[EM] Second order proportional representation.

[Richard Lung]

Hello Kristofer,
Your last paragraph is perhaps the bottom line (in the American idiom).
As you might know from the example, you set me, for my invention of 
Binomial STV, and indeed from the 19th century inventors of STV, 
elections, pure and simple, are a matter of choice, which is what the 
word, elections means. That is to say the (STV) election system does not 
presume to do the voters voting for them, by restricting choice to a 
(party) group vote or a (monopolistic) single member district.
The first lesson I learned, from reading books on philosophy of science, 
was not to presume what one is supposed to be trying to prove (that the 
voters are herd partisans) and not to allow ambiguity in ones 
experiments or tests, such as allows one to believe anything one wants 
to: for example, whether or how much the single member constituencys 
party-monopolising candidates have personal appeal.
My free ebook Scientific Method of Elections includes a fuller 
discussion, as well as of Binomial STV, and many other matters.
from Richard.

On 14/09/2016 21:06, Kristofer Munsterhjelm wrote:
> On 09/02/2016 07:10 AM, Richard Lung wrote:
>> Second order proportional representation.
>>
>>
>>
>> First order proportional representation refers to the election of the
>> legislature by PR. Second-order PR refers to the composition of the
>> executive.
>>
>> Transferable voting can prefer candidates from more than one party, to
>> decide the democratically prefered majority coalition. This single
>> majority government, representing over half the voters in the executive,
>> is the rational representation, that is denied by first past the post or
>> simple plurality elections.
>>
>> But that is still not second-order proportional representation. That
>> requires at least a double majority government, which would represent
>> two thirds of the voters in the executive. A triple majority government
>> would represent three quarters of the voters in the executive. And so
>> on. That is second-order proportional representation.
> I just read about an interesting idea in this vein by Brams. First you
> pick your legislature (using whatever method), then once a majority of
> the parties decide to form a government, the parties sequentially claim
> ministries according to an order given by a divisor method.
>
> For instance, suppose the following parties are represented in
> legislature, with seat counts:
>
> Party A: 55
> Party B: 10
> Party C: 7
> Party D: 1
> Party E: 48
> Party F: 29
> Party G: 10
> Party H: 9
>
> Now suppose that, to make things interesting, parties E, F, and H choose
> to form government. Furthermore suppose there are 10 ministries, and the
> method this legislature uses for the executive ordering is Sainte-Laguë.
> Sainte-Laguë would apportion as follows:
>
> First seat: E
> Second: F
> Third: E
> Fourth: F
> Fifth: E
> Sixth: H
> Seventh: E
> Eighth: F
> Ninth: E
> Tenth: E
>
> The share of seats is: 60% E, 30% F, 10% H, compared to the relative
> legislature share of 56% E, 34% F, 10% H when only seats belonging to
> those three parties are counted.
>
> Anyway, the idea of Brams was to ask the parties (in order) to choose
> ministries. So in the assignment above (EFEFEHEFEE), E would first be
> asked to pick a ministry/department (and would probably choose the PM).
> Then F gets to pick the next, E gets the next after that one, then F, E,
> H, and so on.
>
> The point of the procedure is that it would weaken the need to negotiate
> for a share of the government. If party X is part of the majority
> coalition that decides to form government, how many seats X gets is not
> something the coalition can influence. Furthermore, since Sainte-Laguë
> works like a proportional ordering, it is fair at every step of the
> process (assuming that going first is always beneficial).
>
> Presumably the same idea could be used for more advanced proportional
> orderings, but the system would become more opaque.
>
> Unfortunately, Brams then discovered that sometimes it does pay to not
> go first, and he suggested that trading might help with it. One
> possibility for trading could be that a party, when it's its turn to get
> a ministry, proposes to exchange a free ministry seat with one that's
> already taken. If the other party (who holds that other ministry seat)
> agrees, they switch. Suppose, for instance, that at some point in the
> process, E has claimed the ministry of justice, and the ministry of
> education is free when F is to choose. F might then propose to E that F
> gets the ministry of justice in exchange for E getting the ministry of
> education, even though nominally the ministry of justice has already
> been claimed.
>
> I suppose Brams' system could be used for supermajority-support
> executives, but then the confidence agreement would have to be supported
> by a supermajority. Perhaps the system above would make this easier
> since less negotiation would be required beforehand, and thus diminish
> the chance of a deadlock or, looking at it another way, enable greater
> supermajorities to reach a decision about what government to have for
> the same risk of deadlock.
>
>> Note that it requires a considerable first-order proportional
>> representation to ensure even a single majority government. We saw this
>> in Ireland, when the then largest party, Fianna Fail whittled down the
>> constituencies to 3 or 4 members, so that they could win a majority of
>> seats on only 45% of the votes.
> More complex apportionment systems could base the number of executive
> seats on support among the voters rather than on legislative support.
> However, it may be difficult to use that kind of apportionment, which is
> fundamentally party-based, if the legislature is elected using
> non-party-list methods like STV.
>


-- 
Richard Lung.
http://www.voting.ukscientists.com
Democracy Science series 3 free e-books in pdf:
https://plus.google.com/106191200795605365085
E-books in epub format:
https://www.smashwords.com/profile/view/democracyscience

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