[EM] (3) EM: VoteFair/Kemeny-Young: Steve's 3rd dialogue with Kristofer and Richard

[steve bosworth]

Hi Kristofer and Richard, Richard
Fobes says that his VoteFair popularity ranking method is just another name for
the Condorcet-Kemeny or Kemeny-Young method. 
Accordingly, Richard’s relevant pages in his book (Ending the Hidden
Unfairness…) are basically the same as the relevant part of the ‘Kemeny-Young’
Wikipedia article.

Still,
I have a question about the way these articles explain how the ranked alternatives
are to be scored in order to find the winner. 
The ‘Kemeny-Young’ Wikipedia article offers the follow:


 
  
  All
  possible pairs

  of choice names
  
  
  Number
  of votes with indicated preference
  
 
 
  
  Prefer X over Y
  
  
  Equal preference
  
  
  Prefer Y over X
  
 
 
  
  X = Selden

  Y = Meredith
  
  
  50
  
  
  10
  
  
  40
  
 
 
  
  X = Selden

  Y = Elliot
  
  
  40
  
  
  0
  
  
  60
  
 
 
  
  X = Selden

  Y = Roland
  
  
  40
  
  
  0
  
  
  60
  
 
 
  
  X = Meredith

  Y = Elliot
  
  
  40
  
  
  0
  
  
  60
  
 
 
  
  X = Meredith

  Y = Roland
  
  
  30
  
  
  0
  
  
  70
  
 
 
  
  X = Elliot

  Y = Roland
  
  
  30
  
  
  0
  
  
  70
  
 
 
  
   
  
  
   
  
  
   
  
  
   
  
 
 
  
   
  
  
   
  
  
   
  
  
   
  
 


The sum of the
counts in each row must equal the total number of votes.

After the tally
table has been completed, each possible ranking of choices is examined in turn,
and its ranking score is calculated by adding the appropriate number from each
row of the tally table. For example, the possible ranking:


 Elliot
 Roland
 Meredith
 Selden


satisfies the
preferences Elliot > Roland, Elliot > Meredith, Elliot > Selden,
Roland > Meredith, Roland > Selden, and Meredith > Selden. The
respective scores, taken from the table, are


 Elliot
     > Roland: 30
 Elliot
     > Meredith: 60
 Elliot
     > Selden: 60
 Roland
     > Meredith: 70
 Roland
     > Selden: 60
 Meredith
     > Selden: 40


giving a total
ranking score of 30 + 60 + 60 + 70 + 60 + 40 = 320.

Calculating the overall ranking[edit]

After the scores for every possible ranking have
been calculated, the ranking that has the largest score can be identified,
and becomes the overall ranking. In this case, the overall ranking is:


 Roland
 Elliot
 Selden
 Meredith


with a ranking
score of 370.

S:  I had to confirm this as follows:


 
  
  1.     
  Roland>Elliot    
  70            
  2.      Roland>Selden   60
  3.      Roland>Meredith70
  4.      Elliot>Selden      60
  5.      Elliot>Meredith  60
  6.      Selden>
  Meredith50
  7.      _________________
   Total Score       370
  for this sequence
  S: 
  My question is, why could we not always find the winning sequence
  without have to score every possible
  sequence as illustrated above?  Why
  not simply add how many times the 100 voters have preferred each
  alternative?  At least in this example,
  the same winning sequence would have been discovered in this way:
  
   Roland   200
   Elliot      150
   Selden    130
   Meredith
       110
  
   
   
   
  
  
   
  
  
   
  
  
   
  
 


My
second question responds to Kristofer’s answer in our 4th [EM] dialogue.
He suggested that ‘Ranked Pairs/MAM’ {i.e. maximize affirmed majorities} is  ‘a
simple yet good Condorcet method, how about [1]? It works like this:

 1. Sort all the pairwise contests in
order of strongest to weakest. 

 Discard those that are weaker than a
majority.

 2. Go down the list and lock in a
pairwise contest unless it contradicts 

 a contest you locked in earlier[2].

 3. Once you're done, reassemble the
pairwise contests into a ranking. 

 The candidate that is ranked first on it
wins.

 

 Some additional details are required for
breaking ties, but I've left 

 those out here.’

S:  Is MAM
significantly different from Kemeny-Young/VoteFair?  Might VoteFair popularity ranking also Maximize
Affirmed Majorities as does MAM? If so, perhaps James
Green-Armytage’s following findings with
regard to MAM might equal characterize VoteFair:

The following part of JGA’s analysis of the different preferred results
when using the following different pairwise calculations to discover the winner,
her reports that: 

“Judging from who beats whom, max. length, mean length, or sum
of

defeats, we get MAM
> River+ > Beatpath.

Judging from number of defeats (= Copeland score), we get

either MAM >
River+ > Beatpath

or MAM >
Beatpath > River+.”

 

[This is quotation from page 8 of JGA’s post 11
years ago:

From: James Green-Armytage 

Subject: Heitzig method

Newsgroups: gmane.politics.election-methods

Date: 2004-09-20 06:29:21]

 What do
you think? 

 		 	   		  
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