Vacancy Rule - STV cycles rule

Norman Petry npetry at
Fri Jul 31 22:33:15 PDT 1998


Your last two postings regarding Ranked STV have brought to light a subtle
difference in the way our two methods solve the problem of non-monotonicity.
Looking back on my original posting, I realised what the problem was.  On
July 28 1998 in describing my method I said:

>2) Fill the remaining ranks by holding repeated STV elections with
progressively >lower quotas (Droop Quota = votes/(currentRank+1)]+1).  For
these STV counts, >you would need to employ an additional rule: no candidate
whose ranking has >already been determined may be eliminated (even if they
are ranked lowest).

I realise now that I've created confusion through the sloppy use of terms.
To be precise, I should have said:

"no candidate whose ranking has already been determined may be eliminated
(even if they have the fewest votes)."

By "eliminated" I meant the type of elimination that occurs _during_ an STV
count, where there are unfilled vacancies and none of the remaining
candidates have reached the quota.  Conventional STV then resorts to
eliminating the candidate with the fewest votes.  Normally, it would be
reasonable to say that this candidate is "ranked lowest", in the sense that
the currently unelected (or "continuing") candidates can be ordered
according to their vote totals.  It's misleading, however, when we're also
talking about using STV results as part of a larger process to prepare a
_ranked_ list of candidates.

Therefore, because of my undefined use of the word "eliminated", and
positively misleading use of the word "ranked", you reasonably assumed that
my rule was the same as yours (at least for N>C, where C is the previous
caucus size), since "elimination" might also mean removal from the
established set of rankings.  Sorry for the confusion!

To be perfectly clear, then: the meaning I had intended (which is, I think,
how Don Davison interpreted my method) was that this requirement would be
applied _within_ the stages of each STV election.  So, where a conventional
STV procedure would have an elimination rule like:

"In the event that there are unfilled seats and no continuing candidates
have reached the quota, eliminate the candidate with the fewest votes and
transfer the ballots to subsequent choices."

Ranked STV[NP]'s elimination rule would be:

"In the event that there are unfilled seats and no continuing candidates
have reached the quota, eliminate the *previously unranked* candidate with
the fewest votes and transfer the ballots to subsequent choices."

Therefore, Ranked STV[NP] is necessarily house-monotonic, and doesn't
require the use of a single-winner method (except for dealing with ties, as
in conventional STV).  The implication of this rule, of course, is that the
candidate to be eliminated will not be the one with the fewest votes, in
cases where house-monotonicity would be violated under a conventional STV

In contrast, my understanding is that Ranked STV[MO] uses a strictly
conventional STV count, and then tries to reconcile incompatibilities
between successive counts caused by the effects of house-monotonicity
violations.  The set of candidates produced by each STV count is compared to
the previous set of rankings.  If exactly one new winner appears, no
problem -- just assign it the last ranking.  If house-monotonicity has been
violated, however, 2 or more new candidates will have appeared in the
current set of winners (and 1 or more previously ranked candidates will be
missing).  Assuming we're dealing with the case where N (the current rank
being determined) is greater than C (the previous caucus size), the
previously ranked candidates may not be replaced by the new winners.
Therefore, a single-winner method is needed, since there's no way of
shoe-horning the 2 or more new candidates into the one available slot.


So, I hope now that this difference between Ranked STV[NP] and Ranked
STV[MO] is clear.  I've prepared an example with analysis showing how these
differences in elimination methods might affect candidate ordering, which
I'll be posting tomorrow.

Norm Petry

-----Original Message-----
From: Mike Ositoff <ntk at>
To: election-methods-list at <election-methods-list at>
Cc: election-methods-list at <election-methods-list at>
Date: July 31, 1998 2:48 PM
Subject: Re: Vacancy Rule - STV cycles rule

>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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