[EM] Binary dropping of candidates

[Michael Rouse]

It's probably already been discussed before (most likely with a more 
descriptive name), but the election methods list has been quiet, so...

Has anyone looked at making a ranked list  of candidates -- either by 
number of first place votes, as in IRV, or Borda order, as in 
Nanson/Baldwin -- and dropping candidates in a binary rather than unary way?

By way of example, in Instant Runoff Voting, you see if a candidate has 
a majority. If not, you drop the lowest candidate. If there is still no 
candidate, you drop the next lowest candidate, and so on. With five 
candidates, you have something like this:

.....   First round (no one dropped)
....1 Second round (one person dropped, ballots redistributed)
...11 Third round (two people dropped, ballots redistributed)
..111 Fourth round (three people dropped, ballots redistributed)
(for five candidates, three drops are sufficient)

It's a method analogous to a unary counting system.

Under a binary dropping method, you have:
(Note: If there is no winner after a round, you use the original 
candidate ranking and proceed to the next round.)

00000 First round (no one dropped)
00001 Second round (bottom candidate dropped, ballots redistributed)
00010 Third round (second-to-last candidate dropped, ballots redistributed)
00011 Fourth round (bottom two candidates dropped, ballots redistributed)
00100 Fifth round (middle candidate dropped, ballots redistributed)
00101 Sixth round (middle and last candidate dropped, ballots redistributed)
00110 Seventh round (middle and second to last candidate dropped, 
ballots redistributed)
00111 Eighth round (bottom three candidates dropped, ballots redistributed)

In effect, you drop the group of candidates representing the lowest 
number of first place votes (or lowest combined Borda score, or some 
other method) that result in one candidate having a majority of first 
place votes, instead of just dropping the lowest candidate and repeating.

Unfortunately, the first-place-only version suffers from being 
non-monotonic (like IRV does). I'm not sure what criteria a Borda-count 
variety but it would be interesting to compare the results of a 
"binary-drop IRV" and "binary-drop Baldwin" to other methods. (The Yee 
pictures might be interesting.)

As I mentioned at the start, it's probably already been discussed at 
some point with a better name, but I thought I'd throw it out there as 
an interesting variation on the "drop the lowest candidate" method of 
vote aggregation. It might have an unusual array of voting paradoxes, 
anyway. :)

Michael Rouse