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

[VoteFair]

Steve, you are suggesting a possibly new single-winner method.  As I 
understand it, you are suggesting the use of pairwise counting, putting 
those pairwise counts into a (tally) table, and calculating a score for 
each candidate, where the score is the sum of associated pairwise counts.

I do not know if this method has a name.  Does anyone else know?

This method is certainly superior to plurality counting ("first past the 
post").  It is probably superior to instant-runoff voting.

I'll let the supporters of approval voting voice their opinion about 
whether this method is better or worse than approval voting.

However, the only advantage it has over the various Condorcet methods is 
that it can be easily calculated using paper and pen.

The disadvantages of this method can be summed up by saying that it 
would fail many fairness criteria.  In other words, if it were added to 
the comparison table in the Wikipedia "voting systems" page, then it 
would not appear to be a good choice as a voting method.

You suggest that this method might be a "shortcut" for VoteFair 
popularity ranking (which is mathematically equivalent to the 
Condorcet-Kemeny method).  But it is not a shortcut to any kind of 
voting.  It is a completely different method.

For your benefit, and for the benefit of anyone else who is learning 
about voting methods, pairwise counting can be thought of as the first 
step in the process of calculating the Condorcet-Kemeny, 
Condorcet-Schulze/Beatpath, Ranked Pairs, and other Condorcet methods. 
These different methods use the pairwise counts in different ways. 
Steve, your new suggested method uses the pairwise counts in yet another 
way.

You have speculated that your suggested method would "always" produce 
the same results as VoteFair popularity ranking.  As I tried to explain 
before, that is not the case.

I looked for an example in which your method produces different results 
compared to VoteFair popularity ranking.  I did not find any specific 
example, yet if I had lots of time I could fabricate such an example.

The reason I know that the two methods produce different results is that 
I use "your" kind of calculation for some of the graphical bars that 
appear in the results that are calculated at my VoteFair.org website, 
and I have seen cases where the graphical bars do not consistently 
lengthen with higher rankings.  Those cases are uncommon, but they occur.

Specifically, if you look at the American Idol page on the VoteFair 
website you will see results that have a column labeled "VoteFair 
ranking score," and there are many links on that page that lead to other 
computed results that show the same graphical-scoring column.  This 
"score" (which I could not find a better name for) is not used in any 
aspect of VoteFair ranking.  I created these horizontal bars in order 
for them to be visually compared to the horizontal bars that indicate 
plurality results.  In all the American Idol results that I recently 
looked at, the graphical bars consistently progress from shorter to 
longer as the ranking priority increases.  For those cases, your 
suggested method and VoteFair popularity ranking do produce the same 
ranking results (and, by extension, the same "winner").

Yet I have seen cases where these horizontal bars do not progress in 
this typical pattern.  In other words, VoteFair popularity ranking 
produces a ranking that would be different compared to your suggested 
method of just summing pairwise counts for each candidate.

Such atypical ("non-typical") cases tend to occur when a relatively few 
number of ballots have been cast.  As more ballots are cast, those 
atypical patterns disappear.

What this means is that your suggested method might be useful in 
situations where lots of people are voting, and where the pairwise 
counting can be done on a computer, but where voters do not want to rely 
on a computer for the final calculation step.

Someone else on this forum might be familiar enough with this method to 
quickly identify which fairness criteria this method passes, and which 
ones it fails.

I suspect that it fails the Condorcet criterion, which is a serious 
weakness for a method that cannot be "hand counted."  (Pairwise counting 
by hand is tedious and error-prone.)

If you want to promote this method to voters as an improvement over 
plurality voting and instant-runoff voting, please do so!

Perhaps such usage will be like training wheels on a bicycle, where 
those extra wheels provide a comfortable halfway point between not 
riding a bicycle and riding a bicycle.  But just as training wheels need 
to be taken off before someone can really ride a bicycle, this method is 
not useful as an end result because there are multiple better 
vote-counting methods.

Now that you are better understanding how to improve vote counting, I 
also encourage you to apply this understanding to improve the counting 
methods you propose in your APR method.

I apologize for the long delay (weeks!) in replying to your message. 
Thanks for being interested in my feedback.  I hope it's helpful.

Richard Fobes

On 9/17/2015 3:13 PM, 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?
>
> Steve
>
>  >
>  > On 9/13/2015 12:22 PM, steve bosworth wrote:
>  > > ...
>  > > [...] please [...] 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.
>  >
>  > Yes, sometimes -- in SOME situations -- a simpler calculation (such as
>  > this one) can identify the same winner and even the same ranking.
>  >
>  > However, typically a shortcut fails to provide fair results in ALL
>  > situations.
>  >
>  > Consider that plurality (first-past-the-post) voting is a shortcut that
>  > mistakenly assumes that the candidate with the most first-choice votes
>  > is always the most popular. This shortcut does not work if the
>  > candidate with the most first-choice votes does not ALSO get a majority
>  > of (more than half) the votes.
>  >
>  > In a similar way, instant-runoff voting is a shortcut that does work in
>  > some situations. It is based on the shortcut of (mistakenly) assuming
>  > that the candidate with the fewest first-choice votes is least popular.
>  >
>  > Also in a similar way, your APR method will work in some situations.
>  > Yet it too puts too much emphasis on first-choice votes without
>  > considering secondary preferences (or somewhat-equal preferences for
>  > those who prefer approval voting).
>  >
>  > In contrast to methods that work SOME of the time, full fairness
>  > requires that a method must produce fair results either ALL the time
>  > (which is mathematically impossible if all fairness criteria are
>  > considered), or MOST of the time. In the best methods, unfairness
>  > (according to any fairness criteria) is rare. To get this level of
>  > fairness, the voting method must look beyond the first-choice counts.
>  >
>  > Back before computers became available, mathematical shortcuts were
>  > often useful in some situations. Now, both in terms of calculation time
>  > and the work of coding software, it's easier to do full calculations
>  > using a fully-fair algorithm, compared to writing code that handles both
>  > the shortcut and all the needed validity checking and related decision
>  > handling (to handle the cases where the validity checks fail).
>  >
>  > I hope this information helps not only you/Steve, but also helps some
>  > other participants in this forum.
>  >
>  > Richard Fobes
>  >
>  > BTW, page numbers in an ebook reader do not match the page numbers in a
>  > different ebook reader, and do not match the page numbers in a printed
>  > edition.
>  >
>