User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions

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This idea only requires two passes of all ballots for each winner elected; one to compute the round's matrix, and the second to isolate the ballots that are in a candidate's quota. It is possible to use the below-discussed idea for SPAV in SMV by, between rounds, only keeping track of the changes in scores for ballots that were reweighted. For example, it is possible to find the second round's matrix by noting that 5 voters are no longer giving a candidate a 4, with 3 of them now giving that candidate a 2.8 and 2 of them giving the candidate a 0. Thus, only changes would have to be made to the first round's matrix.
This idea only requires two passes of all ballots for each winner elected; one to compute the round's matrix, and the second to isolate the ballots that are in a candidate's quota. It is possible to use the below-discussed idea for SPAV in SMV by, between rounds, only keeping track of the changes in scores for ballots that were reweighted. For example, it is possible to find the second round's matrix by noting that 5 voters are no longer giving a candidate a 4, with 3 of them now giving that candidate a 2.8 and 2 of them giving the candidate a 0. Thus, only changes would have to be made to the first round's matrix.

Here are the first two rounds of a 5-seat SMV election done using this idea:
{| class="wikitable"
|+Hare quota is 400
!Number of voters that
scored a candidate a

certain way

(Cumulative voters in

parentheses)
!A
!B
!C
!D
|-
|Scored the candidate a 5
|305
|380
|375
|250
|-
|Scored the candidate a 4
|270 (575)
|220 (600)
|80 (455)
|100 (350)
|-
|Scored the candidate a 3
|''<small>300</small>''
|''<small>400</small>''
|''<small>500</small>''
|200 (550)
|-
|Scored the candidate a 2
|''<small>500</small>''
|''<small>600</small>''
|''<small>300</small>''
|''<small>20</small>''
|-
|Scored the candidate a 1
|''<small>150</small>''
|''<small>100</small>''
|''<small>200</small>''
|''<small>100</small>''
|-
|Hare quota scores:
|1905
(305*5+

95*4)
|'''1980'''
(380*5+

20*4)
|1975
(375*5+

25*4)
|1800
(250*5+

100*4+

50*3)
|}
The small, italicized cells are irrelevant to determining each candidate's Hare quota score.

With a Hare quota of 400 voters, candidate B is the first winner. Spending 400 of those ballots yields:
{| class="wikitable"
!Number of voters that
scored a candidate a

certain way
!A
!B
!C
!D
|-
|Scored the candidate a 5
|200
| ---
|150
|250
|-
|''Scored the candidate a 4.54''
|35 (235)
| ---
|70 (220)
|0
|-
|Scored the candidate a 4
|100 (335)
| ---
|60 (280)
|80 (330)
|-
|''Scored the candidate a 3.63''
|20 (355)
| ---
|20 (300)
|10 (340)
|-
|Scored the candidate a 3
|40 (395)
| ---
|100 (400)
|100 (440)
|-
|''Scored the candidate a 2.72''
|5 (400)
| ---
| ---
| ---
|-
|Scored the candidate a 2
| ---
| ---
| ---
| ---
|-
|''Scored the candidate a 1.81''
| ---
| ---
| ---
| ---
|-
|Scored the candidate a 1
| ---
| ---
| ---
| ---
|-
|''Scored the candidate a 0.90''
| ---
| ---
| ---
| ---
|-
|Hare quota scores:
|1765.1
| ---
|1680.4
|'''1786.3'''
|}
Because fractional reweighting was used here, we have to now take into account that every voter who scored candidate B a 4 has 10/11th of their ballot weight remaining, since 1/11th of them (20 out of 220) were necessary to fill out B's quota. This is why there are 5 additional positive scoring possibilities.


=== Negative pairwise counting approach ===
=== Negative pairwise counting approach ===
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