[EM] Ranked Preference benefits

[Juho]

Ranked Preferences adds strength of preferences to the flat  
preferences of Condorcet methods. Here are some examples in which  
this increased expressiveness may be of use in practical elections.

All the examples deal with two big party candidates and one  
compromise candidate. I'll call them R (Right), L (Left) and C  
(Compromise, Centre) since that is the traditional setup.

With preference strengths it is possible to make a difference between  
good and bad centrist candidates. Basic Condorcet methods are unable  
to make that difference.

Example 1. Large party voters consider C better than the other large  
party candidate, but not much.

45: L>>C>R
40: R>>C>L
15: C>L=R

Ranked Preferences elects L. (first round: L=-10, C=-70, R=-20;  
second round: L=-10, R=-20)

Example 2. C is considered good by all voters.

45: L>C>>R
40: R>C>>L
15: C>L=R

Ranked Preferences elects C. (first round: L=-10, C=+100, R=-20;  
second round: L=-10, C=+10)

Example 3. C is ideologically close to R and distant from L.

45: L>>C>R
40: R>C>>L
15: C>L=R

Ranked Preferences elects C. (first round: L=-10, C=+10, R=-20;  
second round: L=-10, C=+10)

C would have won also if C voters had voted 15: C>R>>L. (as would be  
natural if C and R are ideologically close to each others) (first  
round: L=-10, C=+10, R=+10; second round: C=+10, R=-20)

Example 4. Some of the large party voters think C is good but  
majority of them think C is no good.

15: L>C>>R
30: L>>C>R
14: R>C>>L
26: R>>C>L
15: C>L=R

Ranked Preferences elects L. C loses to it marginally at the second  
round. (first round: L=-10, C=-12, R=-20; second round: L=-10, C=-12)

Basic Condorcet compatible methods would have elected C in all of the  
examples. This kind of situations are quite typical in real  
elections, and therefore these differences are worth a study.  
Preference strength information makes it possible to separate  
different kind of compromise candidates from each others. There are  
also other methods that are in theory able to make the difference,  
e.g. Range. But since Range tends to approximate Approval in  
competitive elections it may not be that useful in competitive  
elections.

Are there other known methods that would be able to do this (in  
competitive elections)? There could be e.g. some hybrid Condorcet +  
Approval cutoff methods doing something similar.

Note that in examples 1 and 4 above Ranked Preferences did not  
respect the Condorcet criterion. That can be justified when  
preference strengths are known.

Juho Laatu

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