Your PAV vs STV example revisited

[Forest Simmons]

I guess STV isn't all that bad after all!

On Mon, 22 Jan 2001, LAYTON Craig wrote:

> Forest,
> 
> Thanks for your analysis.  I suppose one could also point out that the STV
> winner gives 65% of voters their choice, as opposed to 50% or 30% for the
> tied PAV winners, and gives 85% of voters either their first or second
> choice, compared to 75% and 70% for the other two.
> 
> I am sceptical about focusing on electing candidates with 'broad, middle of
> the range support'.  Single winner systems require this, certainly, but an
> artificial emphasis on electing particular candidates in mulit-winner
> systems might throw out the proportionality; eg, an electorate where there
> is 45% support for (right wing) faction A, 46% support for (left wing)
> faction B, and 9% support for candidate C (a middle of the road candidate,
> who is the second choice for factions A and B).  If there are four members
> to be elected, I would assume that the fairest distribution would be 2
> faction A members and 2 faction B members.  Trying to incorporate candidate
> C will skew the proportionality, resulting in 1 member from A, 2 members
> from B and C.  Depending on how the factions vote, this may be the result in
> PAV (STV would return 2-2).  A coalition between B and C will mean
> compromises on both sides, but effectively a government more left of centre
> than the populace, while the 2 - 2 balance will mean that policies are
> closer to what the people want, or what the people would otherwise have
> decided if they voted directly on policies.
> 
> We should perhaps be looking at what we want from a multi-winner system.
> The single winner criteria are sometimes useful, but not alltogether
> appropriate.  I would like to hear your (and other people's) ideas about
> this.
> 
> -----Original Message-----
> From: Forest Simmons [mailto:fsimmons at pcc.edu]
> Sent: Saturday, 20 January 2001 12:44
> To: LAYTON Craig
> Cc: 'election-methods-list at eskimo.com'
> Subject: Your PAV vs STV example revisited
> 
> 
> Craig, I still haven't checked all 56 combinations for the case where the
> approval voters approve their top four of the eight candidates, but the
> ones I didn't check probably wouldn't beat the ones I did.
> 
> The winners are ABF and BDE.  Each of these combinations covers 100% of
> the voters with at least one representative (from their top four
> preferences), as well as 75% of the voters with two representatives (from
> among their top four).
> 
> Compare this with AEH which covers only 90% of the voters from among their
> top seven choices, and only 45% of the voters with two representatives
> from among their top four.
> 
> Of the tied PAV winners I would say ABF is better because it covers 95% of
> the voters with at least one vote from their top three preferences, and
> 55% of the voters with two repsentatives from their top three choices. 
> 
> Compare this with STV winner AEH which covers 90% of the voters from among
> their top seven choices, and 20% of the voters with two representatives
> from their top three choices.
> 
> The ordinary AV winner (based on top 4 preferences) would be BDF, which is
> contained in the union of the tied PAV winners ABF and BDE, but has only B
> in common with both of them, so PAV does give something different from AV,
> yet keeps some candidates with widespread popularity.  
> 
> I haven't carried out the full Condorcet calculation, but it looks to me
> like it could give a three way tie to ABD, which is also contained in
> the union of the tied PAV winners, again showing the close association of
> the PAV winners with candidates having broad popularity.
> 
> Note that B is in both tied PAV winners, the ordinary AV winning circle
> (whether based on top three or top four), and is in a tie for the
> Condorcet winner (check me on this one), and yet STV threw it out.
> 
> If I'm not mistaken, a complaint about existing PR methods is that they
> require ad hoc solutions for the inclusion of candidates with broad,
> middle of the road support.
> 
> Do we have something worth pursuing here?
> 
> Forest
> 
> On Fri, 19 Jan 2001, Forest Simmons wrote:
> 
> > Craig, without trying all 56 possible subsets of size three I did verify
> > that under PAV the combination ABH wins against AEH, and even more so when
> > we assume that the voters approved half of the candidates.
> > 
> > I think this is reasonable for the following reasons.
> > 
> > The two combinations disagree only on whether B or E should be in the
> > winning circle. 
> > 
> > It is true that B and E tie in the rankings; the voters are fifty-fifty on
> > that question.  But the rankings where B beats E have greater separation
> > between the two than where E beats B. So although B and E have a Condorcet
> > tie, so to speak, B soundly beats E in a Borda Count comparison.
> > 
> > Of course, this by itself doesn't tell us which would be better, we need
> > to know which one better compensates for the two 10% factions of the
> > population not covered by the {A,H} combination. 
> > 
> > In this regard, B is first choice of one of these factions and third
> > choice of the other, while E is second choice of one of the factions and
> > last choice of the other.
> > 
> > In other words, if B is included in the winning circle, then 100% of the
> > voters have representatives from their top three choices.  If B is
> > replaced by E, then 10% of the voters do not have a representative from
> > their top seven choices.
> > 
> > Which do you think is better?
> > 
> > Forest
> > 
> > On Thu, 18 Jan 2001, LAYTON Craig wrote:
> > 
> > > 
> > > I made up a fairly random (ordinal ranking) voting pattern with 8
> > > candidates.  I assure you, it was the first (and so far only) example I
> > > tried, so it isn't contrived in order to prove a point.  The eight
> > > candidates are ranked by an electorate of 100 voters in the following
> way;
> > > 
> > > 30 A>B>C>D>E>F>G>H
> > > 10 B>F>G>D>A>H>C>E
> > > 5  C>H>D>F>G>A>B>E
> > > 5  D>B>A>H>C>E>G>F
> > > 15 E>D>A>F>H>B>G>C
> > > 10 F>E>B>G>A>D>C>H
> > > 5  G>A>E>B>H>C>D>F
> > > 20 H>G>F>E>D>C>B>A
> > > 
> > > There are to be three winners.
> > > 
> > > In STV with a droop quota, candidates A,E,H are elected.
> > > 
> > > In PAV I assumed that every voter's first three choices were approved.
> Using
> > > the divisors in Michael Welford's explaination, candidates A,B,H are
> > > elected.
> > > 
> > > The results varied quite a bit between the two systems.  Although in
> STV,
> > > A,B,H was very close to the elected combination, in PAV, A,E,H was not
> > > (there are at least two combinations with a significantly better score) 
> > > I then invented an ad-hoc formula for assigning utility values to the
> 
> 
> 
>