Supporting Resources

for Lecture 10: Overlay Combinations

Index of Resources:

• Commensurability
• Rules of Combination
• Relation to Multi-Criteria Decision Techniques

Commensurability

In the philosophy of science, there is much attention paid to situations in which groups (disciplines, schools of thought) cannot understand each other due to having different definitions of terms, etc. This is called the incommensurability problem. It is a huge topic of discussion (even has its own .com).

• a definition (Philosophical Dictionary)
• Kuhn is the origin of the interest in the term. (There is a Kuhn industry with many academic papers and disputes arising from what is, at its origin, a fairly fuzzy presentation with multiple interpretations. Here is one reflective article from Studies in the Philosophy and History of Science)
• Feyerabend had a particularly radical approach (anarchist...) [from a philosophy course in England]
• Lakatos wants to retain the idea that theories change rationally... a paper on this arguments
• A huge bibliography on the topic

Rules of Combination:

Rules of Combination might be discussed, but rarely considered in all the depth of handling all interactions. Rules emerge from the science of the layers studied - no magic bullets (no procedures that will solve all problems).

"Linear Combination" - the Weighting and Rating Game
Vj = [[SUM]]i wi rij /[[SUM]]i wi

(or the value for item j is the sum of the product of the values times the weights divided by the sum of the weights...)

• influence of roundoff (integer values) on ratings and weights
• standardized ratings make weights easier to understand
• Independence of factors

When the variables are continuous, suitability might have some functional form; total cost, elapsed time, ... which is not simply an average; it could be a total.

Multi-Criteria Decision Methods

International Association for Multiple Criteria Decision Making (MCDM)

Based Hobbs: Choosing how to choose (Envir. Impact Assess. Review 1985: 5: 301-319)
see also Carver (1991) International Journal of GIS.

"Amalgamation" (purpose to commensurate the incommensurable) part of multicriteria decision making

Defends commingling of attributes, but recognizes requirements:

1. "attributes" (variables/factors/maps) completely describe impacts and characteristics of alternatives while avoiding redundancy; values (importance) or prob. dist. known
2. all relevant alternatives be included (to be considered)
3. decision makers have stable preferences and can voice them

Steps:

1. attribute scaling: value-based - midpoints/ tradeoffs (conjoint measurement)/"holistic" scaling OR utility-based - indifference between midvalue OR p (better) * (1-p) (worse)
2. attribute weighting: how much of one attribute to trade for another
3. decision rule (procedure) from simple weighted addition to fancy methods (ELECTRE)

Issue of "preference independence": are tradeoffs between pairs of variables independent of third variables?

In my estimation, this shows that the multi-criteria literature recognizes the problems with interaction of variables, at least conceptually. In practice, many practitioners simply use addition or a weighted score without really thinking about the tradeoffs and the indifference issues....

Carver's open internet interface for nuclear waste in Britain

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Version of 20 October 2003