The Ugly Index: Part II

A dumpy, middle-aged man entered a sports pub near a University known for its beautiful coeds.  He scanned the room and saw his friend near the back of the room.  Near the door was a table of young, comely, young beauties who looked like they had just stepped out of a St Pauli Girl poster.  Immediately, his step gained the spring of youth and energy.

His table companion noticed and inquired about it.

The middle-aged man commented that the table of beauties near the door had unanimously rated him a "Nine"!

That's odd, remarked his table companion.  They were speaking German when I came in.

Rating items on a scale of one-to-ten is deeply ingrained in our culture.  And typically, we rate 10 as more (or better) and 1 as less (or worse).

This essay will discuss some of the pitfalls of those choices in framing will propose a solution.

The typical process

The typical process of kludging together a selection index involves selecting the parameters, choosing the endpoints that correspond to the endpoints (i.e., the choice of durable referencea to use as boundary samples), and choosing the weighting factors for the various parameters.  The values between one and ten are generally assigned in a casual, linear manner and values that fall outside of the boundary samples are typically given values like zero or eleven.

There is never discussion regarding the advantages/disadvantages of using value (the typical default, bigger numbers being better) versus loss.

Prospect Theory

Note that there is a kink in the curve at the origin.  Decisions are three times more sensitive to losses than to gains.

Prospect Theory tells us that humans are exquisitely attuned to loss.  In general, a loss is felt three times more acutely than an equivalent gain.  This may have to do with evolution...a loss is tangible, a future gain is a promise and not-yet-real.  That "bird in the hand" thing.

That suggests that an selection index based on "Loss", or "Ugly" will be more sensitive and better replicate our internal cognitive landscape.  Further, the advantages of "Ugly" will become more apparent and the issues of non-linearity and out-of-bounds alternatives are discussed.

Taguchi

The Goldilocks curve.  Not "too cold", not "too hot".  You want to be right in the center where it is "Just Right!"

The life work of Genechi Taguchi is beyond the scope of this essay.  Specific to this topic, he determined that the simplest function that mimics the true cost-to-society for a given attribute is parabolic.  In small deviations from the ideal very little loss is accrued.  As the deviation becomes farther from the ideal the incremental cost-to-society increases at a very rapid rate.

Consider the seal margin of an automobile door.  If the seal margin is too wide then the rubber seal-strip is not compressed and water will run into the vehicle.  The carpet and seats will get wet as will any electronics on the inside of the door.  In short order the vehicle will become musty, moldy and the electronics subject to failure.  If the seal margin is too narrow then the door will be impossible to close.  It will bounce off the seals before the latch can engage.  The door will leak (because it is not shut) and the same losses to the customer's investment will result.

Short of too wide the seal-strip might seal under normal conditions but leak when slightly challenged by a commercial car wash.  Short of too narrow the door may be difficult to close leading the customer to assess the factory as guilty of shoddy workmanship.

Within a range of +/-1.5mm of the nominal seal margin setting the performance of the sealing system is uniformly good.

The Ugly Index presumes that the exact center of the range be assigned a loss (to society) of zero.  Further, the Ugly Index proposes that the "point-of-indifference" be assigned a loss of one.

Point-of-indifference defined:  As a person who bids in auctions it is advisable to determine the top price you are willing to pay for an item.  That price is where you do not care whether you "win" the auction or not.  At prices below the point-of-indifference you value the item more than the transaction price.  At prices above the point-of-indifference you value the purchasing power represented by that number of dollars more than the item.