[EM] Ranked Preferences, example calculations

[Juho]

As promised in my previous mail here are some example calculations to  
demonstrate how the Ranked Preferences work. Plus some additional  
notes at the end.

- I use * to mark numbers that are based on the tied at top/bottom  
rules.
- I use "A-B" as a shorthand for "A compared to B"
- I use "[ ]" to mark changes in the preference matrix calculations


Example 1.

55: A>B>>C
45: B>>A>C

A-B = +55* -45 = +10
A-C = +55 -45* = +10
B-A = +55* +45 = +100
B-C = +55 +45 = +100
C-A = -55 -45* = -100
C-B = -55 -45 = -100

C will be eliminated. Top strength of the 55 first votes is now ">".

A-B = [+55] -45 = +10
A-C = +55 -45* = +10
B-A = [-55] +45 = [-10]
B-C = +55 +45 =+100

B will be eliminated. A wins.

Having majority of the voters on A side made her the winner.


Example 2.

40: A>>C>B, 40: B>>C>A, 20: C

A-B = +40 -40 -20* = -20
A-C = +40 -40* -20 = -20
B-A = -40 +40 -20* = -20
B-C = -40* +40 -20 = -20
C-A = -40 -40* +20 = -60
C-B = -40* -40 +20 = -60

C will be eliminated. Top strength of the last 20 votes is still  
">" (the minimum level).

The matrix values will be the same.

A-B = +40 -40 -20* = -20
A-C = +40 -40* -20 = -20
B-A = -40 +40 -20* = -20
B-C = -40* +40 -20 = -20

Either A or B is eliminated and the other one will be the winner.

Flat preferences Condrcet winner was eliminated since she was  
disliked by 80% of the voters.


Here are some more comments on the method that I missed in my first  
description of it.

I should have included this rule (maybe obvious but maybe better to  
explain still).
- The strength of preference when comparing two candidates on a  
ballot is the strongest preference relation between these two candidates

I should have defined as well:
- The top strength of a ballot is always ">" or higher

One possible maybe interesting option that I didn't mention is not to  
use the tied at top or tied at bottom rules when there are no  
stronger preferences than ">". This makes the "flat preferences" case  
more similar to traditional Condorcet methods. This might be of  
interest if majority of the voters do not bother to use the stronger  
preferences but rely on basic Condorcet instead.

Juho Laatu

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