# [EM] RE: Election-methods digest, Vol 1 #388 - 7 msgs

MIKE OSSIPOFF nkklrp at hotmail.com
Sat Dec 20 01:55:02 PST 2003

```Someone wrote:

One of the side effect of the Markus and Mike chat is that I understand
Mike is programing something

No. I'm not programming anything. Yes, quite some time ago I posted a Python
program to implement BeatpathWinner. And yes, I re-posted the BeatpathWinner
algorithm a few days ago, this time not in any particular programming
language.

But I'm not now programming anything.

What started this discussion was when Markus said that my BeatpathWinner
algorithm wouldn't work, because it isn't the Floyd algorithm, whatever that
is.

The algorithm that Markus posted as the Floyd algorithm differs from mine
(actually Steve Eppley's) by only making one pass through the 3-candidate
permutations.

As I say in my reply to Ernie, my algorithm works. It looks at every
permutation of 3 candidates, i, j, and k. If the beatpath from i to j, and
the beatpath from j to k, are both stronger than the beatpath from i to k,
then the value of the minimum of B(i,j) and B(j,k), which is the strength of
the beatpath made by concatenating the ij and jk beatpaths, becomes the new
value of B(i,k)--the strongest beatpath from i to j found as-yet at that
time.

It repeatedly makes passes through the permutations until doing so doesn't
make any changes. Then its task is completed. Each pass finds one or more
new, longer beatpaths that replace a previous one that wasn't as strong.

The beatpaths that it initially looks at are single-step beatpaths, pairwise
defeats. But, via the process described above, the algorithm eventually
finds the strongest beatpath from each candidate to each other candidate.

If Markus believes that it doesn't work, I'd be curioius how he justifies
that claim.But sometimes he says it merely takes longer to execute than the
Floyd algorithm, and not that it doesn't work.

It was irresponsible for Markus to say that that BeatpathWinner algorithm
wouldn't work, unless he can justify his claim, tell why he thinks it
wouldn't work.

False statements, statements that he can't justify,  have always been
Markus's stock-in-trade. But this time he's doing the disservice of
misinforming people about a practical matter. But Markus doesn't care, he
just enjoys being on the attack.

Now, Markus says that it's possible to find all the strongest beatpaths by
making just one pass. He says the Floyd algorithm did that. According to
websites that I looked at, the Floyd algorithm doesn't find strongest
beatpaths, it finds shortest paths. I guess what Markus is saying is that it
can be modified to find strongest beatpaths. He says that, by changing the
order of the indexes in the line that tests and changes B(i,j) values, it
can complete its job in one pass. But, if that's true when its job is
finding the shortest path between each pair of graph-nodes, that may or may
not mean that it's true when its job is finding the strongest beatpath from
each candidate to each other candidate.

I'm not debating whether that's so. I don't know, and I don't reallly care.
It doesn't matter because, though Markus says that the one-pass procedure is
faster, both procedures are fast enough for all practical purposes.

As I said, the only reason why I said anything was because of Markus's
mistaken statement that the BeatpathWinner algorithm wouldn't work.

Mike Ossipoff

That person continued:

... The more I think about it, the more I
believe it might be this:
http://www.fairvote.org/ChoicePlus/
http://votingsolutions.com/

I have nothing to do with the fairvote website. The other one, I'd have to
check to find out what it is. But I'm not programming anything there.
There's an interactive BeatpathWinner counting website, and it uses an
algorithm similar to the one that I've posted here. But the website owner
didn't get the algorithm from me, and I'm not working on it.

That person continued:

If it is... I will come with more on that...

It isn't. I'm not programming anything there, and I'm not programming the
BeatpathWinner algorithm. I did that a long time ago.
Mike Ossipoff

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