[EM] An Alternative to Symmetric Completion

[Forest Simmons]

In the weighted median method of determining the approval cutoff,
everything goes straightforward when we have fully ranked ballots.

If some of the ballots are not fully ranked because of truncation or
equally ranked candidates, what are we to do?

Symmetric completion doesn't seem acceptable because it dilutes the
approval so much that much of it is wasted.

Here's an alternative based on inferring the most likely rankings for my
ballot from the relation of it to other ballots:

Step 1.  Convert each ballot into CR ballot form in the usual way.

Step 2.  For each candidate average together all of the (converted)
ballots that rank this candidate first.  Call the results the "candidate
ballots."

Step 3. (a) If two candidates have the same rating on my ballot, give
preference to the candidate whose candidate ballot gives the lowest
average rating to the candidates that my ballot rates at the bottom.

(b) If that doesn't distinguish them, then give preference to the
candidate whose ballot gives the highest average rating to the candidates
that my ballot rates at the top.

(c) If that doesn't distinguish them, then give preference to the
candidate for which my ballot gives the lowest average rating to the
candidates that it (the candidate ballot) rates at the bottom.

Thus we have three rules for distinguishing candidates ... a, b, and c.

Distinguish as many as possible by rule a, then fall back successively on
rules b and c.

No time for examples now.

Bye,

Forest