[Election-Methods] Approval based equal ranks in PR-STV and Meek's method

[raphfrk at netscape.net]

I was thinking about Meek's method and how to handle equally ranked ballots.


Meek proposed that in such a case, each candidate should get an equal share of the remaining vote.


My thoughts were that it should be handled like approval voting where each candidate gets the full strength of the vote, I made a previous post about this.


This means that intra-faction/party elections can be effectively handled with approval voting rather than IRV.? 


A voter could vote:


(favourite of party's candidates)>(party's other candidates)>(other candidates)


This would ensure that the party still gets one candidate elected, but result in candidates that are closer to the party's centre.


However, once the candidate gets elected, his vote is no longer given at full strength to all the hopeful candidates at that rank.? If you approve A and B, your vote goes to A or B if either of them are elected and only the surplus is available for the other.? This is needed to maintain proportionality.


The problem is that if you equally share the vote between all equally ranked elected candidates, it is possible that you could unelect a previously elected candidate.


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For example, assuming 3 seats 


note: 
all elected at a rank get first share of the incoming vote
all hopefuls at a rank get the remainder of the vote at full strength


40:? A=B>C
75:? A>B>C
10:? X>B>C (9 of these with X = different candidate)
94:? C
51:? D>E
50:? E>D


Round 1:

A: 40+75 = 115
B: 40
X: 10 (all 9 of them)
C: 94
D: 51
E: 50


Quota = 100


A elected


Round 2:


A's surplus is all given to B
In effect, the A=B>C vote becomes A>B>C as elected candidates are assigned vote share before the remainder is given to any hopefuls.


A: 100
B: 15
X: 10
C: 94
D: 51
E: 50


Each X is eliminated in turn and B gets their votes.


Round 11:

A: 100
B: 105
C: 94
D: 51
E: 50


Quota = 100


B is elected


Round 12

The problem occurs here with the 


40: A=B>C votes


A used to get nearly all of these votes as A was the only elected candidate at the top rank.


However, now both A and B are elected.? Also, B's keep value needs to be kept reasonably near one as B was elected with only a 5 vote surplus.


This means that even if A's keep value is set to 1.0, B will be entitled to nearly 20 of the votes.

A: 20 + 75 = 95
B: 20 + 90 = 110


This means that A no longer has a quota and possibly should be unelected.? I am not sure if doing that would cause infinite loops though.


Unelecting candidates would break later no harm, but mightn't be an issue if loops couldn't happen.

Anyway, this post is to long (didn't intend the summary of the problem to be so long), will post another later dealing with the issue.

Raphfrk
--------------------
Interesting site
"what if anyone could modify the laws"

www.wikocracy.com

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