[EM] Schwartz//Tideman for meetings & small committees

[MIKE OSSIPOFF]

I'd said:

 > If anyone is concerned that, in a meeting, Tideman will embarrass
> > them by choosing outside the Schwartz set, they can use
> > Schwartz//Tideman. But that's something that won't happen in
> > public elections.
> >
> > Schwartz// may seem an inelegant patch, but sometimes a combination
> > like that can combine advantages of 2 kinds of methods.
>

Markus wrote:

>Does Schwartz//Tideman resp. Schwartz//MTM meet monotonicity?
>
>I am always very sceptical when someone proposes an iterative method
>or when someone proposes that candidates who could influence the
>result of the elections in later steps should be eliminated.

I've learned to not make claims about that. I don't think anyone
has proven one way or the other whether or not Tideman(wv) is
monotonic. I think there's a widespread opinion that it likely
is, because Tideman's own Tideman(m) surely must be, or Tideman
wouldn't have proposed it, and maybe were just hoping that that
one change, from "m" to "wv" wouldn't affect monotonicity.

It hadn't occurred to me that limiting the choice to the Schwartz
set could cause nonmonotonicity. Maybe that's another case where
no one has proven one way or the other whether that can or can't
cause nonmonotonicity.

Isn't it true that, sometimes, proving that a method is monotonic
can be difficult, prohibitively difficult, or impossible
(maybe one of those true but umprovable propositions that we've
heard about)? That being so, isn't it reasonable to consider
a method innocent till proven guilty of nonmonotonicity?

***

Speaking of demonstrations of nonmonotonicity, your 7-candidate
SD nonmonotonicity example, like Blake's 9-candidate example,
doesn't specify all of the defeats. You showed why it isn't
necessary to specify the rankings, but I don't believe that you
ever showed that it isn't necessary to show all the defeats.
If you're assuming that all of the defeats you didn't specify
are smaller, and will be dropped first, I remind you that
leastness isn't enough to drop a defeat in SD: The defeat must
also be in a cycle, not only initially, but also at the time
when it is being considered for dropping.

Norm is the only one who has posted an SD nonmonotonicity
example, with no pair-ties or equal defeats, which specifies all
of the defeats. But Norm, did you actually run that example with
your SD count program? Because it seemed to me that Blake's
posting about his example contained a count error.

***

Isn't it true that PC is monotonic? Why that seems so to me:

PC can be restated: If no one is unbeaten, then the winner is the
candidate whose greatest defeat is the least.

By lowering Gore in my ranking, there's no way that doing that
can lower any of Gore's defeats or increase any of anyone else's
defeats. There's no way that it can get rid of any of Gore's
defeats or cause a defeat for someone else. Because all it's doing
is adding preference votes against Gore and removing preference
votes against other candidates.

***

The fact that PC is monotonic, and that SSD is monotonic when
there are no pair-ties or equal defeats, makes it surprising that
SD is nonmonotonic without pair-ties or equal defeats.

I assume that Markus has proven Schulze's method's monotonicity,
which means that SSD is monotonic when there are no pair-ties or
equal defeats.

***

Mike Ossipoff



>
>Markus Schulze
>schulze at sol.physik.tu-berlin.de
>schulze at math.tu-berlin.de
>markusschulze at planet-interkom.de
>

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