[EM] Preferential voting and non-monotonicity

[Tom Round]

I think the "randomness" of non-monotonic results that are possible under
STV and AV (ie, preferential systems with elimination -- as opposed to
points, pairwise comparisons, etc) is often grossly exaggerrated with the
effect, intended or not, of making "largest remainder" non-preferential
systems look better by comparison.
	By "largest remainder" non-preferential systems I mean
first-past-the-post, as well as party-list systems (whether Droop or Hare
quota, or d'Hondt or St-Lague divisors) where, in the final resort, if no
parties have any whole quotas remaining, the last seats go to the parties
showing the highest remainder or highest average. Their effects, for
present purposes, are all the same -- there is no elimination of the lowest
candidates/ parties and transfer of their votes until the remaining
contenders have enough full quotas to win the remaining vacant seats
(assuming for the moment no exhausted ballots).	
	Thus, eg, William Riker in "Liberalism Against Populism" (1982, p 51)
argues "that some kind of monotonicity be required is ... simply a
straightforward matter of making the voting system do what it is supposed
to do ...It is hard to believe there is any good justification for the
single transferable vote ... when there exist proportional representation
systems (such as list systems) that are at least weakly monotonic."
	However, STV/ AV are only "the worst offenders against monotonicity" if we
take the view that a voter is "unrepresented" unless his/her vote helps her
first-choice party win a seat. But if we define "monotonicity" more broadly
-- ie, that a voter wants to maximise the electoral success of his/her
_entire preference scale_, ie to help her second choice defeat her third
choice as well -- then STV/ AV perform much better than the "highest
remainder" non-transferring systems. While preferential-elimination systems
lose some efficiency in ensuring more first preferences always help a
candidate, they guard against the much worse risk that by splitting your
votes among two or more parties or candidates you let your most hated
opponent slip through on a plurality. When unintended vote-splitting is a
real danger, then XYZ can increase its chances of winning even if the
combined anti-XYZ votes rise dramatically. 
	So highest-remainder systems bear exactly the same fault that their
supporters raise against STV/ AV. By voting for the Light Blue party, you
help the Red party win on a plurality when you "should" have given your
vote to the larger Dark Blue party instead.
	Don't get me wrong -- I think a voter is _better_ represented if her
first- rather than her second- or third-choice candidate is elected. But I
recognise that in an imperfect world, keeping out the "worst of all" is
something most voters also want very keenly to do. A system that counts
only first preferences but discards all others is thus a worse bet than one
that might occasionally sacrifice a first for a second choice but never
lets a majority's "absolute last" preference defeat its first- and
second-preference candidates.
	Ironically, supporters of first-past-the-post systems often use these
arguments -- "voters care more about kicking out the Government than about
having a local MP they can approach", or "MPs elected on second-preference
transfers under STV/ AV are less legitimate than MPs elected on a plurality
of first preferences". Yet FPTP violates both of these virtues supposedly
claimed for it. First, it makes "kicking out a bad Govt" much harder by
requiring a rigorous electoral pact among the Opposition parties long
before polling day (one that greatly limits the voters' choice of parties)
as a virtual precondition. And second, it strongly encourages minor-party
supporters to put their X for their least-hated major party under threat of
that X being utterly wasted -- and then has the gall to claim these
grudging, disguised second preferences as counting towards a plurality of
"real" popular consent.

=============================================================
Tom Round
BA (Hons), LL.B (UQ)
Research Associate -- Key Centre for Ethics, 
	Law, Justice and Governance (KCELJAG)
(incorporating the National Institute for Law, Ethics and Public Affairs)
HUM[anities] Building, Room 1.10, Nathan Campus
Griffith University, Queensland [Australia] 4111
Ph:	07 3875 3817
Fax:	07 3875 6634
E-mail: 	T.Round at mailbox.gu.edu.au
Web:	http://www.gu.edu.au/centre/kceljag/
	http://www.gu.edu.au/school/ccj/
=============================================================