Judgmental drag

Take 1

What is the population of Greenland? Record your estimate before you look up the actual number. The difference between your estimate and the true number is an index of accuracy (or error, depending how you look at it). How can you reduce the error? You can take five, and guess again, perhaps after thinking how your initial estimate may have been mistaken. Then you average the two estimates and look up the truth. If your two estimates bracket the true number, their average is more accurate than the two individual estimates are, on average. This nifty result is an extension of the "wisdom-of-crowds" effect, a fanciful label for the familiar benefit of statistical aggregation (also known as "dialectical bootstrapping" or "brainstorming for one"). In the original studies, the estimates came indeed from different individuals, not from a single one. The statistical implication of aggregation is the same.

Take 1

Take 2
Before estimating the population of Greenland, suppose you respond to the question "Is the population of Greenland greater than 1 million?" Naturally, you say "No." Now you proceed to make your own estimate. Alternatively, you first respond to the question "Is the population of Greenland smaller than 100?" Again, you say "No," and proceed to make your estimate.

Anchoring and insufficient adjustment
When comparing the two estimates you will find that the one following your first "No" response is larger than the one following your second "No" response. This difference is known by the header of this paragraph. The phenomenon is noteworthy because reasonable people agree that the "anchor" (1M vs. 100) is arbitrary; it is recognized as such and therefore rejected. Yet, it "drags" your estimate as if by gravitational pull. Evidence for anchoring is discovered and documented in experimental research. The crucial feature of experimentation is that it comprises (at least) two conditions (here: high and low anchor). It is the difference between measurements taken in different conditions that tells the story and that constitutes evidence for or against hypotheses.

Back to life
How much do experiments tell us about real-life events? Not as much we would hope! Here's an example. I went to a faculty meeting as one among many (hence the title of my blog). We voted using clickers. That felt like progress because it set aside unwanted normative influence with its attendant discomfort of being in a publically visible minority. First, we were treated to clicker practice. ‘A' is for ‘yes' and ‘B' is for 'no' (and ‘C' is for ‘abstention,' which is funny because what if you literally abstain and press none of the keys?). To see how it works, we were given a mock proposition, namely the motion that "All faculty, except administrators, will have free parking on campus." Sure enough, the motion carried with an overwhelming majority (going with my inner Mephistopheles I dissented). Notice that what we have done is cast an anchor. Next, we get a motion that matters and again there is a great majority supporting it. Extrapolating from research, we would have to conclude that the motion would have garnered less support without the anchor. Sadly, this inference must remain an educated guess; there is no way of knowing what the percentage of yes votes would have been without judgmental drag. There was another vote and here the majority vote was no, despite two anchors pulling to yes. Again, we suspect that opposition to that motion was greater than measured. Oh well.

Self-deception?
Although the clicker method remains open to contamination, e.g., by anchors, I prefer it over public voting. Public voting opens the door to influences on judgment that have nothing to do with personal opinion. This is well known since Solomon Asch's famous conformity experiments in the 1950s. It is also well known that people tend to overestimate their ability to resist normative majority influence. When I suggested the clicker method in a different faculty committee on the grounds that individuals could be influenced merely by seeing how others are voting, the response was mirth and reassurances that oh no, we are not susceptible. We are independent. We unanimously agree that we are independent. It was kind of a Monty Python moment.

By the way, the population of Greenland is 57,637 (see here).