## The Monty Hall paradox and the design of experiments

by

M. Keith Chen, an economist at Yale, questions whether half a century of research on cognitive dissonance is fundamentally flawed. (The New York Times has a nice article on his work, and the TierneyLab blog has continued the discussion at the Times.)

What the party line on Cognitive Dissonance has been: Well yadda, and then yadda yadda. Or so it seems.

(I originally wrote that as visual filler, but in hindsight it kinda works.)

One of the early studies of cognitive dissonance showed that when faced with three equally enticing options, if a subject was forced to choose between two of them and was then given a choice between the rejected item and a third item (as equally enticing as the first two), the subject would reject the same item again about 2/3 of the time. This was interpreted as the subject justifying their first choice by downgrading the estimation of the initially rejected item.

This phenomenon has been repeatedly tested in an array of experiments since the late 1950s, has been observed to occur in a variety of contexts, and even in several species.

Professor Chen points out, though, that the same phenomenon would be expected to occur if we assume that the subject regards the three objects as not all being of precisely equal interest, but rather if the subject has slight preferences for one over the other.

Suppose (the New York Times explains) a monkey is presented with three M&Ms, colored green, red, and blue, and has an internal ranking of these three colors.

At the first selection, the monkey is asked to choose between the red and the blue M&Ms. Suppose they prefer red to blue.

Of the six possible color rankings the monkey might have, three of them involve a preference for red over blue:

Notice that in two of those three cases, the monkey also prefers green over blue.  In other words, if we now ask the monkey to choose between blue (the rejected color) and green (the untested color), we see we should expect them to reject blue again about  2/3 of the time. This is a result of simple combinatorics rather than the monkey deciding to reject blue again to justify its earlier rejection.

Professor Chen argues that the accepted experimental designs for measuring cognitive dissonance are unable to distinguish between rational behavior on the part of the subject, and the cognitive dissonance effect they set out to measure, and that much of the empirical evidence gathered to date for CD could be accounted for by this Monty-Hall-esque phenomenon.

Professor Chen’s paper is still a working paper; it will be interesting to track its progression through the peer review process.