# [EM] Cloneproof SSD

Markus Schulze schulze at sol.physik.tu-berlin.de
Thu Jan 18 01:51:42 PST 2001

```Dear Mike,

you wrote (17 Jan 2001):
> Markus wrote (17 Jan 2001):
> > Both heuristics, the beat path heuristic and the Schwartz set heuristic
> > for the Schulze method, have advantages and disadvantages. Therefore I
> > suggest that one should always use both heuristics simultaneously. The
> > main disadvantage of the Schwartz set heuristic is that one has to
> > explain and justify too many tiny little details.
>
> Probably so. But the overall SSD procedure is compellingly plausible
> & natural. As I said, I defined it for someone who had no experience
> with voting systems, and she immediately understood the rightness of it.
> The details that you refer to are for small committees. Public proposals
> don't much need the details.

For public proposals there is no need to concentrate on only one of the
two heuristics. The unique situation where one has to concentrate on only
one heuristic is where one has to write the laws of a given organization.
And I suggest that here the beat path heuristic is better because fewer
details have to be specified.

******

You wrote (17 Jan 2001):
> Markus wrote (17 Jan 2001):
> > Example 2: Suppose that there are 5 pairwise defeats of equal
> > strength. Then some people will suggest that all these pairwise
> > defeats should be dropped simultaneously. Some people will suggest
> > that all 5!=120 ways to drop one defeat after the other should be
> > checked to calculate the winners. Some people will suggest that one
> > should decide randomly which of these defeats should be dropped.
> > Some people will suggest that the pairwise defeats should be
> > dropped in such a manner that the strengths of the then following
> > dropped pairwise defeats are lexicographically minimal.
>
> Good point. There could be argument about that. But, for one thing,
> would any of those plausible solutions cause a problem in small
> committees?

Not all solutions guarantee that the strong version of clone
independence is met.

You wrote (17 Jan 2001):
> Even if so, there'd be plenty of time to explain that.
> I don't think anyone would seriously insist on the 5! solution.

Tideman suggests for his "Ranked Pairs" method that all n! ways to
drop one pairwise defeat after the other should be checked. And I
believe that this is the unique way to guarantee that Tideman's
method meets the strong version of clone independence.

I guess that it will be difficult to explain why you have to do
this when Tideman's method is used and that when the Schwartz set
heuristic is used.

You wrote (17 Jan 2001):
> Markus wrote (17 Jan 2001):
> > Example 3: It isn't clear (and as far as I remember correctly
> > you haven't explained) what has to be done when the winner of
> > the Schwartz set heuristic is not unique.
>
> Existing electoral law covers that: Draw lots. For small
> committees, sure one should mention that possibility, and
> suggest randomly choosing between alternatives tied for winner.
> But that would be so obvious a solution that it wouldn't be a
> problem.
>
> Anyway, my solution for more than winner is to choose randomly
> among the winners. I don't think it's necessary to use Random
> Ballot instead of Random Candidate, because if two alternatives
> are pair-tied, then Random Ballot & Random Candidate become the
> same. Random Candidate is more familiar, and if the committee is
> at all large, it's easier to choose from among the smaller number
> of tied alternatives than from all those ballots.

Of course, Random Candidate is simpler than Random Ballot.
But when you use Random Candidate, then the strong version of
clone independence is violated.

******

You wrote (17 Jan 2001):
> But most of the details are crucial only in small committees. And
> final ties for winner are provided for in existing electoral law.
> Defeats tied for weakest, that could require a special rule, unless
> the "draw lots" law is construed to apply to all ties, even ties
> for weakest defeat, in the middle of the count.
>
> Anyway, I acknowledge that BeatpathWinner may have fewer details
> to deal with. That makes it appealing for a committee that would
> appreciate BeatpathWinner, but it doesn't seem to outweigh SSD's
> greater overall plausibility for people who are completely new to
> voting systems.

Again: When one only wants to explain this method, then there is no
need to concentrate on only one heuristic. Only when one wants to
write the laws of a given organization, one has to concentrate on
only one heuristic.

Example: Suppose that you have used the Schwartz set heuristic to
motivate this method. Suppose that someone asked you to explain
whether this method meets monotonicity. Would you consider it to
be inconsequent to use the beat path heuristic to explain this?

Markus Schulze

```