[EM] Proportional Representation via Approval Voting (fwd)

[Michael Welford]

I'd like to point out that by its own standards PAV does quite well in this
example. Under the ABH solution every voter has at least one of the candidates
they approved of get elected. It turns out that ABH is tied with ABF under
PAV.  But under the ABF solution 5 voters didn't elect anyone, while the number
of voters who had 2 candidates elected is 10 higher than with ABH. The exact 2
to 1 ratio is significant. It's related to the principle under party list PR
that a party with more than m/(n+1) of the votes ( where there n
representitives to be elected ) should get m representatives. Something similar
happens in the example.

Consider in isolation just the ABC and EDA faction of voters, imagine for a
moment that the EDA voters voted ED and suppose that they are vying for two
seats. The ABC faction has exactly twice as many members as the ED(A) faction,
so even ignoring the BFG faction, it's a tossup whether the ABC should get two
seats and EDA none or whether they each should get one. So when the BDG faction
is put back in and the ED votes are changed back to EDA, it's clear the ABH is
preferable to AEH.

LAYTON Craig wrote:

> Thanks for this, it gives me a clearer idea of the count rule.
>
> -----Original Message-----
> From: Forest Simmons [mailto:fsimmons at pcc.edu]
> Sent: Thursday, 18 January 2001 12:24
> To: election-methods-list at eskimo.com
> Subject: Re: [EM] Proportional Representation via Approval Voting (fwd)
>
> >Michael Welford has independently hit upon the same method as mine for
> >Proportional Representation via Approval Voting.
> >
> >I'm forwarding his brief explanation, since I still haven't had time to
> >get around to the "inexorable" logic that leads to it, and some of you are
> >still waiting for a simple explanation.
>
> Assuming I understand PAV correctly, I did a quick test of this method vs
> STV with a droop quota.  I did it quickly, and all the calculations were
> done manually, so I apologise in advance for errors.
>
> 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
> election of combinations of candidates.  It is a cross between a borda count
> and the actual PAV election count rule, whereby the highest ranked candidate
> on any ballot that is elected yields a full borda score (7 for a first
> preference, 6 for a second etc.).  The second highest ranked elected
> candidate yields a borda score divided by 2, and the third higest ranked
> elected candidate yields a borda score divided by 3.
>
> The result? A,E,H (elected using STV) get a utility score of 828
>                 A,B,H (elected using PAV) get a utility score of 800
>
> STV wins!
>
> Okay, it doesn't mean much, but I think I'd need some convincing before I
> dumped STV for PAV, even allowing for the somewhat arbitrary nature of
> eliminations in STV (as you point out Forest).  I should point out that the
> example uses full preferences, and truncated preferences make the results
> much worse in quota STV.  Some time ago I proposed some additions to the
> count rule to improve the chances of high choices on truncated (and
> non-truncated) ballots being elected, but a better alternative is to dump
> quotas and add variable voting power (Demorep calls it a "proxy" system).
> The results are more arbitrary again, but it doesn't matter so much becuase
> it is only the candidates who will end up with very little voting power
> anyway who are effected by the arbitrariness of the system.