[EM] A Question about Pages 22-29/58 of Chapter 12 of Fobes' 'Ending the Hidden Unfairness of U.S. Elections

[steve bosworth]

 Hi Richard,
Unfortunately, my other obligations have
not allowed me to reply to your answers to our 20th VoteFair/APR dialogue
until today.  However, before I do so, I
would very much appreciate it if you would clarify a question that I have about
your book, ‘Ending the Hidden Unfairness of U.S. Elections’.  With regard to pages 22 to 29/58 of Chapter
12, I finally understand how you arrived at the ‘score’ of 400 for the winning
sequence i.e. Elliot(E)>Selden(S)>Meredith(M)>Roland(R):  

You started by adding up the number of
the 100 voters who had preferred each of the three candidates to the left of R,
over R, i.e. 60+70+70 = 200.  You then
added the number who preferred those to the left of M, over M, i.e. 70+70=140.  Next you added the number who preferred E
over S, i.e. 60.  The sum of these 3
totals is 400, i.e. the largest score for any one of all the possible
sequences.

However, please also explain why the following simpler set of
calculations would not also always allow us to discover the most popular
sequence:

 

Firstly, find the grand total of preferences given by the 100
voters to each of all the candidates (4 in this example) over each of the
other candidates (3 in this example).  The result is:

Elliot         200

Selden      180

Meredith   90

Roland       80 

 

At least in this case, the same sequence is produced: Elliot 1st, Selden 2nd,
Meredith 3rd, and Roland 4th.

Why do we also have to calculate the score for each possible sequence?

 

What do you think?

Steve

 

Re: (21) APR: Steve's 20th dialogue
with Richard Fobes

 

>
From: election-methods-request at lists.electorama.com

> Subject: Election-Methods Digest, Vol 134, Issue 1

> To: election-methods at lists.electorama.com

> Date: Sat, 1 Aug 2015 12:02:14 -0700

> 

>> 1. Re: (20) APR: Steve's 20th dialogue with Richard Fobes

> (Richard Fobes)

> 

> 

> ----------------------------------------------------------------------

> 

> Message: 1

> Date: Fri, 31 Jul 2015 17:07:34 -0700

> From: Richard Fobes <ElectionMethods at VoteFair.org>

> To: "election-methods at lists.electorama.com"

> <election-methods at lists.electorama.com>

el 		 	   		  
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