# [EM] Intro to list - Beatpath reps

Ernest Prabhakar drernie at mac.com
Sat Nov 1 11:42:04 PST 2003

```At 1:52 PM -0800 10/28/03, Rob LeGrand wrote:
> I generally prefer Schulze's beatpath to Ranked Pairs, but the ranking
> returned by Ranked Pairs has an important advantage:  Every candidate
> beats
> pairwise the one just below him in the ranking.

Hi all,

I'm new to the list, but I've been following the Yahoo archive for a
while, and have been playing around with some Python implementations of
a Condorcet beatpath strategy.    The one issue I'm particularly
concerned with -- which I think this thread started with - is the
question of how best to present information.  I actually think that's
pretty critical, since (for anything more complicated than Approval)
transparency to the average voter will be essential to acceptance.

I'm trying to tackle this in two stage.  One, I'm trying to find an
output format that concisely summarizes all the essential information,
so that it can be easily audited.   Then, I hope to find a simple way
to explain the results using ordinary concepts (for example, perhaps
Condorcet could be described as an "Instant Round Robin", since it is
effectively a series of pairwise matchups).

The format I am exploring for expressing a relative beat is:

A -- x/y -> B

For a 'primitive' beat, this is simply:
x = votes for A over B
y = votes for B over A

Yes, I know that Beatpath explicitly ignores 'y' (though I've always
been unclear why, since it seem like it would implicitly get elided
anyway), but at any rate I think it is important to track.

For a formal beatpath, this format would expand to:
x = weakest link of the chain from A to B
y = weakest link of the chain from B to A
as in:
x:	A -- x1/y1 -> C -- x2/y2 -> D -- x3/y3 -> B
where x[i] are the primitive beats, and x = min(x1,x2,x3)
and similary for B

If I understand it correctly, Beatpath can in principle be used
repeatedly to define a well ordered list of candidates (assuming no
actual ties).    Thus, it should only be necessary to list how each
candidate beats the one below it.  My hypothesis is that the resulting
sequence:

A -- x/y -> B
x:	A -- x1/y1 -> C -- x2/y2 -> D -- x3/y3 -> B
y:	B .... E .... F ... A
B -- w/z -> C
w:....
z:....
C....

should in fact contain all the information needed to audit the process,
with a minimum of redundancy. It might also provide enough information
for people to post-mortem the results using alternative Condorcet
tiebreakers, though I'm not sure about that.

Does this make sense?  If people are interested, I can clean up and
post my Python code (under the GPL, derived from Mike Ossipoff's
CondorcetSSD).  I would love to see this sort of "easily-auditable"
results become the norm, and would be happy to work with people to tie
it into some online or Open Source voting tools.

-- Ernie P.

```