[EM] IRV and PR-STV Re: examination of plaintiff's memorandum re IRV in Minneapolis

[Raph Frank]

On Mon, Nov 10, 2008 at 3:32 AM, Abd ul-Rahman Lomax
<abd at lomaxdesign.com> wrote:
> Is this complicated? Yes. Is it fair? Well, up to the election of the last
> candidate, yes, it is clearly fair. With the last candidate, the election
> effectively becomes the same as an instant runoff voting election, with the
> problems associated with that.

I don't see why the last seat being filled is that much different from
the others.  The negative effects are always there, though because
factions aren't quite solid coalitions in practice, PR-STV doesn't
display the effects quite so much (maybe).

For example, assume that 2 seats are being filled

A faction

16: A1>A2>A3
5: A2>A1>A3
14: A3>A2>A1

B faction

14: B1>B2>B3
5: B2>B1>B3
16: B3>B2>B1

C faction

30: C

A2 and B2 (and C) are the condorcet winners in their own factions.

PR-STV will run as follows

Quote = 35 (approx)

Round 1
A1: 16
A2: 5
A3: 14

B1: 14
B2: 5
B3: 16

C: 30

B2 and A2 both eliminated as their total is less than the next highest (14)

Round 2

A1: 21 (+5)
A2: 0
A3: 14

B1: 19 (+5)
B2: 0
B3: 16

C: 30

A3 eliminated

Round 3

A1: 35 (+14)
A2: 0
A3: 0

B1: 19 (+5)
B2: 0
B3: 16

C: 30

A1 elected as met the quota.

No surplus transfers as exact quota, so B3 is eliminated

Round 3

A1: 35 (+14)
A2: 0
A3: 0

B1: 35 (+16)
B2: 0
B3: 0

C: 30

B1 elected.

So, the winners are (A1,B1).

However, they were not the condorcet winners of their respective
factions.  Within each faction, standard PR-STV elects the IRV winner.

CPO-STV would solve the issue.

Comparing (A1,B1) to (A2,B2)

A1: 16
A2: 19
B1: 14
B2: 21

A1+B1 = 30
A2+B2 = 40

Thus (A2,B2) would be CPO winners.

Also, the 30 C voters would be able to upset factional 'purity' by
also voting for B and C faction candidates.

It is like in condorcet voting where voters of the minority party get
to pick which of the candidates of the majority party gets elected.