IRO and Condorcet

Tom Round TomR at
Thu Nov 21 23:30:00 PST 1996


While still reserving my main reply to the points that Mike Ossipoff
raised concerning Approval Voting's [AppV] superiority over
Instant Run-Off [IRO], I'd like to add a couple of early
clarifications, plus some comments on Condorcet versus IRO.
(Perhaps we could call IRO "Hare-Ware", after
its two creators, to distinguish it from "Hare-Clark" the
multi-seat version?)

Deane Crabb, my PR Society of Aust colleague from South
Australia, responded that he supports the use of Hallett's
system for single positions, and that the Australian Democrats
(for which party he is national returning officer) use Hallett
for policy referendums of the membership.

[As far as I know, Hallett's method is very much like
Condorcet's and like Prof E Nanson's, of Melbourne Uni last
century. I assume it's one that guarantees the election of a
candidate who defeats all rivals in single combat, although
perhaps it has a different fallback rule to decide the result
when no candidate is the "absolute Condorcet winner" by this
criterion. For the purposes of the following comments I will
speak of Condorcet, Hallett, Nanson and other pairwise methods
en bloc as opposed to IRO/ AV/ single-seat STV.]

I believe that John Taplin, and the PRSA West Australian
Branch as a whole, also support Condorcet for single positions
and for referendums, as does one of my Queensland Branch
colleagues. (I am curious how the WA Branch got away with this
under the National PRSA Constitution, which requires Branches
to advocate the STV system set out in the "PR MANUAL" for
_all_ elections.)

Over the past year, I myself have been persuaded by the able
advocacy of Mike Ossipoff and Steve Eppley that Condorcet is
superior to IRO. I believe that Condorcet can be seen as
extending more exhaustively the logic behind STV (ie, of not
wasting a vote on a candidate who's going to be defeated
anyway) and expunging from STV a remnant of first-past-the-
post's logic (if the candidate with most primary votes is not
necessarily the one to be elected, why should the one with
fewest primary votes necessarily be the one to be defeated?)
If the Smith set and smallest pairloss are the best
refinements of Condorcet for defining a winner when no
candidate defeats all rivals, then so be it.

Of course, with multi-seat STV the above objections to IRO do
not apply. The candidate with fewest first preferences is only
defeated if, perhaps after several transfers, she receives not
many surplus votes from elected running-mates. We PR advocates
are quite willing to recognise that STV, though quite
satisfactory for filling five or seven seats, is much less
satisfactory for filling two or three seats; it's not that big
a leap then to conclude that it's not satisfactory at all for
filling only one seat. By analogy, party-list PR systems are
quite satisfactory (so far as _party_ proportionality is
concerned!) for filling five or ten or twenty seats; but if
d'Hondt, St-Lague or Highest-Remainder is used for a single
seat, it reduces to crude first-past-the-post. Thus most
European nations which use PR-List for multiple seats add a
second ballot when there's only one seat.

(I note parenthetically that runoff, _if_ used without
automatic elimination and _if_ there are disciplined parties,
is likely to see the election of a Condorcet winner. Absent
the "low man out" rule, a higher-polling party may well agree
to "stand down" for a centrist rival which is better placed to
win the second ballot. This has often occurred in France for
parliamentary elections, although at the Presidential level
the Constitution limits the runoff round to the highest two
contenders from the first ballot. It is ironic that France's
two main voting systems - PR-List and runoff - have ended up,
by evolution rather than by design, emulating the
recommendations more than two centuries ago of les deux
Marquis, Mirabeau and Condorcet, respectively.)

If a community wants to refine STV by adding pairwise elements
 - such as the Eppley-Condorcet, the Hallett or the Nanson
system - then well and good. (Hoag and Hallett themselves, in
their 1926 classic "PROPORTIONAL REPRESENTATION", suggest such
refinements, eg, for a national legislature electing delegates
to an international assembly. Perhaps Mr Boutros-Boutros Ghali
might take an interest in this (:- ?) But plain STV for five
or more seats is adequate as it stands.

Certainly I think it's good tactics to publicly point out the
flaws in IRO since that would be the first step to getting
proper PR introduced. In Australia, one of the biggest
obstacles to PR's introduction is that IRO is not as
_obviously_ unfair as plurality. Back in 1989, Laurie Oakes, a
prominent Canberra political journalist, wrote in "THE
BULLETIN" magazine that IRO was a "nice compromise between
first-past-the-post and proportional representation". Rather
like saying that Rhode Island is exactly midway between London
and New York! Our national President, Geoff Goode, got a
letter published in reply pointing out that IRO is not a
system of PR.

