# [EM] K)Alternative Vote (or IRV) using residual approval weights

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Wed Oct 16 00:13:02 PDT 2002

```Summary:

Alternative vote with residual approval weights mixes both IRV
and Approval methods. The only difference with IRV is the winner(s)
selection. It is determined by the highest residual approval
weight(s), not necessarily the latest eliminated candidate(s).

Explanation:

The input is Demorep's preferential and
approval ballot. We use ? to represent
unranked candidates. Using the election-methods-list
notation, we will use >> to indicate the approval limit.
So acceptable candidates >> unacceptable candidates.
For example: A > C > E >> D > B.
We simply apply usual IRV.
In case of equality, each elimination scenario is done,
the final result is the average of the scenarios (well weighted).
When the candidate with the least 1st place vote is eliminated,
we check what is his residual approval rating.
He receives one residual weight for each ballot where he is the last
active candidate higher than >>.
If the approval limit >> is not mentionned we suppose it could be
added at the end. The winner is the candidate with the highest
approval rating, not necessarily the latest eliminated.

Example:

26: A > E > B >> C ? D
25: B > E >> A ? C ? D
24: >> C > E > A = B ? D (None ballots with lesser evil details)
23: D > E >> A ? B ? C
1: E >> A ? B ? C ? D
1: A ? B ? C ? D ? E (Blank ballot, a none ballot would start by >>)
Eliminations produce:
1st round:
E: 1 vote
Blank => 1 vote
E eliminated => residual weight of 1.
2nd round:
D eliminated => residual weight of 23.
3rd round:
C eliminated => residual weight of 0.
4th round:
B eliminated => residual weight of 25.
5th round:
A eliminated => residual weight of 26.
=> 24 none ballots.
Final Results: A(26) > B(25) > D(23) > E(1) > C(0)
and 24 none ballots and 1 blank ballot.
A wins.

The method does not encourage cloning.
Trying to identify a lesser of two evil cannot help elect it.
The method has weights as output so it can be incorporated
into a fully proportional multiple-winners method.
None and blank ballots can be differenciated, so they could have
different consequences in a multiple-winners method.

It is not monotonic.
This methods does not guarantee the election of a Condorcet winner
even if it exists and it is approved by all ballots.
It does not resist well against vote-splitting.

Previous explanations available at:
http://groups.yahoo.com/group/Electoral_systems_designers/message/73

Steph.

----