[EM] Ranked Preferences, example calculations

[Juho]

Ok. I agree that B has the best social utility from "Range  
perspective". But I'm trying to balance between different criteria  
here. One strict rule for me when designing this method was to keep  
sincere voting possible and probable. If that would not have been the  
goal I could have picked e.g. Range (that has good utility with  
sincere votes, but that unfortunately can not maintain the sincerity  
in contentious elections).

Ranked Preferences tries to find one optimal spot in the space of  
election methods. Let's see if it can be proven to fail or if it can  
be improved.

Juho Laatu


On Oct 27, 2006, at 7:56 , Abd ul-Rahman Lomax wrote:

> (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
>>
>> Send instant messages to your online friends http:// 
>> uk.messenger.yahoo.com
>

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