[EM] Median Mediated Approval

[Forest Simmons]

For each candidate X let r(X) be the number of ballots on which X is ranked
ahead of at least one candidate. This r(X) is sometimes called the
"implicit approval" of X.

Also,let f(X) be the number of ballots on which no candidate is ranked
ahead of X. This f(X) is often called X's  "equal first" or "top" count.

Elect the candidate X with the greatest value of the sum r(X)+M×f(X), where
M is the Median of all of the voter suggestions for the number M,
restricted to the interval between zero and one inclusive. [If there are an
even number of suggestions, throw in an extra zero so that there will be a
well defined median.]

There are at least three ways to get the voter suggestions for M.
1. Voters include suggestions for M in a field provided on their ranked
preference ballots.

2. Ranked ballots are counted and the results published for various values
of M between zero and one. If the value of M actually makes a difference in
who wins, have the voters vote on the value of M. Otherwise, M is not
needed.

3. Elect the CW if there is one, otherwise check to see if M matters. If
there is no CW, and M does matter complete the election with a call for
votes on M.

It seems like this third version would be ideal for small group settings
... any kind of deliberative assembly customarily governed by Robert's
Rules.

Any venue that currently admits runoffs could profit by replacing their
current system with one of these versions.

It seems like the third version is an ideal marriage (for generic single
winner elections) between Condorcet and Implicit Approval. Am I
over-looking something?

How close does it come to satisfying the Favorite Betrayal Criterion?

-Forest
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