[EM] Cloneproof Schwartz Sequential Dropping / Schulze

[Markus Schulze]

Dear James Green-Armytage,

I wrote (18 July 2003):
> Example:
>
>    A:B=50:50
>    A:C=50:50
>    A:D=50:50
>    B:C=75:25
>    B:D=40:60
>    C:D=65:35
>
> SSD would declare A the winner since he is the only
> candidate who isn't beaten by anybody.
>
> CSSD would drop B:D to get rid of the B>C>D>B cycle.
> And then it would report a tie between A and B.

You wrote (6 Oct 2003):
> Thank you very much for the example. It certainly helped to
> show how SSD and CSSD can produce different results. The one
> thing that I don't seem to understand yet, though, is what
> makes CSSD cloneproof where SSD is not. In the example above,
> I don't think that there are any clones. Do you by any chance
> know of an example where the addition of clones changes the
> result in SSD but does not change the result in CSSD? I would
> be very much obliged.

In the example above, simply by looking at the pairwise defeats
it is not possible to exclude that B, C, and D are a set of
clones. The underlying voter profile could look as follows:

   40 ABCD
   35 DBCA
   10 ACDB
   15 CDBA

Therefore, independence of clones says that A's winning
probability in the example above must be the same as
in the following example where the candidates B, C, and D
are shrinked to a single candidate B:

   50 AB
   50 BA

CSSD guarantees this, SSD doesn't.

Markus Schulze