Seat Allocation in Parliaments.
A key institute in old and modern democracies is the
parliament: a collection of persons that have been elected to represent the
people, and whose main task is to control legislative power – we will refer
to these elected persons as members of parliament or MPs. Almost always, members of
parliament are grouped into different parties, and members of the same party
share a basic point of view on how society should be organized. To exercise
their right and duty of controlling power, there is a physical location where
the members of parliament meet, discuss, vote, gossip, and do all the things
that members of parliament are supposed to do – in the sequel, we will use the
term ”parliament” to denote this physical location. In this note, we are
especially interested in distributing MPs over the seats in the parliament so as
to optimize the functioning of the parliament. Of course, this objective can be
concretized in different ways – we intend to inventarize different, not
necessarily conflicting ways of achieving this objective. It is also interesting
to observe that the particular physical lay-out of the seats in the parliament
matters for this objective; most parliaments have a (half-) circular shape where
sets of seats are separated by corridors. We will close this note by giving a
list of some parliaments that we find interesting, give the current seat
allocation, and give our “optimal” seat allocation.
Let us list a number of properties present in almost all
seat allocations in parliaments all over the world:
(i)
MPs from the same party are grouped. Thus,
neighboring seats (to be defined later) are as much as possible allocated to MPs
of the same party. This facilitates intra-party discussion.
(ii)
Not all seats are equally important. Seats in the
front have more visibility, and allow direct access to the debating spot (a term
we use for the physical position from where the government representative, or
other MPs can be interrupted and questioned). Usually, large parties (i.e.,
parties with more MPs than others) occupy one or more front seats. Seats in the
back may be considered less important, while seats with access to corridor may
be preferred over seats between other seats. Notice that there are parliaments
such that each seat has access to a corridor.
(iii)
Western democracies have parties that are often
labelled somewhere in a “left-right” spectrum. In many parliaments, this
left-right positioning is reflected in the allocation of seats. In a way, MPs
from different parties that are considered to hold similar views, are allocated
to neighboring positions in the parliament.
A way to precisely model the interconnection between
different seats in a parliament is to define the concept of neighboring seats.
We use the following definitions. Two distinct seats are neighboring when direct
contact between two MPs in these seats is possible. With direct contact we
understand that whispering and drawing attention (without alerting others) is
possible. In practice, this means two seats that are positioned next to each
other on the same row, or that are positioned such that one seat is directly
behind another seat, are called neighboring. Of course, in some cases deciding
whether two seats are neighboring can be a debatable choice. Further, seats are
called half-neighboring when the seats are on opposite sides of a corridor.
Indeed, MPs on opposite sides of a corridor can still easily make contact. We
realize that much more fine-grained ways exist to define the concept of
neighboring – we use this as a first proxy.
Our model is an integer programming model that maximizes a
particular objective function representing intra-party communication. In this
objective, one point is gained when a pair of neighboring seats is allocated to
members of the same party; half a point is gained when a pair of
half-neighboring seats is awarded to members of the same party. The model has
constraints that ensures that large parties receive front seats, and depending
on the physical lay-out of the particular parliament, the model has constraints
to ensure that a left-right allocation is adhered to. If desired, many other
constraints can be added; we mention here: (i) particular seats that, for
historical or nostalgical reasons should be allocated to a particular MP of some
party, or (ii) parties whose members hold wildly different views, and in order
to avoid conflicts should not receive (half-) neighboring seats.
A crucial advantage of a model-based proposal for a seat
allocation is its neutrality; once there is agreement over the basic principles
that should guide the seat allocation, the outcome of the corresponding model is
should be perceived as unbiased.
The Netherlands, Second Chamber – Facts
Number of Seats: 150
The Layout (including neighboring seats)
Number of Parties with MPs: 12
Parties and number of seats:
(33 20
19 19 14 14 9 6 5 4 3 3 2)
Our solution, value
Current solution, value
Remarks
The Netherlands, First Chamber – Facts
Number of Seats: 75
The Layout (including neighboring seats)
Number of Parties with MPs: 12
Parties and number of seats:
(13 12 10 9 9 8 4 3 2 2 2 1)
Belgium, Kamer der Volksvertegenwoordigers – Facts
Number of seats: 150 (notice however)
Our solution, value
Current solution, value