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Participants,<br>
I have discovered that QLWA (Quota Limited Weighted Approval), appropiately
adapted, makes an excellent <br>
ranked-ballot PR method .<br>
<br>
Single-Winner QLWA:<br>
Voters rank the candidates. Equal preferences and truncation ok.<br>
(1) Symetrically complete the ballots.<br>
(2) Based on these now symetrically completed ballots, give each candidate
a weight of 1 for each ballot on which it is<br>
ranked in first place. (The total weight of the candidates will now
be equal to the total number of original before-step-1<br>
ballots. Any candidate with a weight equal to or greater than half
the total weight of all the candidates wins).<br>
(3) Each ballot fully approves the highest-ranked candidates whose combined
weight is less than half the total weight of<br>
all the candidates. Each ballot also fractionally approves the next highest-ranked
candidate, so that the combined weight<br>
of the candidates approved by each ballot is equal to half the total
weight of all the candidates.<br>
(4) The candidate with the highest approval score wins.<br>
<br>
QLWA Proportional Representaion:<br>
Voters rank the candidates. Equal preferences and truncation ok.<br>
(1) Symetrically complete the ballots.<br>
(2) Based on these now symetrically completed ballots, give each candidate
a weight of 1 for each ballot on which it is<br>
ranked in first place. (The total weight of the candidates will now
be equal to the total number of original before-step-1<br>
ballots.)<br>
(3) Each ballot fully approves the highest-ranked candidates whose combined
weight is less than one Droop quota. Each <br>
ballot also fractionally approves the next highest-ranked candidate, so
that the combined weight of the candidates <br>
approved by each ballot equals one Droop quota.<br>
(4) Elect the candidate with the highest score.<br>
(5) Reduce the value of the ballots that approved the previously elected
candidate by a total value of one Droop quota, <br>
in proportion to their contribution to that candidate's approval score.<br>
(6) Based on the ballots as they are now valued, give the remaining
candidates new weights as in step (2). A remaining <br>
candidate who was ranked second on a ballot that approved a previous
winner, inherits first place on those ballots.<br>
(7) Using the new weights and the newly re-valued ballots, repeat step
(3) and then step (4).<br>
(8) If there remain seats unfilled, repeat in turn steps (5),(6) and
(7) until all seats are filled.<br>
<br>
I believe this method retains all the important good features of the
single-winner version, like Clone Independence, Mono-raise<br>
(Monotonicity) and Participation. It is less chaotic and capricious
than other PR ranked-ballot methods.<br>
<br>
I have been told that in this example QLWA agrees with Sequential STV.<br>
400 ballots, 7 candidates, 3 seats, Droop Quota = 100.<br>
96:A>C1>C2>C3<br>
96:B>C1>C2>C3<br>
96:D>C1>C2>C3<br>
88:E>C1>C2>C3<br>
08:C1>C2>C3<br>
08:C2>C3>C1<br>
08:C3>C1>C2<br>
QLWA elects C1, C2, C3. <br>
<br>
Normal STV simply culls the C candidates for not having enough first
preferences, and then then elects ABD. <br>
A, B, D, and E's voters all rank each other's favourites as their bottom
three and so can't put together a Droop quota.<br>
C1 is ranked first or second on 98% of the ballots, and with 7 candidates
and no mutual Droop quotas, C1's case is <br>
compelling. I think the case for picking one or two of ABD at random
is weak. <br>
<br>
This from a "Voting Matters" (issue 15, June 2002) article on Sequential
STV:<br>
<p>"With 5 candidates for 2 seats, consider the voting pattern </p>
<pre> 104 ABCD
103 BCDA
102 CDBA
101 DBCA
3 EABCD
3 EBCDA
3 ECDBA
3 EDCBA
</pre>
Plain STV elects BC. Sequential STV chooses BC as probables, then tests
BCD, BCE and BCA in that order. BC win each time and are elected.
<p> Suppose, however, that the voters for A, B, C and D had all put in E
as second preference to give (the example used in reference 1).
</p>
<pre> 104 AEBCD
103 BECDA
102 CEDBA
101 DEBCA
3 EABCD
3 EBCDA
3 ECDBA
3 EDCBA
<span
class="bodytext">
This evidently makes E a very much stronger candidate, for if any one of
A, B, C or D had not stood, E would have been the first elected, but plain
STV takes no notice, electing BC just as before. Sequential STV chooses BC
as probables but then tests BCD, where BC stay as probables and D goes to
the end of the queue, followed by BCE where BE become the new probables and
C goes to the end of the queue. It then tests BEA and BED, BE winning each
time. There is no need to test BEC again as that result is already known,
so BE are elected.</span>"
QLWA again gives the same results as Sequential STV.
Here is an example of Condorcet Loser Elimination STV being a bit unstable and giving an
order-reversal incentive.
300 votes, 3 seats, Droop quota = 75.
74 A B C D X E
39 B A C D X E
75 C
37 D X E C B A
73 E D X C B A
02 X E D C B A
CLE elects CBD, but if the two X voters reverse their top 2 preferences, then E has a quota
and the result changes to CEB (a preferable result for the two Compromisers).
QLWA elects CEA in both cases (like normal STV).
Chris Benham
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