# Replies (miscellaneous)

Tom Round TomR at orgo.cad.gu.edu.au
Mon Dec 2 00:08:43 PST 1996

```Dear Steve,

Here is my reply to a collection of various points you have
raised in response to my last few postings ...

(1)  "INSTANT-RUNOFF-1"

(ie, allowing/ encouraging equal preferences for 2 or more
candidates at once; counting each such preference as a full
vote, rather than dividing them equally.)

Thanks for the explanation. Perhaps this method might more
illustratively be called something like "Approval-
Preferential"? It sounds quite workable and, like Mike and
yourself, I would also rank it above Approval though below
Condorcet.

It seems analogous to the use, in PR-STV, of voters giving
equal preferences to be split equally (or parties opting for a
rotated rather than a party-determined order for their
candidates on the ballot). That is, the voter (or party) must
choose either "quality" or "quantity" - either ranking her
first choice over her second to ensure the first's election,
OR else ranking first and second equally so as to increase the
chance that either will defeat her third (or last) choice.

(2)  BAD "FALLBACK RULE" = INSINCERE PREFERENCES

I agree with Steve's point here. A system may elect a
Condorcet/ Beats_All winner if voters cast sincere votes, yet
at the same time encourage tactical voting through its
"default winner" rule. Borda's method might be one example,
since I _think_ (and seem to remember having read) that it
will elect a candidate ranked over every other, but at the
same time undermines this by tempting voters to misrepresent
their points for various candidates.

(3)  "SMALLEST PAIRLOSS"

Yes, I did mean "smallest pairloss" as shorthand for "smallest
largest pairloss". Like John Rawls (A THEORY OF JUSTICE, 1971)
we are focusing on the "best worse-case scenario", the
"maximum minimum" or "maximin".

(4)  "EPPLEY-CONDORCET PR"

By this I was referring to the method you posted a month or
two ago, whereby (a) one candidate is elected per stage to
fill one vacant seat, via Condorcet's method, and (b) after
each candidate is elected, a quota is deleted from the count
by reducing the transfer value of the ballots that elected the
last winner.

(In my mind I'd labelled it "Eppley-Condorcet", and had
thought over it so much that I ended up kind of forgetting
that that label wasn't yet in common use in the public domain ...)

It did seem a complex system. Eg, if used in a typical
Australian Senate election it would require 6 counts among 30,
29, 28, 27, 26 and 25 candidates respectively for the 6 seats.
The first count would require (30 x 29)/2 pairwise
comparisons, the second would require (29 x 28)/2 pairwise
comparisons among the remaining candidates, and so on ... plus
ballots would need to be adjusted in value after each stage.
Ordinary STV-PR will produce an entirely adequate result much
more quickly. So I agree with you that "Plain STV is probably
better than trying to mix in Condorcet compromise principles,
and is of course simpler."

(5)  MY TERMINOLOGY

Apologies for having used some peculiarly Australian terms in
my posting and confusing people. Again, these terms are used
so frequently here that it's easy to forget that they may
appear obscure to others. Here goes:

"BY-ELECTION": special election held to fill a seat that has
fallen vacant in mid-term.

In popular usage, often stretched to refer also to a
supplementary special election held when the general
election for a particular electoral district is either
(1) delayed [Dickson in Queensland, 1993 Federal election
- one candidate died, so nominations re-opened] or (2)
overturned for irregularities [Mundingburra in
Queensland, 1995 state election - defence personnel in
Rwanda had votes rejected because plane returned late].
It would probably also be [mis-] used for a supplementary
election held (3) to fill an uncontested seat not filled
at the general election. (This is rare in federal and
state elections here, but occasionally local council
seats are uncontested.) However, technically "by-
election" should be used only for a seat that is validly
filled at a general election but later vacated.

The name derives originally from the English term "by-"
meaning "local", as in "by-laws". As P J O'Rourke once
commented, "Why do you British politicians make such a
fuss about by-elections? I mean, why don't you just let
them go _BY_?"

