[EM] Query, Clones, MCA levels, Participation

[Forest Simmons]

On Thu, 4 Sep 2003, [iso-8859-1] Kevin Venzke wrote:

>
> Out of curiosity, do you think sixteen is not too many levels?  I think
> even four is too many.  There would be three ways to win: Majority favorite,
> greatest approval, and something in-between that we have difficulty
> describing ("median at second-highest level").
>

I think three levels are just right for single winner MCA.

More levels should be used when there are many winners.

Here's my suggestion for a many winner method based on CR style ballots:

Let's say that there are eight levels of CR and five vacancies to be
filled.

After the ballots are collected we start with the approval cutoff just
below the highest level.

Let's say that there is exactly one candidate who has approval from more
than one sixth of the voters (at this level).

This candidate is moved into the winners' circle.

Then the approval cutoff is lowered a notch at a time until there is at
least one other candidate that has one sixth approval in a partition of
approval that gives everybody in the winners' circle so far this minimum
quota of approval at this level.

If there is more than one way to do this, then conditional PAV
(conditioned on the previously decided winners) is used to choose the new
winners. [Sequential PAV is conditional PAV in the case where the number
to be added to the winners' circle is just one.]

This is continued until the winners circle has the required number of
winners or until the next to bottom level is reached, in which case
conditional PAV is used to complete the winners circle, even if there is
no partition of approval at this level that gives five candidates the
minimum quota of one sixth each.

Forest