# [EM] J)Ranked pairs using relative margins, sequential dropping...

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Wed Oct 16 00:14:01 PDT 2002

```...and residual approval weights

Summary:

This method is like the previous one (K) excepted that the elimination
order is definer by a ranked pair path instead of the number of 1st
preference votes. It mixes IRV, Ranked Pairs and Approval methods.

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 apply ranked pairs with relative margin.
In case of equality, each ranking scenario is done,
the final result is the average of the scenarios (well weighted).
When the last candidate 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 >>. Elimination should not
modify the ranked pair order.
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 >>)
Locking produces:
E>D (53/99)
E>C (51/99)
E>B (49/99)
E>A (47/99)
B>C (27/75)
A>D (3/49)
B>D (2/48)
A>C (2/50)
C>D (1/47)
A>B (1/75)
Resulting ranking: E > A > B > C > D.
Elimination produces the weights:
D => 0 residual approval.
C => 0 residual approval.
B => 0 residual approval.
A => 0 residual approval.
E => 75 residual approval.
and 24 none ballots and 1 blank ballot.
Final ranking: E(75) > A = B = C = D  (0)
E 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.
This methods guarantees the election of a Condorcet winner
if it exists and is approved by all ballots.
It resists well against vote-splitting because it is pairwise
comparison based.

It is not monotonic.

Previous explanations:
http://groups.yahoo.com/group/Electoral_systems_designers/message/77

Steph.

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