# [EM] Second order proportional representation.

VoteFair ElectionMethods at VoteFair.org
Thu Sep 15 20:52:12 PDT 2016

```On 9/14/2016 1:06 PM, Kristofer Munsterhjelm wrote:
> 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.

Here is yet another approach:

http://www.negotiationtool.com/cabinetministers.html

The MPs (members of parliament) rank their preferences for possible
cabinet members, and then a variation of VoteFair ranking calculations
fills the cabinet positions.

It mostly uses the algorithms explained at VoteFair.org
(http://www.votefair.org/calculation_details.html).  Of course a few
modifications are needed.

time-sensitive election article that I will announce later.

Richard Fobes

On 9/14/2016 1:06 PM, 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.
> ----
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