In any case, I'd abolish single-seat popular elections if I
had my way, replacing them with PR-STV, and by-elections with
count-back. And I support the executive being elected not
directly by popular vote but by the legislature - in which
case, party deals and discipline would make the precise voting
system a secondary issue, the real crux being the coalition
negotiations among parties. Therefore I envisage the main use
of Condorcet in Australia being for referendums, these being
the only popular elections by majority vote that would remain.
And this use should be largely uncontroversial, since
multiple-choice referendums are unknown so far in Australia.
Counting the votes by a pairwise system would seem less
unfamiliar than would having preferential voting in
referendums in the first place. The likely alternative that
would be adopted for referendums if Condorcet isn't used is
the non-preferential California rule - "whichever proposition
polls more YES votes, prevails" - according to most Australian
CIR draft bills that I've seen.

Deane Crabb challenged my statement about electoral reformers
seeming inconsistent if we advocate different systems for PR
elections and for majority decisions (referendums, single-seat

I should clarify that what I regard as most important is that
the METHOD OF VOTING should be uniform, as far as possible.
How the ballot is filled out is the aspect that most directly
impacts on the average voter. The exact details of how the
ballots are counted are less obvious. Thus, STV for multi-seat
elections with Condorcet for referendums and (occasional) by-
elections would not seem arbitrary to the voters. Under both
systems, every voter could pretty much safely vote her true
order of preference. Whereas voting by numbers to elect two
county comptrollers, while voting using ticks of approval to
elect the county chairperson, would look highly arbitrary. The
voting strategies required for different elections would then
vary greatly.

I used to believe that uniformity of electoral rules were non-
negotiable. Much of the argument in my thesis "A MATTER OF
PREFERENCE" (1992) is based on this "transferability" of STV.
I would still agree that electoral rules should as far as
practicable be uniform, without distinctions based on
irrelevant factors. However, I do think now that the
difference between a majority decision (where, to quote the
bad guy from "HIGHLANDER", "there can be only one") and a
proportional decision (where, ideally, all viewpoints should
be heard) is sufficiently deep to base a distinction upon.
When only one can be selected, then extra care ought to be
taken to ensure that that one really is the majority choice.

For one thing, with only one winner, elected candidates'
surplus votes are never counted. As Enid Lakeman wrote in the
appendix to "HOW DEMOCRACIES VOTE" (1974), in a multi-seat
election the candidate who is "everyone's second choice" will
probably be elected anyway. One might say that STV-PR counts
one preference at a time to fill numerous seats, whereas
Condorcet counts numerous preferences at a time to fill one
seat. Both ensure - unlike IRO - that the voter ends up with
most of her highest preferences counted before anyone is
defeated. (Of course, in Condorcet no one is actually
"defeated", as such, until the final seat has been filled.)

The uniformity which I believe is mandatory for all elections
is that the voting system ought to encourage every voter to
cast a sincere vote, by guaranteeing - as far as practicable -
that giving a preference to one candidate will help to elect
her at the expense of a lower-ranked, but not a higher-ranked,
candidate. Thus, I would reject such electoral variations as
that prescribed by Queensland's Local Government Act, which
lays down IRO for single-seat local elections and first-past-
the-post block vote for multi-seat elections. This variation
serves no good purpose other than the convenience of shire
clerks who want the simplest system to administer as returning

Thus I would still support a uniform principle for all
elections (single- or multi-seat) and referendums, though
phrased slightly more broadly than previously. If writing
rules to entrench for all time in a Constitution, I'd lay down
something like the following _VERY_ rough draft ...

(a)  The primary goal is that whichever voting system
     encourages, to the maximum extent, every voter to cast a
     sincere vote [etc, as above], shall be used.

(b)  For elections to fill 2 or more identical positions
     together -

     (i)  A proportional system shall be used, with a quota of
          votes based on the number of seats being sufficient
          to elect a candidate, and with ballots being
          proportionately reduced in value whenever they elect
          a candidate.

     (ii) The system set out in Schedule _1_ is deemed
          adequate to meet the above requirements and shall
          apply unless replaced by the legislature with
          another system that is demonstrably better at
          meeting these requirements.

     (iii)     In particular, having the last seat, the last
          several seats, or all of the seats filled one by one
          by using the system set out in Schedule _2_, instead
          of by eliminating the candidates with fewest votes,
          is deemed better.

