[EM] VoteFair Ranking software version 6.0 in C++ with MIT license

[VoteFair]

On 1/22/2020 3:49 PM, Kristofer Munsterhjelm wrote:
 > Given this definition, there are two possibilities. Either the VoteFair
 > software implements the VoteFair method, or it does not. ...

If the default settings are used, and if the number of candidates is no 
more than the check-all-sequence-scores setting (which I think is 6), 
then the software implements the VoteFair popularity ranking method, 
which yields the same results as the Condorcet-Kemeny method.

In other words you are not allowing for a third possibility, which -- of 
course -- depends on the number of candidates.

 > ... It seems that you instead are saying that, as you
 > define the VoteFair ranking, it does agree with Kemeny all the time, but
 > the software doesn't.

Yes, this is the third possibility. The software CAN always yield the 
same results -- simply by limiting the number of candidates it can 
handle (or, up to a limit based on computing power, increasing the 
number of candidates checked by the full/slow method).

 > Could you give me a definition of the VoteFair method itself? Without
 > knowing what bit is the software and what bit is the method, it's
 > difficult to get further. For instance, it would be hard to know whether
 > the results that the VoteFair software gives when Kemeny orderings are
 > tied is a property of the method or of the software, because the
 > definition of the Kemeny method itself doesn't say what should happen in
 > such a case.

Originally I wrote the definition of VoteFair popularity ranking (which 
at that time I called VoteFair ranking) on Wikipedia, and Markus Schulze 
re-named the article to the "Kemeny-Young method" claiming that the two 
methods are the same. So the definition there matches VoteFair 
popularity ranking because I wrote it.

Yes, the issue of how to handle Condorcet-cycle ties is not stated by 
John Kemeny (as far as I know), and I have not explicitly stated how 
such ties are handled in VoteFair popularity ranking. If I did make such 
a statement then you or others might argue that the two methods are not 
the same.

The software does attempt to handle ties, either to use a tie-breaking 
criteria or to declare an official tie. In the latter case, the VoteFair 
approach presumably matches the Kemeny approach. In the former case the 
candidates in the cycle can be re-sequenced and the sequence sums yield 
the same highest sum, yet SOME of those "tied" sequences can yield 
different sums. If this seems complex it's because it IS complex. It 
took lots of work to get the software to handle these and other "edge" 
cases. This approach is unlike what many software developers do, which 
is to dismiss edge cases with some kind of error message. In other 
words, my software looks deeper into the "tie."

So, keeping in mind that neither John Kemeny nor I have officially 
stated how ties (in the sequence sums) are to be handled, both methods 
are mathematically equivalent.

I avoid using the word "same" because John Kemeny defines the sequence 
score in terms of counting votes that OPPOSE a candidate (and finding 
the minimum score), whereas VoteFair popularity ranking (which I came up 
with without knowing about the Kemeny method) defines the sequence score 
in terms of counting votes that SUPPORT a candidate (and finding the 
maximum score).

If this still isn't clear, please keep asking for clarifications. Thank 
you for seeking to understand this method.

Richard Fobes


On 1/22/2020 3:49 PM, Kristofer Munsterhjelm wrote:
> On 12/01/2020 05.34, VoteFair wrote:
>> Kristofer ~
>>
>> It occurs to me that you might be thinking that the VoteFair Ranking
>> SOFTWARE provides the definition of VoteFair popularity ranking.  That
>> is not the case.
>>
>> VoteFair popularity ranking is defined in two of my books -- "The
>> Creative Problem Solver's Toolbox" and "Ending The Hidden Unfairness In
>> U.S. Elections" -- and in the Condorcet-Kemeny ("Kemeny-Young")
>> Wikipedia article.
>>
>> Those definitions should make it clear to anyone who understands
>> mathematics that the difference between VoteFair popularity ranking and
>> the method John Kemeny published is that Kemeny counts opposition and
>> VoteFair counts support, and that otherwise the two methods are
>> mathematically equivalent.
>
> Let me try to restate that to see if I got it right, because it seems
> like an odd distinction.
>
> A ranked voting method is a function that takes, as an input, a set of
> ballots, and produces either a social ranking or a winner set (depending
> on what definition you agree with).
>
> What happens inside the function is irrelevant to the definition. You
> could, if you had infinite memory, implement it as a huge table that you
> would just look up to find out what the output would be for a given input.
>
> Given this definition, there are two possibilities. Either the VoteFair
> software implements the VoteFair method, or it does not. By "implements
> the method" I mean that running the VoteFair software on some input
> election always provides the output that the method would.
>
> Now, I was assuming that the software was an accurate implementation of
> the method, so that instead of a method, you actually had a family of
> them (parameterized by that constant), none of which would agree with
> Kemeny all the time. It seems that you instead are saying that, as you
> define the VoteFair ranking, it does agree with Kemeny all the time, but
> the software doesn't.
>
> Could you give me a definition of the VoteFair method itself? Without
> knowing what bit is the software and what bit is the method, it's
> difficult to get further. For instance, it would be hard to know whether
> the results that the VoteFair software gives when Kemeny orderings are
> tied is a property of the method or of the software, because the
> definition of the Kemeny method itself doesn't say what should happen in
> such a case.
>