"COUNT-BACK": procedure for filling casual vacancies by re-
examining the votes cast at the previous poll, and
electing one of the candidates who was a runner-up at
that poll and who re-nominates. Used in Tasmania, Malta
and now the Australian Capital Territory where STV-PR
systems operate. There are two different ways to apply
the count-back principle (usually, but not inevitably,
only one seat is vacant at a time):

(a)  re-run a count for all vacant seats according to STV,
with the proviso that no elected candidate can be
unseated. Otherwise such unseating might occur (didn't
someone, Hugh Tobin or Bruce Anderson I think, ask about
this a few weeks ago in response to a proposal by either
Donald or Demorep?), since the field of candidates will
probably be different, and this may affect the order of
elimination.

OR

(b)  re-examine only the ballots that elected each vacating
member (perhaps including some or all of the ballots that
would otherwise be "wasted" on losing candidates)
according to the system for filling a single seat.
Hitherto in STV systems this has been AV (Instant Run-
Off), but there's no reason why it couldn't be
Condorcet's method instead. Effectively this sets up the
quota of voters who elected the vacating representative
as a single-seat electorate.

I personally think Option (b) preferable on several
grounds. It is much simpler; it avoids the embarrassment
of a sitting member being seen as "defeated" and saved
only by a special deeming provision; and it allows the
use of Condorcet's method. The "single-seat constituency"
that is "assembled" to fill the vacancy is, it must be
remembered, a voluntary one, not one imposed on voters by
the drawing of lines on a map.

"C.I.R": Citizen-Initiated Referendum, the usual Australian
term for what in US parlance is usually called Initiative
and Referendum, in both the "positive" and the "negative"
senses (ie, both for enacting and for vetoing laws).

(6)  PARLIAMENTARY VERSUS PRESIDENTIAL

I'll wait until I've seen Steve's full reply before I respond.
However, I will tentatively say at present that having a
parliamentary executive has not seemed to deter voters from
supporting small parties in PR countries like Israel, Belgium,
Italy, The Netherlands, or the Scandinavian nations.
Conversely, in the USA voters have not indulged in the luxury
of electing many representatives outside of the Big Two
parties even though the Presidential executive allows them to
do so. (Use of single-seat plurality is one deterrent, but it
would not deter the rise of Canadian-style regional parties
with localised strongholds, so some other explanation must be
sought, given the strength of regionalism in US politics.)

In fact, France found that its politics became MORE bipolar
when it adopted a Presidential executive chosen by direct
election. There are still multiple parties, but now they had
to align themselves either for or against the incumbent
President, or for one of the two candidates in the
Presidential run-off. This is so even though about half of the
National Assembly elections held since direct Presidential
elections were begun in 1965 have been conducted under List-
PR.

Admittedly, Condorcet's method would be much more favourable
to small parties in a Presidential race than either runoff or
plurality (as in French and US presidential elections
respectively). However, Giscard d'Estaing's surprise 1974
victory - coming second on the first ballot and then winning
the "tour decisif" [decisive contest], overtaking the Gaullist
favourite whose first-round vote dropped to a mere 15% -
suggests that runoff does not always succeed in entrenching
the "big two" election after election.

For a more thorough discussion of this, refer the passages on
the US and French Presidencies in Samuel Edward Finer's text
"COMPARATIVE GOVERNMENT" (1974). Finer also "came out" as a PR
supporter when he wrote "ADVERSARY POLITICS AND ELECTORAL
REFORM" in the late 1970s.

(7)  "Sometimes, though, all else isn't equal, such as when a
minority will be very, very upset by a decision ..."

I agree with Steve that voting systems that try to measure
intensity of preference leave themselves vulnerable to
misrepresentation by the voters (or else to official
paternalism). At this point we leave the realm of voting
systems and enter that of rights and constitutional
entrenchment; we might need to replace the ballot-box with the
courts as the remedy.

