[EM] Proportional Representation via Approval Voting (fwd)

[Forest Simmons]

Craig, I'm sorry I haven't had time to check your calculation or consider
the results, but I do have a couple of comments.

1. If I'm not mistaken, when the approval voters have equally spaced
utilities for the various candidates (and no other strategic information)
they should vote the top half of their preferences, so it would make more
sense to assume that the approval ballots would each approve four of the
candidates, rather than three. (I believe that this property is true for
multiwinner AV as well as single winner, but I could be wrong.)

2.  This example is on the home court of STV, so to speak, since that
method is adapted to rankings, while Approval Voting is not. Of course, if
I gave an example of approval ballots, and asked you to turn them into
rankings, that wouldn't be fair either.  So I suggest that when comparing
the two methods by simulation we start from the neutral (and more
expressive) ground of the honest utilities of the voters, and derive or
impute their rankings and approvals from those utilities.

3.  Any method of gauging the results with a function that purportedly
decides which of the methods is better from the ballots alone, must itself
yield a better method than the two methods being compared.  Therefore, the
gauging should be based on the honest utilities of the hypothetical voters
from which we derived their ballots, rather than from the ballots
themselves. I suppose it is possible that some excellent but unwieldy
method could exist for the purpose of judging more practical methods, but
I don't know of any for the context of PR. 

4. Instead of gauging with a function ("ad hoc") it might be better to
pick examples that illustrate some strengths or weaknesses of the
competing methods, where these strengths or weaknesses are noted either on
the grounds of intuition or on the grounds of general principles of
fairness and equity.

5. It would be useful to know of the simplest cases where STV gives
unsatisfactory results to see if PAV suffers from the same weakness or
not. 

I am interested in yours and others' opinions on these comments.

Best Wishes,

Forest

On Thu, 18 Jan 2001, 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.
> 
>