[Election-Methods] Mixing Condorcet and Approval...

[Elisabeth Varin]

I read several ways to mix Condorcet and Approval on recent mails.
This is my favourite, using the latest proposed ballot example.

I would suggest a Condorcet method usind residual approbation weights
with an approval cut-off (noted "|" ).
It's a mix of Condorcet, IRV and approval.

The idea is:
1) to rank candidates using a Condorcet (ranked pairs, winning votes for 
example) method;
2) eliminate last candidate like in IRV and give him the weight according to 
the number of voters
having that candidate as last approved;
3) repeat 1) and 2) until winner selection.

Eliminated candidates have no more influence on the result,
but voters that approved an eliminated candidate can still contribute
to the last decision. Losing does not mean you don't care.

Let's see the result without information (with info,
ACB voters could strategically alter their range to get A elected)

Without info:
55 voters: A 100, C 80, B 0
45 voters: B 100, C 80, A 0

Step 1):
-----------
should translate:
44: A > C | B
11: A | C > B
37: B > C | A
9:   B | C > A

With full preferences any criterion used for Condorcet is equivalent, but 
winning votes gives:
55: A > C
55: C > B
55: A > B

Thus the majority ranking prevails: A > C > B.

Step 2:
----------
B is eliminated getting 9 votes as support.

Step 1 - 2nd Tour:
--------------------------
Eliminating B does not change the ranking:
55: A > C

Step 2 - 2nd tour:
-------------------------
C is eliminated getting 37 support.

3rd Tour:
-------------
A receives 55 votes as support.

A wins.