As I think we all agree, if you can pick a single winner, you should by straightforward extension be able to rank all the candidates. In ranking the candidates we have, then, linearized the matrix. If it can be linearized in a reasonable way, I believe it can be done such that each candidate has not only an order, but a scalar dimension, i.e. a score -- in an equally reasonable way, that does not conflict with the ordering. Maybe this is a naive leap of logic (or maybe intuition) on my part, but I have yet to see an argument which leads me to believe otherwise.
Hi all,
Interestingly, I have been playing around with some Python implementations of a Condorcet beatpath strategy, and the one issue I'm particularly concerned with (since I currently work in Marketing) 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 AYes, 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 BIf 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.
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