A Spatial Decision Support System (SDSS) for Electoral Districting
The following components were used to compute the constituency
boundaries in the Kenya and South African examples:
 A locationallocation model to
represent the problem.
 Data items to implement the model.
 An objective function to define
the user’s objectives.
 An algorithm to solve the
problem.
 Special features to find noninferior solutions.
 A GIS to map solutions.
The pmedian locationallocation model
 The SDSS uses a locationallocation
model to make these maps
 The classic locationallocation model finds regions for
which the sum of the populations of the enumeration areas times the distance
to their respective centers is least.
 These electoral districts are maximally compact
regions adjusted for the different population weights. In the pmedian model,
the sum of person distances to their centers is least and the function Z is
minimized.
where:
 w_{i }=
population of the ith enumeration area
 d_{ij} =
distance from ith enumeration area to jth regional center
 x_{ij }= {_{ }1 for the closest regional center (j) and
0 for all others}. This definition ensures that each enumeration area belongs
to one, and only one, electoral district and that every enumeration area is
assigned to an electoral district. It also ensures that electoral districts
are comprised of contiguous territories.
 the total number of electoral districts to be generated
by the model is denoted by p.
The model is solved by selecting p districts, defined as
nodal centers and their assigned enumeration areas. The model is solved by
an algorithm that minimizes the function Z.
Data
items to implement locationallocation
models
Four
data items for each enumeration area :
 area (km^{2})
 shape
 population
 distances (km) to the centers of all other enumeration
areas
The Objective
Function
 The objective to be optimized in generating regions
 Here, compactness and equality in the number of voters.
 This is a multiobjective function.
 The two objectives are “tradedoff” in multiple runs
of the SDSS.
 Spatial constraints can be introduced:
 Electoral
districts can be prevented from crossing provincial boundaries.
 Opposite
sides of a lake can be prevented from being in the same electoral districts.
Copyright © 2001 by
Joel D. Barkan, Paul Densham and Gerard Rushton
