Comparison of latest Condorcet Variants

[Mike Ositoff]

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