Tuesday, September 16, 2014

The Ugly Index: Part I

The human brain has some limitations that hinder our ability to make "rational" choices.

Perhaps the severest limitation is the inability to process more than one pair-wise comparison at a time.  The human brain is truly a "one holer".

Think back to school when we learned to do a difficult task like Long Division.  Essentially, we were taught an complex set of instructions that broke the task down into a series of simple tasks.  We did not divide 8 into 1026.  First we tried to divide 8 into 1.  Then we divided 8 into 10.  Then we subtracted.  Then....

The reduction of tasks into simple sequences that iterate until the task is completed is one of the great accomplishments of civilization but there are some tasks where it fails.

Consider the task of moving to a new city.  The city has many neighborhoods or suburbs.  We seek to optimize multiple attributes in the choice of our new community, and then the individual house within that community.  A great price per square foot must be weighed against factors like waste water treatment plants that are located upwind.

Iterating fails because multiple iterations are, in effect, compound interest.  Consider a choice that is being made when there are only two variables.  Suppose one variable is weighted with 0.8 in importance and the other variable is weighted with 1.2.  To make it real, suppose ERJ were contemplating the purchase of a new firearm and he assigns 0.8 to the choice of caliber and a weight of 1.2 to the capacity of the magazine.

Applying those weights over 10 comparisons (internet research, reading magazine articles, visiting multiple gun stores....) would result in a relative weighting between the two variables as (0.8/1.2)^10 or, the caliber would influence the final decision 1.7% as much as the magazine capacity.  The single, highest weighted factor always dominates and all of the other variables are discounted into oblivion.

While this is fairly easy to see with a simple one-variable comparison that deficiency becomes hidden in more complex decisions.

History


This shortcoming was recognized as far back as Benjamin Franklin.  His proposal was to take a sheet of paper and draw a line down the center.  Label the left side of the paper PLUS and the right side of the paper MINUS.  Then list all of the advantages of a given course of action on the PLUS side of the paper and all of the disadvantages on the MINUS side.  Whichever side of the paper has the longer list should indicate the best course of action.

The advent of computers resulted in additional sophistication and cost.  Shortly before he died Robyn Dawes revisited the Benjamin Franklin method.  He found that it gave up little to the more modern methods.  What it gave up in precision it gained in resistance to gaming the outcome.

How to "game" the system


Suppose you must move to a new city and you ask your spouse to list the factors that are important to them.  They list:
  • Good schools
  • Low violent crime rate
  • High standardized test scores for students
  • Residual value upon resale of house
  • Many special services available within the school
  • No racial tension
  • Advanced placement and talented student progra ms at the school
 Did they list seven independent variables or did they list seven manifestations of a single variable?  It is pretty clear that all of those elements are correlated and that by listing it seven times it weights it by a factor of seven vis-a-vis other "variables".

Summary


An ideal system would reduce many complex choices down to a single number, an index, that is immune to  the compound interest effect of multiple iteration process.

An ideal system would armor the decision against stakeholders loading the dice to bias the outcome in their favor. 

The author intends to define the Ugly Index which meets those requirements in the next few essays.

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