[EM] Cloneproof SSD

[MIKE OSSIPOFF]

Markus wrote:
>I don't consider the Schwartz criterion to be "intuitive" and
>"obvious."
>
>The main justification of the Smith criterion is the fact that
>an additional candidate can change the Smith set only if he is a
>Smith winner. But it is possible that an additional candidate can
>change the Schwartz set without being a Schwartz winner.

Sure, that can give the Smith Criterion more appeal than the Schwartz
Criterion. Also, I sometimes argue that violating the Schwartz Criterion,
while not violating the Smith Criterion won't cause any strategy problems, 
and that violation doesn't sound very wrong to me, because
if a candidate ties one candidate in the Schwartz set, but doesn't
beat any of its members, the people, when voting him equal to that
Schwartz set member, have said that he's equally good as that Schwartz
set member. So how wrong can it be to elect him? I always say, then,
that violating the Schwartz Criterion is merely an aesthetic gaffe.
For instance, I don't consider Tideman's ability to fail the Schwartz
Criterion to be a serious problem. That violation is an embarrassment,
and it's nice to avoid it, but it isn't a serious problem or wrong.

But none of that changes the fact that it's the Schwartz set, and not
the Smith set, that means something when we're dropping defeats.
Dropping defeats increases the size of the Smith set, but decreases
the size of the Schwartz set. And you know that no one is going to object if 
we say that if there's a set of candidates who are unbeaten
from outside that set, there's something special about those candidates,
and it isn't unreasonable to say choose the winner from among that set.

We agree that there's no reason why choosing from the Schwartz set is
essential. But it's also true that it isn't objectionable either.
In fact, it's un-aesthetic to not choose from the Schwartz set. For that
reason, SSD is very plausible & natural.

>
>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. Existing electoral law says to draw lots in
the event of a tie. Ties for winner are so rare in public elections
that it doesn't matter how they're solved. Equal defeats tied for
dropping? I'd just drop them simultaneously, but if the existing
law can be applied instead, and isn't explicitly limited to final ties
for winner, then there'd be nothing wrong with dropping the equal
defeats in random order "by lots".

In a small committee, one has much better opportunity to discuss the
tie contingencies, and the committee-members will understand the
necessity of that.

>
>Example 1: Most people will simply proceed only until there is an
>unbeaten candidate (especially in so far as the runtime of the Schwartz
>set heuristic is giantic when the number of candidates is large). They
>will not understand why they have to proceed until there are no cycles
>any more.

That's ok, because, in public elections, pairwise ties are so rare
that there will be no clone problem, for all practical purposes.
And so, for public elections, I would propose ordinary SSD rather
than Cloneproof SSD. "Stop as soon as someone is undefeated".

For small committees, again, there's plenty of opportunity to
cover the contingencies and justify the cloneproof stopping rule.

>
>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? 
Even if so, there'd be plenty of time to explain that.
I don't think anyone would seriously insist on the 5! solution.
The simultaneous dropping solution is my solution, and I think people
would appreciate how much easier it is than the others.

Of course, in some small committees, one could successfully propose the
beatpath version. I just like the Schwartz version because it's a useful
public precedent.

>
>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.

My solution for equal defeats that are the weakest in the Schwartz set
would be to simply drop them all simultaneously.

>
>All these tiny little details have to be formulated when a given
>organization wants to adopt this method. Actually I believe that
>it will be significantly more simple to define the beat path
>heuristic than the Schwartz set heuristic in an exact and
>justifiable manner.

That's true, 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.

Mike


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