Saturday, June 9, 2012

It Is Not Hard to be Thorough

One useful trick in dissecting a complex problem and performing thorough analysis of it is what statisticians called Factorial Experiment.  Intuitively, in analyzing an phenomenon, once one identify some underlying key factors and their possible levels/values, one can generate exhaustively all possible combinations of these factors and values.   Often, with such a brute force exercise, one finds some surprises of missing cases which have not been noticed previously.

To appreciate what the techniques is, let us look at the smallest examples when there are two factors with each taking possibly two distinct levels/values.  Thus, in total, they constitute 2 by 2, or 4 cases.
Professor Daniel Kahneman has the following discussion of decision makings with what he called “the fourfold pattern” in his book Thinking, Fast and Slow.  He noted two key factors in making decisions with risks: one factor is the perceived value of the outcome which can be gains or losses.  The second factor is the likelihood of the outcome which can be high or low.  Four cases or patterns can thus be identified:
  1. High probability of gains
  2. Low probability of gains
  3. High probability of losses
  4. Low probability of losses
 Now, one can systematically analyze easily the behavior of people when they are in each of these situations.  I bet you would agree that people tend to be risk-averse (i.e., prefer certainty) when in situation 1 and 4, and be risk-seeking (i.e., prefer gambling or taking a chance) when in situation 2 and 3.    Kahneman’s examples include: being risk averse for case 1 and 4, the acceptance of unfavorable settlement when there is a 95% to win $10,000 and 5% chance to lose $10,000, respectively.   The formal is the reason why many settle a law suits even when there is a chance to win much bigger and the latter is the reason why insurance business exists and why people buy insurance even when it is overpriced.  And being risk seeking for case 2 and 3, the rejection of favorable settlements, when there is a 5% chances to win $10,000 or 95% chances to lose $10,000.  The former is the reason why gambling business exists and the latter is the reason why some people refuse to be relocated during disasters or eminent domain cases.  

I am sure you can relate or find more interesting examples and observations using such fourfold pattern or factorial design trick.  Here are two interesting ones to get you going.

Two decades back, I heard in a Broadband Networking Conference what I thought was the best characterization of the difficult notion of “virtual”.  At the early part of his keynote speech, Bob Kahn, one of "the fathers of the Internet" (along with Vint Cerf), drew on a transparency a two by two grid.  In one dimension, he noted the factor of visibility (of an object) which can be visible, or invisible. And in the other dimension, he noted the factor of existence which can be yes (is there), or no (is not there).  While we are familiar with the physical world where objects are visible and there, networking researchers have created long ago a world of virtual objects and resources which are visible but not there!  This is actually one fundamental reason why Internet-based services can be inexpensive but more volatile.   Now I think you can understand easily and intuitively what all these virtual xyz’s (world, game, reality,…) you have been hearing about are.

In closing, let me give you one more example of fourfold pattern.  In my previous life as a manager, one report of mine related the following quiz to me during our annual performance review discussion.  He asked “How would you rank order the following four types of employees?”
  1.  Smart and hardworking
  2. Stupid and hardworking?
  3. Smart and lazy?
  4. Stupid and lazy?
His insight is that stupid and lazy is preferable to stupid and hardworking since the latter produces far greater negative impact and rework to the team!  Can you guess which type of employees is he?
Talk to you soon!

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