# [EM] How to convert a set of CR ballots to a set of Approval ballots

Forest Simmons fsimmons at pcc.edu
Tue Jul 29 16:32:02 PDT 2003

```This method recursively converts a set of CR ballots with resolution n to
a set of CR ballots of resolution n-1, and stops at resolution two, i.e.
approval ballots.

We start with a set of Cardinal Ratings (CR) ballots on which every
candidate is rated by a whole number in the range one to n.

Provisional CR scores are calculated for the candidates by summing or
averaging their ballot ratings.

Then each ballot is modified to a CR ballot with resolution n-1 as
follows:

Let X be the candidate with the highest provisional score whose rating on
this ballot is not precisely at the midrange value.

If X is above midrange, then move all of the candidates except the lowest
level candidates down one level, i.e. decrement their ratings in such a
way that the lowest two levels are amalgamated.

Otherwise lower only the top level, i.e. amalgamate the top two levels.

Now recursively convert these n-1 resolution CR ballots to resolution n-2,
etc. until they are completely converted to approval ballots.

The approval winner is the method winner.

That's it.

I'll explain the rationale behind this in another posting.

I like it best with Five Slot grade ballots.  Each voter gives an A to the
candidates that she is sure that she wants to approve in any case, and an
F to each candidate that she would approve in no case.  The undecided are
sorted into three piles ... leaning towards approval, leaning away from
approval, and not knowing which way to lean.

Forest

```