Section 39 Strength / importance

39.1 Including the idea of strength in our functional equation

Usually we think of functions as having the form \[E = f(V)\] where V is some set of influencing variables e.g. B, C etc, possibly just a set of one variable like B. Lately we have been using an extended form: \[E_{posterior} = f(E_{prior}, V)\].

In order to include the important idea that influences rarely have the power to completely shift the consequence variable from 0 to 1, we have already allowed for functions of the form \[E_{posterior} = f(E_{prior}, V, s)\] where \(E_{prior}\) is the prior level of E, the level without the influence of V, and where s is the strength of the influence, between 0 and 1.

There are different possible versions of the rules which govern the way strength information is processed, (and which therefore determine exactly what we mean by it). For example how much the prior value of the consequence variable is taken into consideration.

So really this means revisiting and expanding our basic coding rule to include coding for strength.

“Strength” uses a generic way of tempering or weakening causal information, in particular we use it when the respondent themselves says that the connection is weak.

We can imagine applying this kind of “tempering” transformation for a variety of other purposes, for example because the causal link has only a small amount of evidence, or we don’t trust the respondent. I have added another attribute which tempers the effect of a variable in the same way. It is actually called “trust” but it works at the moment as a placeholder for any of a range of different qualifiers -– trust/trustworthiness, confidence, explicitness (Gary/James version 6) etc. These issues are of course not the same and should (probably) not be encoded with a single attribute.

If “trust” is 100%, we treat the information as gospel. If it is zero, it has no influence on our causal map at all.

• From: “source P believes / asserts that ‘A causes B’ and we trust source P 100%” we can (by definition) conclude that A causes B
• and, from “source P believes / asserts that ‘A causes B’ and we trust source P 0%” we have no information about whether or how much A causes B

But with values in between 0 and 1, the equation is a bit more difficult to formulate.

Basically, from a Bayesian perspective,

The strength of the upgrade to our information due to a report with a standard tempering of .3 would be correspondingly reduced, i.e. multiplied by a factor of .3.

39.2 Direct ways of eliciting how important is one variable’s contribution to another. (Fiona)

Where the coding of the strength of an influence is particularly important, we might want to specifically ask our respondents questions about it. The coder should consider this information when coding the “strength” attribute of the package of influencing variables.