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Can using logarithms overcome scope insensitivity bias? Answered

Say you perform the following type of psychology experiment:
  • You describe an undesirable event to people,
  • tell them that X instances of the event can be prevented, and
  • ask them what they would be willing to pay in order to prevent those X instances.
  • The responses you get (Y) are not even close to being linear with respect to X, but rather
  • the responses are roughly logarithmic. That is, X=ABY, or Y=logB(X/A) for some constants A and B.

So does anyone know of an experiment (or real-life situation) where subjects are asked to answer in terms of log(Y) instead of Y? Do such responses show a linear relationship to the corresponding X?



Best Answer 9 years ago

Have you tried searching Google Scholar? It's a separate Google database strictly for peer-reviewed and related publications, including preprints (e.g., from arXiv) and conference proceedings. It isn't well known, unfortunately. It also has the limitation that a number of results (in particular, anything from Elsevier-published journals) are pay-per-view, so you don't get much beyond abstracts.

What I often do (for physics) is use Google Scholar to find interesting articles, then look for the corresponding preprints directly on arXiv.

I did not think of using Google Scholar. In fact the first result that appeared was, while acknowledging that it existed, impressively critical of the notion that scope insensitivity was an inevitable fact of CV (contingent valuation) surveying. "First, the scope insensitivity hypothesis is strongly rejected (p<.001) by two large recent in-person contingent valuation studies, Carson, Wilks and Imber (1994) and Carson et al. (1994), which used extensive visual aids and very clean experimental designs to value goods thought to have substantial passive use considerations." "Rejection of the generic insensitivity to scope in CV surveys should not be taken to imply that one cannot design a CV questionnaire and administer it in such a way as to find scope insensitivity. Indeed this can be done fairly easily. The remedies for the problem are straightforward in concept but often difficult and expensive in practice to implement. The respondent must (i) clearly understand the characteristics of the good they are asked to value, (ii) find the CV scenario elements related to the good's provision plausible, and (iii) answer the CV questions in a deliberate and meaningful manner."

I don't know, but I would be willing to guess that if you tried to present people with log(x), you'd get a dilog response curve (i.e., log(log(x))). Human perception in general is driven logarithmically (consider e.g., sound perception in bels/dB, light intensity, and so on). The broad reason is that logarithmic response provides a huge dynamic range with roughly uniform sensitivity.

Oops. You're right. Substituting log(x) for x in the function y=logb(x/a) does indeed give a log of a log. Thank you for pointing that out; I'll fix the question.

With regard to the uniform sensitivity comment, I am aware of that. However, there are some situations in which uniform sensitivity might not be a good thing: e.g. "this leads to three cases of cancer" vs "this leads to three hundred cases of cancer".

You're right that logarithmic response isn't always the "best" design. However, we are, as you know, constrained by our history. Nature tends to re-use (and overuse :-) constructions and systems which are successful. My suspicion is that humans' "analysis" of numbers on relative scales (i.e., proportions, which leads to logarithmic sensitivity) is an example of reusing the same kind of brain structures that work for sensory information in a more abstract area. Doing something differently would require separate and special-case neural constructs for abstract numerical analysis. Humans haven't been doing numbers for long enough, nor are the "shortcomings" of our current system significant enough, for such a separate system to have evolved.

Hence my question about whether a few pre-calculated mathematical tricks could force some extra usefulness out of the mental tricks we do have. I am looking for some experimental evidence, though, since what is actually going on in the mind may be too complicated to be 'fixed' by such a simple trick. I may just need to write to some university professor who looks like he or she has an interest and ask for a heads up if the professor ever happens across some relevant literature.