STV without Elimination

[David Catchpole]

> I've tried to follow your subsequent posts ("Patching Up Condorcet In
> Multi-Winner Elections", August 25th), but have had difficulty visualising
> how the method would work.  Would you be willing to provide an example,
> showing how the result satisfies IIA (in that particular case, of course),
> where conventional STV would not?

Stay with me; this one is chocka with obfuscatory tables!

Say in a two-winner election, there are four candidates: John Apple,
Martha Banana, Kylie Cucumber and Daryl Dewberry. The following ballots
are submitted:

	Apples	Banana	Cucumber	Dewberry
	1	3	4		2
	1	3	4		2
	1	3	4		2
	4	1	3		2
	4	1	3		2
	3	4	1		2
	4	3	1		2
	3	2	4		1

We consider the 3-way contests:

ABC [A,B]	ADB [A,D]	ADC [A,D]	DBC [D,B]
ABC		ADB		ADC		DBC
ABC		ADB		ADC		DBC
BCA		BDA		DCA		BDC
BCA		BDA		DCA		BDC
CAB		DAB		CDA		CDB
CBA		DBA		CDA		CDB
BAC		DBA		DAC		DBC

so [A,D] is the obvious "Condorcet slate" with STV and Apple and Dewberry
win.

Now, if we had conducted the election using either plurality exclusion or
"quota significance" exclusion, we would end up with a different answer (C
and D manage to split their vote). A would obviously win and its votes
would transfer with a value of 1/3- to D:

(A wins a seat and transfers its votes)

BDCx2
CDBx2
DBCx4/3-

by either quota significance or plurality exclusion, D would be excluded.

(D excluded)

BCx10/3
CBx2

B is elected along with A.

If, however, C hadn't nominated, the election would have looked like this:

ADB [A,D] would have won- the orthodox methods can miss absolute IIA when 
ADB it might well exist.
ADB
BDA
BDA
DAB
DBA
DBA

(PS. "reverse ranking", avoiding surplus transfers until a
quota-significance exclusion reduces the contest to the manageable size,
may work in this election to resist splitting, but if A's preferences had
flowed in a different way, the same problems as above would appear)