[EM] VoteFair popularity ranking Scored: Steve's dialogue with Richard Fobes

[Kristofer Munsterhjelm]

On 09/18/2015 12:13 AM, steve bosworth wrote:
>> Date: Thu, 17 Sep 2015 11:44:23 -0700
>> From: ElectionMethods at VoteFair.org
>> To: election-methods at electorama.com
>> CC: stevebosworth at hotmail.com
>> Subject: Re: A Question about Pages 22-29/58 of Chapter 12 of Fobes' 'Ending the Hidden Unfairness of U.S. Elections
>
> Hi Richard ( and everyone else),
>
> Later I want to continue our dialogue compare VoteFair and APR for
> electing multiple winners, but now, please let me focus only on your
> explanation below about 'VoteFair popularity scoring' for electing
> single-winners and the need not to rely on shortcuts:
>
> S:  As you may recall, I currently favor your VoteFair popularity
> ranking method for electing single-winners -- presidents, governors,
> majors, etc.  It has the virtue of discovering the most popular
> candidate by counting all the preferences of all the voters and without
> eliminating any candidate until the most popular one has been
> discovered.  It seems simpler and better than any other method that I
> have read about, including those I've seen discussed in EM.  Still, I
> would like to receive any criticisms from anyone of this method for this
> purpose, or any arguments that prefer a competing method.
>
> Richard, I think your method would be even more appealing if it were
> safe to score its results by the 'shortcut' I asked about.  It would be
> more appealing because more people would be able to understand exactly
> how it works, as well as it requiring a much simpler computer program.
>
> I understand that 'shortcuts' in general can be dangerous and that the
> particular ones you mention below with regard to 'plurality' and 'IRV'
> are flawed by the reason you give, i.e. their mistaken assumptions which
> motivate them.
>
> However, I am not yet aware that VoteFair popularity ranking makes any
> mistaken assumptions.  Therefore, it currently still seems to me that
> simply counting the number of times each candidate is preferred over
> every other candidate would not be an unreliable 'shortcut' because
> would always enable us to discover the most popular candidate, as well
> as give use the whole correct sequence.  Is there specific reason why I
> am mistaken in this view?

That shortcut sounds like a variant of the "sum of defeats" method 
mentioned here: 
http://miroirs.ironie.org/condorcet/condorcet.org/emr/methods.shtml. The 
variety would be in that the shortcut uses sum of victories rather than 
sum of defeats, and on what it sums (in Condorcet terms, sounds more 
like pairwise opposition than WV).

That page states that the sum-of-defeats method is not cloneproof and is 
vulnerable to vote-splitting. That means that similarly aligned 
candidates can sometimes hurt one another. I'd suspect that 
sum-of-victories would also be vulnerable to cloning. E.g. suppose party 
X would like to increase the score of their main candidate X1; they 
could then introduce another candidate (say X2) and tell party 
supporters to rank X1>X2>others. If I'm wrong about the shortcut being 
sum-of-victories, do let me know, of course.

If you'd like a simple yet good Condorcet method, how about Ranked 
Pairs/MAM[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.

-

[1] River is somewhat better, but its additional clause might sound 
strange. It doesn't provide a social ordering either, just a winner.

[2] E.g. if you lock in A>B that means that A will be ranked higher than 
B in the outcome. If you've locked in A>B and B>C, you can't lock in C>A 
later on because that would put C above A, which would contradict A>B>C.