[EM] Ranked Preferences, example calculations

[Abd ul-Rahman Lomax]

(You sent this personally to me, not to the list.)

I still don't understand it. My time is quite limited, so if I can't 
get it by reading it over, I don't have time to figure out what each 
clause might possibly mean. That's the kind of analysis it would 
take. I assume that you *do* mean something, that there is a defined 
method, but I could not even come close to applying it to a vote. I 
don't understand *at all* how you derived the winner from the votes.

But this stares me in the face. From the presented vote data, B 
should *clearly win,* though this violates the Majority Criterion. 
Your method, apparently, selects A. I'm not highly motivated to 
figure out how a complicated method that seems to pick the wrong winner works!

At 04:37 PM 10/26/2006, Juho wrote:
>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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