For my part, I regard equal votes/ majority rule as a
derivation of the general principle of "equal consideration
and respect" for every person - a requirement of the Golden
Rule that we treat others justly, as we want ourselves to be
treated. When the requirements of the Golden Rule are clear
either way (eg, it would clearly prohibit a regime of racial
apartheid or genocide), then the majority has no power to vote
anything contrary to that requirement. But in the majority of
borderline cases, the G Rule does not give any clear-cut
guidance as to the RESULT. It does, however, dictate the
proper PROCESS - ie, equal voting, which in turn entails
majority rule.

I would re-phrase my earlier statement to say, not that a
majority choice is sufficient for a valid collective binding
decision, but that it is necessary.

(8)  "Of course, in Condorcet no one is actually "defeated",
as such, until the final seat has been filled" (TR).
"Final seat? In an election for only one seat? I think
I've lost the context" (SE).

In a single-seat election, that is still the "final seat". I
was also phrasing this so it could also apply to the "Eppley-
Condorcet" system referred to. What I meant is that, unlike
STV and AV, no candidate is conclusively eliminated from the
count until all seats, whether one or several, in that
electorate have been filled.

(9)  PRIMARY GOAL FOR A VOTING SYSTEM

Here's an improved wording for my draft of a primary goal:

"The system of rules for casting and counting votes
in every election and referendum must, to the
maximum extent practicable,
(a)  encourage every voter to cast a ballot expressing
his or her own order of preference among the
candidates, by guaranteeing that doing so will
always help higher-preferred candidates to defeat
lower-preferred candidates; and
(b)  ensure that all votes in each electorate have equal
weight in law and equal effect in practice."

I think that what para (a) "guarantees" should cover the
problems of wasted votes and representation by the highest
choices possible (preferably first choices; ie, it's tolerable
if your 9th choice is elected over your 10th, but ideal if
your 1st choice is elected over your 2nd. If your 9th choice
is elected but your 1st choice is defeated, then that
shouldn't be tolerated unless it is unavoidable.)

"His or her own order of preference" is specifically worded to
rule out party lists. If I prefer Green Candidate 2 first, Red
Candidate 5 second, and then the other 9 Green candidates as
my 3rd to 11th preferences inclusive, any list system
positively discourages [and, in fact, any "closed" or "fixed"
list system precludes] me from expressing my true p[reference
order. A vote given to the Green list for Green-2's sake may
well help Green-1, or Green-7, (etc) to defeat Red-5 - ie, a
3rd or 4th (etc) or even an 11th preference to defeat my third
preference.

If, however, list systems are unavoidable, then an "Open"
lists system (allowing voters to support individual candidates
on the list, not just accept the party's fixed order) is
somewhat less intolerable.

(10) "Rival proposals don't need to be ranked in priority. The
crucial result is to pick one of them ..." (SE).

multiple-choice referenda do have advantages of simplicity,
and also of budgeting as Steve pointed out), but at present I
am tending towards supporting the view that several or all can
be passed, they need only be ranked.

Inconsistency between laws is a matter of degree and there is
no need to disallow one referendum bill in full merely because
it conflicts in part with a higher-preferred bill. Even if two
counter-proposals do conflict so fundamentally that they
cannot exist together, it is better for the courts to adopt a
"wait and see" attitude - ie, not intervening unless both
proposals are carried, nor until a concrete legal case is
brought to test their compatibility - than to rule on them in
the abstract, in the heat of an election campaign, and in a
way that would pre-empts the voters' right to decide that the
two are not irreconcilable.

Moreover, allowing only one winner per referendum might enable
political tacticians to manipulate the system - to "kill" a
popular proposal by putting against it an equally popular
counter-proposal. "You can vote either for campaign finance
reform, or for cleaner air and water, but not for both."

