[EM] Criterions for party-list PR systems

Kristofer Munsterhjelm km_elmet at t-online.de
Fri Sep 4 07:51:16 PDT 2015

On 09/04/2015 01:11 PM, Vidar Wahlberg wrote:
> This list mainly discuss election systems where votes are cast for
> single candidates, rather than for parties. When voting for single
> candidates, the voting system criterions make sense, but to what degree
> can those criterions be used for a party-list proportional
> representation system?

I think an intuitive first approach is to consider party list like a
single-candidate system where each party runs a bunch of clones and
where voting for the party is translated into voting for all the party
candidates in that order.

In open list PR, a voter may rearrange the candidates on the party's
list. This would be similar to the voter voting the party candidates in
a different order, though in practice, it usually is more like each
voter rearranging the order of the clones according to another voting
procedure run only on the ballots for the party in question.

If there are three parties (X, Y, Z) and three candidates for each, and
each party lists the candidates in order 1, then 2, then 3; then voting
for X in a party list system is similar to voting for X1 > X2 > X3 in a
candidate-based system. The analogy is exact (I think) for largest
remainder methods: if you do that kind of expansion with party list and
run the result through STV, you get the same result (per party) as if
you did party list PR allocation by largest remainder with a Droop
quota. I'm not completely certain which candidate methods correspond to
Sainte-Lague; I've heard that Monroe's method does this, but I'm not
sure if it does or if it corresponds to Hare instead.

Part of the reason that you'll find more discussion about candidate
methods than party list, I think, is that there's an idea that candidate
methods give greater freedom. In candidate methods, the voter can decide
which candidates in a party he prefers the most, and thus not only rank
between parties but also within them; and he can also vote for an
independent if so inclined, or mix candidates from different parties
(e.g. rank the candidates he thinks are particularly honest ahead of
those he thinks are less so, irrespective of party affiliation). Thus,
for candidate methods, there's no need to favor parties as such: a
candidate may run with or without party support.

Party list methods are usually a lot simpler than similarly fair
candidate methods, though, and you can do biproportional representation
with them. It is possible to do something similar to biproportional
representation with candidate methods (see e.g. Schulze's STV-MMP[1]),
but again, that's more complex and then parties are part of the system

> As an example, how would the later-no-harm criterion manifest in a
> typical preferential party-list proportional representation system?
> Would the following be a fair translation of the criterion?
> - The criterion is failed if adding a party with lower preference to the
>   ballot may cause a higher preferences to end up with less
>   representation?
> How about the monotonicity criterion?
> - The criterion is failed if ranking a party lower on the ballot may
>   cause that party end up with more representation?

Going by the reduction or analogy above, that seems right. The method
passes LNHarm if appending some parties to your ranking doesn't reduce
the number of seats given to the party/parties you ranked before
appending. The method passes monotonicity if raising a party never makes
it lose seats, and lowering a party never makes it gain seats.

> Are there any criterions you know of or can think of that typically
> would not apply to candidate based systems, but would apply to
> party-list PR system?

In http://www.votingmatters.org.uk/ISSUE3/P5.HTM, Douglas Woodall
defines some clone criteria. In particular, he defines "clone-no-harm"
as "replacing a candidate x by a set of clones should not harm another
candidate y". He then says that this is incompatible with the Droop
proportionality criterion. Imagine, for a candidate method, this election:

1000: A
   1: X>Y>Z

for three seats. The outcome would be {A, X, Y}. But then clone A:

1000: A1>A2>A3
   1: X>Y>Z

and it's evident that the outcome will (and IMHO, should) be {A1, A2, A3}.

But for party list, this is not a problem as long as the rules require
that every party needs to field at least s candidates to run. In the
situation above, nothing would happen between the first and second
instance: A would get every seat in the first election and A1 would get
every seat in the second (assuming a 3-seat election).

So in short, yes: party list can pass independence of clones whereas
candidate methods with fixed seat sizes have to give clones some seats
in certain cases. One way of looking at my question to Steve Bosworth
about cloning is as a question of whether his weighted vote system
suggestion is closer to party list or a candidate method.


[1] In particular, this:
http://permalink.gmane.org/gmane.politics.election-methods/13620 seems
quite akin to biproportional representation.

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