# [EM] Proportional Representation via Approval Voting (fwd)

Bart Ingles bartman at netgate.net
Wed Jan 17 15:43:21 PST 2001

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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!

But only if your utility formula is accurate for a given election.  It
is not enough to say that it is accurate on average, since the unranked
method may adapt better to variations in individual elections, yielding
a higher average utility.

In fact, given STV's slim 3.5% lead using the Borda assumptions, I think
it highly probable that an unranked method would win under more
realistic models (just as single-winner approval consistently beats out
IRV).

> 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.

I have serious doubts about the proxy system.  Would the variable votes
carry over into committee assignments?  Would an individual's larger or
smaller voting power affect the chances of even getting a committee
assignment?  Should an representative's time on the floor be in
proportion to voting power, etc.?  How about fundraising limits and
operating budgets?  It all sounds like a big mess to me.  Much better to
minimize inequity before the candidates are elected.  I think the quest
for proportionality can be taken to excess anyway -- it should be
balanced with other things, such as utility & practicality, etc.

Bart

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