[EM] Ranked Preferences

[Juho]

Here is also one concrete example of the use of the (described  
version of the) method. Maybe this helps in seeing how it works. I  
hope I didn't make many mistakes in it.

Juho Laatu



45: L>C>R
20: C>>R>L
35: R>>C>L

In the first 45 votes > is the strongest relation and the top  
strength of the ballot. In the other votes >> is the strongest  
relation and the top strength of the ballot.

- L compared to C => +45 -20 -35 (tied at bottom) = -10
- L compared to R => +45 -20 (tied at bottom) -35 = -10
- C compared to L => -45 +20 -35 (tied at bottom) = -60
- C compared to R => +45 +20 -35 = +30
- R compared to L => -45 -20 (tied at bottom) +35 = -30
- R compared to C => -45 -20 +35 = -30

C has the worst pairwise comparison result and will be eliminated  
(although C would be a Condorced winner in a regular Condorcet  
election).

At the second round the top strength of the 20 C>>R>L ballots is >  
(since C was eliminated) and as a result the paiwise comparison  
results will be somewhat different.

- L compared to C => +45 -20 -35 (tied at bottom) = -10
- L compared to R => +45 -20 (LOST) -35 = -10
(- C compared to L => -45 + 20 -35 (tied at bottom) = -60)
(- C compared to R => +45 +20 -35 = +30)
- R compared to L => -45 +20 (WON) +35 = +10 (RESULT CHANGED)
- R compared to C => -45 -20 +35 = -30

R has the worst pairwise comparison result and will be eliminated. L  
wins the election.

Roughly what happened was that R supporters clearly indicated that C  
is not a good compromise candidate from their point of view. C was  
therefore eliminated. C supporters' votes went to R (after C lost its  
chances). But that was not enough since L was the second best choice  
from traditional Condorcet (three candidate) comparison point of view.


		
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