Vacancy Rule - STV cycles rule

Mike Ositoff ntk at
Fri Jul 31 13:39:03 PDT 1998

I'm replying to the letter from Don Davison (New Democracy).

I'll reply to his second point first. He has misquoted my proposal.

He says that I said to make part of the list by repeated use of
a single-winner method, rather than by STV. Not so. I suggested
doing STV counts for every possible value of N, from 1, up to
the number of seats in the house. (except that I personally like
using a better single-winner method for when N=1, rather than using
STV for that--but I realize that it's simpler just to use STV for
_all_ N).

As I was saying before, whether the precedence rule is that of
Rank STV(NP), or Rank STV(MO), choices must be made _after_ the
STV winners have been found. In STV(NP), when there's a
house=nonmonotonic contradiction between 2 successive STV counts,
it's necessary to make the _single-winner_ choice of one of the
new STV winners, to determine which of them gets the Nth seat.

And in STV(MO), in the same situation, when N is less than the
current fractie-size, it's necessary to order all of the new STV
winners (the ones not already on the list), to determine the order
in which they'll be added to the list. Again, STV isn't for ordering
candidates; it's only for choosing N candidates. PR isn't for ordering.
Single-winner methods are. A "social ranking" is one of the outputs
from a single-winner method. Of course 1 winner is the other kind
of output. So then, I suggested repeated use of a single-winner
method, in that instance, to choose the order in which to add the
new STV winners to the list.

But please note that then I said that, even though, ideally, I'd
like to use one of the best rank-methods for the choice and the
ordering described in the previous 2 paragraphs, it would probably
be better, as a practical matter, to just go by 1st choice vote
totals instead. To simplify the proposal, and to avoid introducing
any more new rules than necessary, and to avoid extra debate.

You feel that the use of a rank-method would violate PR, but
for that particular choice, it isn't a PR matter. And I don't
think you can complain about the use of 1st choice vote totals
because all you're counting is people to whom the candidates are
favorite, and who, therefore, had very much to do with making them
win the STV count. 

So that objection is settled, is it not?


Don's other issue was about the nonmonotonicity. Of course it
goes without saying that it would be wrong to throw out a sitting
councilmember when doing a new STV count, with the old rankings,
to fill a vacancy.  That isn't what we're doing here, though.

Of course the following wouldn't be good: When Rank STV(MO) has
done (say) its 7-candidate STV count, we call up each winner of
it, and say "Good news! You made the list! Our STV count for 7
seats has chosen you to be on our party list. Tell your parents,
and all of your friends!" Then we call up the guy again and say,
"Sorry, man. The STV count for 8 seats has dumped you from the list."

That would be absurd to do. The output of the method is the final
list. Does house nonmonoticity occur when no one has actually
occupied a seat, and the method's intermediate steps aren't 
called-out as they take place? When you're considering whom
to hire, do you call someone up & say, "Right now I'm considering
you", even though you haven't chosen them?

Aside from all this, as rare as house nonmonoticity is, wouldn't
it be all the rarer for the candidate that it dumps not to be
a winner in subsequent STV counts?

Another house nonmonotonicity problem is in U.S. House of Representatives
apportionment. If you add a seats to the House, and that results
in a state losing a seat, everyone's going to say "What kind of
nonsense is that method?" That's called the "Alabama paradox", because
it was pointed out at one point that it would have happened to
Alabama. Again, none of these problems apply to the problem at

I've already agreed that Rank STV(NP) is likely a more practical
thing to propose to the party members, especially if they'd
accept a briefer rule better than an aesthetic argument.

What you suggested was Rank STV(NP)  (except that you didn't
realize that there are unavaoidable single-winner choices that
sometimes need to be made).


Though I disagree with the house-nonmonotonicity objection,
I've agreed that Rank STV(NP) may well be more winnable if
brevity is the important thing to the people to whom it must
be proposed. And I've agreed that just using 1st choice vote
totals would be simpler to propose, and likely more winnable
among the party members, for the reasons that I gave.

So there isn't really much disagreement.

By the way, speaking of nonmonotonicity, STV is also subject
to vote nonmonotonicity, where you can defeat a candidate by
ranking him higher. We just accept that when we use STV. 
We certainly don't need to accept it in single-winner choices,
which is one reason why the academic authors so dislike IRO.
But single-seat STV is tolerable for Rank STV when N=1,
because it's unlikely to be needed, and for the sake of
greater simplicity & less to define & explain. But if we were
talking about a party with significant likelihood of winning
exactly 1 seat, then I'd strongly oppose using STV when N=1.

Mike Ossipoff

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