(c)  For every election to fill one unique position, or to
     fill several non-identical positions together, and for
     any referendum where two or more competing counter-
     proposals are all carried and must be ranked in priority,

     (i)  A majority system shall be used to fill each
          position, with ballots being unchanged in value
          whenever they elect a candidate.

     (ii) The system set out in Schedule _Y_ is deemed
          adequate to meet the above requirements and shall
          apply unless replaced by the legislature with
          another system that is demonstrably better in
          meeting these requirements.

Schedule _1_ then sets out rules for a Hare-Clark STV-PR
system; whereas Schedule _2_ sets out rules for a Smith-
Condorcet pairwise system, along the following lines:

     (i)  To fill each seat, all candidates are compared

     (ii) If each candidate, in a set of one or more, defeats
          pairwise every candidate outside that set, then
          every candidate outside that set is defeated for
          that particular seat.

     (iii)     Of those candidates not yet defeated, the one
          whose largest defeat margin (that is, the number of
          votes received by any candidate defeating her
          pairwise) is smallest, is elected and all others are
          defeated for that particular seat.

     (iv) In calculating the next seat, any candidates already
          elected are excluded, but all other candidates
          (including any previously defeated) are included.

Of course if the technical experts are divided in their
opinion, then the legislature would enjoy some discretion in
fleshing out the details of this constitutional mandate. But
the courts would step in to strike down laws that clearly went
outside the parameters of this formula. No reasonable judge,
for example, could rule that "single-shot" plurality voting
fulfils these requirements better than does either STV or

Note that criterion (b)(i), although brief, would rule out
various different inferior systems - such as "multiple
transferable votes" (winner's ballots transferred without
reduction, "quota" is a majority; used for Australian Senate
1918-48), "bottom-up" (lowest candidates successively excluded
and preferences distributed until remaining candidates equal
number of seats; votes over quota not transferred), and even
STV with random transfer (Aust Senate 1948-84), or with the
"transfer all ballots, even in different batches, at the same
value" defect (Aust Senate since 1984), which can increase
some ballots' value after a transfer.

Schedule _2_'s formula (in (ii)) will elicit either the
absolute Condorcet winner (if only one in set), or else the
Smith set (if more than one). I assume it's not necessary to
specify that Smith is the _smallest_ such winning set because
merely repeating the application of the "candidates outside
winning set are defeated" rule in successive stages will
ultimately reduce down to the smallest such set.

For a multi-choice referendum, I advocate a system whereby -

a)   Those proposing a proposal can demand that it "compete"
     on the ballot against another proposal already proposed.
     (Thus, if Motion A's proponents want A to compete against
     B, and Motion C's proponents want C paired against B,
     then A, B and C are all listed as "candidates" in the
     same referendum.) "Proponents" may be either legislators
     or, where initiative exists by law, citizen petitioners.

b)   Each referendum offers voters choice between the positive
     options (ie, the single proposal traditional in a yes/no
     referendum, or two or more competing proposals) plus one
     negative option ("NO", "NONE OF THE ABOVE", or whatever).
     Voting is optional-preferential in both cases.

c)   First each proposal is compared pairwise against the
     negative option. Any that polls more "YES" votes than the
     negative option, plus receives a preference from the
     required "quorum" (eg, 25% or 33.33%) of the total
     electorate, is approved. Any others are defeated.

d)   If two or more proposals are carried by referendum at the
     same poll, they are all valid; but they must be ranked in
     order, so that if a conflict arises the higher-ranked
     overrides the lower. (The normal rule that "the later in
     time prevails" is not much help.) I suggest the following
     ranking rule:

     i)   As between two proposals in different referendums on
          the same day, whichever referendum had the highest
          average YES vote for all its proposals, is ranked

     i)   As between two proposals competing in the same
          referendum, whichever is elected earlier using the
          Schedule _2_ pairwise method (as if the proposals
          approved were candidates for that same number of
          seats) is ranked higher.

Tom Round

Overflow-Cc: 100245.2440 at ('Geoff Powell'),
   afreeman at ('Andrew Freeman'),
   bmusidla at ('Bogey M'),
   c-p-r at ('Citizens for Proportional Representation'),
   crabb.deane at ('Deane Crabb'),
   dunnmj at ('Martin Dunn'),
   GGoode at VTRLMEL1.TRL.OZ.AU (Goode, Geoff),
   j.pyke at (John Pyke, QUT Law School),
   jhtaplin at ('John Taplin'),
   lee at ('Lee Naish'),
   martinw at ('Martin Willis'),
   mdt at ('Matthew Townsend'),
   voting-systems at ('Voting-systems')

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