# [EM] I)Ranked pairs using relative margins

Elisabeth Varin/Stephane Rouillon stephane.rouillon at sympatico.ca
Wed Oct 16 00:11:55 PDT 2002

```I need to refresh my explanations and notations to be up to date.

Summary:

Ranked pairs using relative margins uses Mr. Tidemann algorithm
for ordering pairwise comparisons. The only difference with the
classical method is that it uses relative margins as comparison
criteria to select the locking order of pairs.

Explanation:

Using a universal ballot as input, we find 4 different results
when comparing candidates A and B:
A > B   (A preferred to B)
B > A   (B preferred to A)
A = B   (A and B equally preferred)
A ? B   (voter has no opinion and relies on other voters opinions)
The total number of voters is equal to the sum of ballots,
each ballot corresponding to one of these 4 cases.
Thus if A receives more preferences than B:
margin = Nb(A > B) - Nb(B > A)
and relative margin = margin / (Total Nb of voters - Nb(A ? B))

Example:

26: A > E > B ? C ? D
25: B > E > A ? C ? D
24: C > E > A = B ? D (= has priority over ?: A=B, A?D and B?D)
23: D > E > A ? B ? C
1: E > A ? B ? C ? D
1: A ? B ? C ? D ? E (Blank or none ballot)
Locking produces:
E>D (53/99)
E>C (51/99)
E>B (49/99)
E>A (47/99)
A>D (3/49)
B>D (2/48)
A>C (2/50)
C>D (1/47)
B>C (1/49)
A>B (1/75)
Resulting ranking: E > A > B > C > D.
E wins.

This methods elects any Condorcet winner if it exists.
It resists well to cloning and vote-splitting because it is pairwise
comparison based.
Using relative margins minimizes the biggest pairwise reversal.
It is more monotonic than IRV.

It is not monotonic.
Trying to identify a lesser of two evil could help elect it.
It has not weights as output so it cannot be incorporated
into a fully proportional multiple-winners method.

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

Steph.

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