M Baker Thesis: Appendix - Problem of the Use of Average Figures

There will be a problem in any field where pairing of different elements is modelled by collecting the elements into groups, and pairing the groups. It may well be that the paired groups contain very few paired elements (see figure 4).

In many cases the pairing of elements is due to individual decisions. In the model these are fairly realistically represented by pairing elements which produce a minimum (or maximum) for a function which is dependent upon characteristics of each element. However the problem arises when these individual pairing decisions are combined into group pairing decisions. These are again made on the basis of minimising a function which is dependent upon average values of the characteristics of each element. If there is a large spread of values of the characteristics, there is liable to be a significantly large mis-match of elements in the paired groups (see figure 4).

The separate elements in one group of a pair need not be paired with elements in the other group of the pair. Pair A has a large mis-match of elements whereas Pair C has a fairly good match of elements.

Examples

Two examples are given. One from transport planning, another from the methodology being developed in sub-regional studies. They are the assignment process in transport modelling and the use of development potential surfaces in strategy generation for sub-regional studies (see figure 5).


Elements	Individual Person Trips between zones	Routes
Characteristics	Value of time	Time Cost
Sets	All trips between two zones	'Shortest' route
Pair	Trip and route


Elements	Land use i.e. housing	Plots of Land
Characteristics	Importance attached to:-Slope, Site size, 'Environmental quality' Accessibility to jobs " " recreation	Slope Site size 'Environmental quality' Accessibility to jobs Accessibility to recreation
Sets	All of one type of land use i.e. housing	All under-developed plots within Km grid square
Pair	Land use and plot of land

Assignment - A common method of assignment, at present, is to assign all persons trips (on a given mode) (elements) between two zones to the 'shortest' route (element) between those zones, where shortest is defined in terms of the generalised cost.

A fairly accurate predicition of individual behaviour could be made on the basis of assigning separate person trips (individual elements) to the "shortest" perceived route (individual element) between origin and destination, defined in terms of an individual generalised cost. (A function of the characteristics, value of time, time, and cost of the individual elements). However in the model the difference in route lengths is only that occur ing between zone centroid and zone centroid. There is no account of the variation in length due to the finite size of the zone. There will also be differences in 'perceived' lengths due to variations in individuals' variation in time valuation (and also due to errors in perception). In other words within any group of person trips there will be a variation in time valuation, and within any corresponding set of routes there will be a difference in the perceived lengths due to differences in time valuation, errors in perception, and the finite size of zones. These possible differences in perceived lengths may be larger than the differences in route lengths, in which case not all trips between the two zones will use the same route. In the model all the trips are placed on the shortest route on the basis of centroid to centrold, shortest generalised cost, based upon an average value of time, which, in this case, will result in some of the trips being assigned to the wrong route.

Development potential - A development potential surface can be used to locate new development when producing a strategy for a development plan or sub-regional study. (This method was used in the Coventry, Solihull, Warwickshire Sub-Regional Planning Study (1971).) As an example the location of new housing will be considered. It is assumed that housing is located on the basis of the best trade off between several factors or characteristics of each available site. (Each location decision is an element and each site is an element. The trade offs are the characteristics for each location decision). The site characteristics might be slope, site size, 'environmental quality', and accessibility to jobs and to recreation.

The development potential surface is produced by assessing the average value of each factor for all available sites in each kilometer grid square (group of sites) in the area under study. These separate potential surfaces are then combined to give a composite potential surface by adding the separate surfaces multiplied by an average weighting. This average weighting is assumed to represent the average trade off between the different factors. This produces a surface which 'theoretically' shows where the "best" sites for new housing are. The new housing is then allocated (housing location group) to sites in those kilometer squares which have the highest development potential.

The problems arise because separate location decisions will have non-average trade offs, and will in this terminology, be located on the basis of a different surface, and the values of the characteristics of the elements (sites) in each group (grid square) will vary so that any surface produced on the basis of the Km grid squares will only give an average of the potentials of the sites in each square. This means that if there is any difference in trade off (which there is likely to be, for instance between single private houses, private developers and local authorities, housing estates), and any significant variation between the characteristics of each site within a square, the model will locate the housing on a surface which would not be used in individual decisions and does not represent the true development potential of each site. There will consequently be a possibility of a serious mis-location of new housing sites.