(11) "Please lose the word `margin'!!" (SE)

All right. I can see how it would be confusing. Unfortunately
there isn't a commonly-used alternative term for one's
opponent's pairwise total against one. How about "disapproval
rating"? This is common parlance, plus it might explain away
the objection that "X wins because Y has only 55 votes against
Y's 45". Reformers can then say that "X wins because she is
the only candidate whose disapproval rating never exceeds 55

(12) THE SMITH FILTER

I am thinking now that, rather than putting "If any set of
candidates ..." or similar "results" formulas into a
constitution, it would be better to insert the "process"
formula you earlier suggested (ie, start with the candidates
defeated fewest times; add any candidate who defeats them;
continue until every candidate inside the set defeats every
candidate outside it). The "until" clause explains the
rationale of the set. Setting out the process to follow is not
that much wordier than setting out the end result to aim at, I
think.

My currently suggested wording for a "constitutional" formula
is as follows:

1. Primary count. First, a "primary count" is
conducted, at which each ballot credits its current
value to its highest preference among all the
candidates remaining.

2. Absolute majority winner. If one candidate's
progress total on the primary count exceeds those of
all other remaining candidates combined, s/he is
recorded as elected.

3. Pairwise comparisons. If not, then one or more
"pairwise comparisons" are conducted, and on each
such comparison:
3.1  two candidates are compared against each other.
3.2  every ballot credits its current value to its higher
preference (if any) between the two candidates being
compared.
3.3  any ballot that has the same preference for both
candidates, or has no preference for either
candidate, credits each with zero votes on that
comparison.
3.4  whichever candidate is credited with more votes than
the other is deemed to "outpoll" the other on that
comparison.

4. Exhaustive comparisons. As many pairwise
comparisons as necessary are conducted until either
4.1  one candidate outpolls every other candidate, or
4.2  each candidate has been compared against every other
candidate, but every candidate is outpolled at least
once.

5. Absolute pairwise winner. If one candidate
outpolls every other candidate, s/he is recorded as
elected.

6. Minimum winning set. If every candidate is
outpolled at least once, the "minimum winning set"
of candidates is determined, as follows:
6.1  First, those candidate/s who are outpolled fewer
times than any other candidates are included in the
minimum winning set.
6.2  Then, any other candidate who outpolls a candidate
already in the minimum winning set, is added to the
set.
6.3  This procedure is repeated as many times as
necessary until every candidate in the minimum
winning set outpolls every candidate outside the
set.

7. Default pairwise winner. Whichever candidate in
the minimum winning set has the smallest defeat
margin is recorded as elected.
7.1  A candidate's "defeat margin" means the largest
number of votes credited to any other candidate in
the set who outpolls that candidate on any pairwise
comparison.

To answer Steve's question - Step 5 ensures that the Smith set
will always contain 2 or more "joint winning" or "short-
listed" candidates anyway, since if there were only one s/he
would be elected at Step 5 anyway and we would not proceed to
determine the "minimum winning set".

Time constraints prevent me writing much more at the moment,
but I hope this helps answer some of Steve's questions.

TOM

-------------------
Overflow-Cc: 100245.2440 at compuserve.com ('Geoff Powell'),
afreeman at acslink.net.au ('Andrew Freeman'),
bmusidla at email.dot.gov.au ('Bogey M'),
c-p-r at netcom.com ('Citizens for Proportional Representation'),
crabb.deane at pi.sa.gov.au ('Deane Crabb'),
dunnmj at ozemail.com.au ('Martin Dunn'),
election-methods-list at eskimo.com ('Election methods'),
GGoode at VTRLMEL1.TRL.OZ.AU (Goode, Geoff),
j.pyke at qut.edu.au (John Pyke, QUT Law School),
jhtaplin at cygnus.uwa.edu.au ('John Taplin'),
lee at cs.mu.OZ.AU ('Lee Naish'),
martinw at cse.unsw.edu.au ('Martin Willis'),
mdt at ozemail.com.au ('Matthew Townsend'),
voting-systems at netcom.com ('Voting-systems')

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