Party List P.S.

[Mike Ositoff]

Regarding the candidate withdrawal option: Maybe someone could
pay a candidate to refuse to withdraw, & to be a "spoiler", but
that would likely be the end of that candidate's career. Of course
if they paid him well enough, he wouldn't care about the career.
But then we'd be no worse off than if we didn't have candidate
withdrawal as an option.

As for coalitions, I don't know. What is certain, though, is
that when a candidate withdraws, his votes go exactly where
his voters would want them to. His withdrawal when he loses,
but holds votes that could go to my next choice--that withdrawal
is in my interest. Of course maybe I'm in the minority, and
most of his voters have ranked someone after him whom I don't
like, but it's perfectly democratic, since every voter's
Plurality vote goes to his next choice.

(If anyone says that means that IRO is democratic, then I
emphasize that there's nothing democratic about IRO's 
_elimination_, when it eliminates someone preferred by the
majority. Voluntary candidate withdrawals are quite different,
being done in order to _avoid_ that sort of problem in whichever
method they're used with).

It _will_ be obvious to a candidate that he didn't win 
the Plurality count, and that if he doesn't withdraw, then,
because he's holding those votes, someone unnecessarily bad
wins. So he doesn't have to be able to forsee the future--the
present is all he has to go by.

Why not instead use a better method, that has less need for
candidate withdrawal? Of course there's a strong case for that.
But the reason for Plurality With Withdrawal is merely the
fact that Plurality is already well-known, and it avoids arguments
about what new count rule should be used. The withdrawal option
is the obvious answer to Plurality's well-known problem.

The fact that your ballots are mailed doesn't prevent using
the candidate withdrawal option. The ballots would be ranked,
and need only be sent once. Only 1 set of rankings is needed,
on which the Plurality counts are based. It's the candidates,
not the voters, who would react to the results of a Plurality
count.

One problem, if Plurality With Withdrawal were used as the
single-winner method for the system that I've proposed for
choosing & ordering party lists, would be if it were _often_
the case that not all of the N-1 candidates already chosen
for the list were in the current N chosen by the N-candidate
STV count. Because, then it would be often that the single-winner
method would be needed, and each time PWW is used, the candidates
would have to be on hand to withdraw when necessary. 
But if the house monotonicity violations are few, there wouldn't
be a problem.

Anyway, I'm not really _pushing_ for PWW over the other very
good methods from EM. I merely mention it as one of those very
good methods with its own advantages.

It had occurred to me, then, that if it's necessary to apply
the single-winner method often, it would be better to use
one that works well automaticlly, like Condorcet(EM),
Smith//Condorcet(EM), & Schulze.

What does the EM stand for? The name of this list, election-methods.
It's named after this list because here is where that version
of Condorcet's method was proposed & discussed, and we recommended
it to the ER list.

MR. Condorcet, in the 18th century, wasn't specific about how
to measure defeats. He probably assumed that everyone would vote
a complete ranking of _all_ the alternatives. But that does't
happen in real elections. So we don't know if Condorcet would
have favored measuring the defeat of B by A according to
"votes-against" (how many people ranked A over B); or "votes
for" (how few people ranked B over A); or "margins" (the
difference of those 2 numbers); or the ratio of those 2
numbers.

But we've shown here that "votes against" is what gets rid
of the lesser-of-2-evils problem and protects majority rule.

***

Schulze's method?

(Tell me if I'm mistaken)

* A beats B if more voters rank A over B than vice-versa.

* The strength of that defeat is the number of voters who ranked
  A over B.

* There's a "beat path" from A to B if either A beats B, or
  if A beats something that has a beat path to B.

* The strength of a beat path is measured by its weakest defeat.

*If A has a stronger beat path to B than B has to A, then A
 has a Schulze win against B.

*If an alternative has a Sculze win against each one of the
 others, then it wins.

***

However it seems to me that there could be elections without
a Schulze winner. In that case Condorcet(EM) would be a good
way to choose the winner. Or maybe there's always the possibility
that a different tie-breaker could confer new properties.
Maybe one could hope for a method that would avoid _all_
subcycle fratricide, not just in clone-sets. Or a method
that meets Positive Involvement (if Schulze doesn't already).

Schulze automatically chooses from the Smith set, and so avoids
the need to define the Smith set. But Schulze's definition is
(seemingly unavoidably) longer than that of Condorcet(EM), and
that could be an important factor in explainability. So Schulze
is almost surely better than Smith//Condorcet(EM), at least because
Schulze avoids subcycle fratricide in clone sets, and therefore
meets the stronger Independence from Clones Criterion.
But that's a "fine point" compared to the gross problems that
both Schulze & Condorcet(EM) get rid of.

Mike Ossipoff