two cases:

(1) Your ballot is not pivotal (the most likely case).  In this case your ballot makes no difference in the outcome, but it does give moral support in one degree or another to one or more candidates.  In this case you will be glad you had the opportunity to distinguish Favorite with a plus mark, since that shows maximal moral support for Favorite, and no other candidate gets this maximal moral support from you.

(2) Your ballot is pivotal. In other words, it is a tie maker or a tie breaker.  If it is a tie maker, then there is a possibility it will be drawn in the tie breaking process.  If that happens, it makes a big difference who you marked with the plus.  If this Favorite is one of the tied candidates, then your ballot tips it in his favor.  Otherwise, your favorite gets to pick which of the tied candidates wins.

Forest

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