# [EM] Weighted Mean Approval

Forest Simmons fsimmons at pcc.edu
Sat Apr 10 16:48:02 PDT 2004

```On Sat, 10 Apr 2004, MIKE OSSIPOFF wrote:

>
> It seems to me that when I first heard of Weighted Mean Approval, I didn't
> understand its rules. I"ve printed out the rules that you posted, and I'll
> check out its properties. It does sound Bucklin-like. For now, let me just
> say that I suggest that it needs a more descriptive name.

Actually the name is Weighted Median Approval (median not mean).

In stead of using the median rank as the approval cutoff, a weighted
median rank is used.

Weighted Median Approval is analogous to Weighted Mean Approval, better
known as "above expectation approval" which is used with CR ballots.
There the weighted average of the candidate ratings is used as the
approval cutoff. When the weights are the respective probabilities of
winning, this method is called the "above expectation strategy."

Weighted Median Approval is the analogous strategy for ranked ballots. In
particular, the weights are chosen as though the candidates' first place
supports were proportional to their probability of winning.

Weighted median is another name for generalized median, wherein the area
of an histogram is sliced in half by a vertical line at the generalized
median.  The area of a bar or bin above a rank number on the histogram's
horizontal axis is the sum of the weights of the candidates ranked at that
rank on the ballot in question.

In other words, this is Joe Weinstein's idea of setting the approval
cutoff at the rank where there is the same probability that the winner
will come from above the cutoff as from below, or as nearly equal
probability as possible (interpreting the weights as probabilities).

In the weighted mean version the cutoff would be at the point where the
histogram balanced on a fulcrum, instead of the point that halved the
area.

Forest

```