# [EM] Preferential Party-List Proportional Representation (PPLPR)

Toby Pereira tdp201b at yahoo.co.uk
Fri Oct 31 15:55:40 PDT 2014

```I've just had a brief look, but I have a couple of questions/points.

From: Vidar Wahlberg <canidae at exent.net>
To: election-methods at lists.electorama.com
Sent: Friday, 31 October 2014, 21:52
Subject: [EM] Preferential Party-List Proportional Representation (PPLPR)

>Example 1, three parties, L and R voters with C as 2nd preference:
> 40 L>C
> 20 C
> 40 R>C

> Step 1:
> Count up support for each party using only the first preference. This
> result will serve as a base for the next step:
> L: 40%
> C: 20%
> R: 40%

> Step 2a:
> Iterate through all unique combination of 1st preference on votes
> (horizontal header of matrix), and move voter support to the 2nd
> preference on the votes. This will create a matrix:
>    |  L  |  C  |  R    - "Excluded" 1st preference
> ----+-------+-------+-------
>  L |  -  | 40+ 0 | 40+ 0  - L is not 2nd pref. on any C or R votes
>  C | 40+20 |  -  | 40+20  - C is 2nd pref. on both L and R votes
>  R | 40+ 0 | 40+ 0 |  -    - R is not 2nd pref. on any C or R votes
> Sum |  100  |  80  |  100

> Do note that the value before the plus sign is the result from Step 1,
> while the value after is from the 2nd preference on the votes.

Should the C row be 20+40 rather than 40+20 or am I not understanding what that table is?

>Example 2, four parties, one very large, three small:
> This is an exaggerated example, mostly to demonstrate that large
> parties can't "vote away" opposition.
> 90 A>B
>  0 B
> 10 C>D
>  0 D

[snip]

> Step 2c:
> A: 87%
> B:  3%
> C:  7%
> D:  3%
> A voters could not move more than 3pp away from C (and C voters could
> not move more than 3pp from A). If C voters had not ranked D as 2nd
> preference then the result would be A: 90%, B: 3%, C: 7%, D: 0%. Do
> however note that if D was excluded from the election, A voters would
> be able to move more support from C to B (I'll come back to this
> "feature" later).

So is step 2c the result? Just to clarify, if 10% of voters vote C and with no second preference, then C would only get 7% of the seats in an ideal situation (no seat rounding)? Is that a good thing? Also, if A is strictly preferred to B and C to D, does it make sense to award B and D any seats?

Also, presumably already-existing STV methods could be used for preferential party list anyway. For example, if there are five seats and three parties (A, B and C), then if someone's preference was A>B>C, then this would be translated into A1...A5>B1...B5>C1...C5. What are the advantages of your method over using STV in this way?
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