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

VoteFair electionmethods at votefair.org
Wed Dec 18 15:26:59 PST 2019

```On 12/18/2019 2:04 AM, Kristofer Munsterhjelm wrote:
> I can't help myself, but must point out again that I think it's more
> accurate to say (if this is true), that VoteFair popularity ranking is
> an approximation to Kemeny that becomes Kemeny in the limit as a certain
> parameter approaches infinity.

Yes, when there are a large number of candidates, such as 50 candidates
as an example, estimations are done to yield a full ranking, and then
the top 6 or 7 or 8 (this is adjustable) most-popular candidates are
ranked using the exact Condorcet-Kemeny method to determine the ranking
for those top candidates.

Yes, you came up with an example of a carefully constructed case that
involved something like 50 candidates -- and a small number of carefully
balanced groups of voters.  But that example illustrates my point that
such a case would not occur among voters who are sincerely marking their
ballots independently, without coordination with each other.

In elections, where just a single winner is needed, the only way
VoteFair ranking and the full Condorcet-Kemeny calculations can identify
different winners is if the case involves numerous almost-equally
popular candidates (at the top, not the middle or bottom).
(Specifically there needs to be a carefully constructed Condorcet cycle
that involves a large number of candidates and a small number of
carefully balanced groups of voters.)

> Unfortunately, letting that parameter approach infinity destroys
> VoteFair's polynomial runtime. So VoteFair does not prove P=NP :-)

Yes you are correct that increasing the full calculation parameter
further (such as even to 20) would result in a very long computation
time, which is of course not a "polynomial runtime."

Yet for election purposes, as opposed to mathematical-proof purposes, I
cannot imagine needing to increase the full calculation parameter to
check more than a few top candidates.  (If that affects the outcome,
then just a few spoiled ballots also would be just as likely to change
the outcome.)

Richard Fobes

On 12/18/2019 2:04 AM, Kristofer Munsterhjelm wrote:
> On 16/12/2019 07.42, VoteFair wrote:
>
>> VoteFair calculations use pairwise counting to ensure especially fair
>> results. Specifically, VoteFair popularity ranking is mathematically
>> equivalent to the Condorcet-Kemeny method. Although some people dismiss
>> this method as requiring too much computer time when there are lots of
>> candidates, this software is very fast, even when there are 50 choices.
>
> I can't help myself, but must point out again that I think it's more
> accurate to say (if this is true), that VoteFair popularity ranking is
> an approximation to Kemeny that becomes Kemeny in the limit as a certain
> parameter approaches infinity.
>
> I don't remember the name of the parameter; you probably do. But I
> remember I found examples where Kemeny and your method disagreed for
> elections with very large Smith sets. You said that you could always
> increase the value of this parameter to get the correct result.
>
> Unfortunately, letting that parameter approach infinity destroys
> VoteFair's polynomial runtime. So VoteFair does not prove P=NP :-)
>
```