Comparison of latest Condorcet Variants

[Norman Petry]

Mike,

You wrote, in regard to indecisiveness in Schulze:

>To check Schulze for decisiveness, take my mistaken
>indecisiveness example, the one that we've been referring to,
>and multiply all of the defeats in the subcycle by 10.
>
>Now, the subcycle members' defeats of each other  within the
>subcycle are stronger than any other defeats. So now A has
>a Schulze win against B & C. And D & E both have Schulze wins
>against A. So there's no Schulze winner.

Doing as you suggest, the problem becomes:

A>B 20
B>C 30
C>A 10
{A,B,C}>D 7
E>A 8
E>B 5
E>C 4

Analysis:

A>>B 20:10 (A>B vs. B>C>A)
A>>C 20:10 (A>B>C vs. C>A)
A>>D 7:6 (A>D vs. D>E>A)
B>>C 30:10 (B>C vs. C>A>B)
B>>D 7:6 (B>D vs. D>E>A>B)
C>>D 7:6 (C>D vs. D>E>A>B>C)
E>>A 8:6 (E>A vs. A>D>E)
E>>B 8:6 (E>A>B vs. B>D>E)
E>>C 8:6 (E>A>B>C vs. C>D>E)
E>>D 7:6 (E>A>D vs. D>E)

So once again Schulze is decisive, choosing E.

(Pairwise Dropping also picks E).

I suspect that the Schulze method will only be indecisive in cases where
there are large numbers of ties in the beat-paths, which is probably the
basis for his suggested tiebreaker.

Perhaps Markus could devise an example of where his method is indecisive?
I'm interested in seeing how and/or why the tiebreaker he suggested for his
method would work, but that's difficult when we can't find a single example
of when it would be necessary!


Norm Petry


-----Original Message-----
From: Mike Ositoff <ntk at netcom.com>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Cc: ntk at netcom.com <ntk at netcom.com>
Date: August 8, 1998 9:24 PM
Subject: Re: Comparison of latest Condorcet Variants


>
>Hi--
>
>I probably left a few crucial words from my statement of
>Sequential Dropping:
>
>"...until an alternative is unbeaten". That, or words to that
>effect, are in Condorcet's own wording, and I meant to include
>them, and apologize if I left them out.
>
>So, as soon as you dropped E>C 4, C became unbeaten.
>
>***
>
>But thanks for showing me that I'd been mis-applying that rule
>in that example! Again, I'd forgotten about the larger cycles
>that the subcycle defeats are part of. Consequently, I'd thought
>that the method elected E in that example, and complained that
>I disliked that result. So you've shown that I don't have an
>example where Sequential Dropping does something that I don't
>like.
>
>***
>
>Of course, when those additional words are included,
>Sequential Dropping is decisive, because:
>
>At least by the time it eliminates all of the cycles, there
>can't not be an unbeaten alternative.
>
>And there won't be more than one, because the method stops when
>it makes one.
>
>That's the advantage of the sequential process that stops when
>it's no longer needed, as opposed to my wording that simultaneously
>drops every defeat that conflicts with larger defeats.
>
>***
>
>To check Schulze for decisiveness, take my mistaken
>indecisiveness example, the one that we've been referring to,
>and multiply all of the defeats in the subcycle by 10.
>
>Now, the subcycle members' defeats of eachother within the
>subcycle are stronger than any other defeats. So now A has
>a Schulze win against B & C. And D & E both have Schulze wins
>against A. So there's no Schulze winner.
>
>***
>
>Maybe I've overemphasized the importance of decisiveness, because
>a tiebraker like plain Condorcet(EM) is quite briefly worded, and
>seems like it would always be fair, at least as I judge it.
>
>But still, it's another thing to say. Somewhere in that last
>"And if..." clause might be where you lose your listener.
>
>***
>
>I now am not sure if LOP & FOP violate Pareto. Can a cycle
>contain a unanimous defeat. Not with just 3 alternatives, it
>seems to me. But in general I don't know. That question's answer
>may be obvious to some. If so, let me know the answer.
>
>***
>
>Sequential Dropping is looking much better, now that Norm has
>shown me what it actually does in the example. If it won't do
>the somewhat undesirable thing that I though that it did, not
>ever, then it seems surely better than SC. Otherwise, there's
>a trade-off between them.
>
>But of course we don't, at this time, have enough information
>about all the important properties, advantages & disadvantages
>of these few methods to say which one of them is best.
>But Sequential Dropping is simple.
>
>***
>
>Mike
>
>
>
>