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

Wed Jan 17 20:51:13 PST 2001

```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.

```