Subject: Re: street performer protocol
From: (Kevin S. Van Horn)
Date: Sat, 13 May 2000 17:56:29 -0600

> customers are
> typically more motivated to make a decision that avoids potential losses
> than brings them potential gains, in other words "fear trumps greed". (I
> believe this is actually a fairly well researched topic in behavioral
> economics,

Von Neumann and a colleague showed many years ago that, given certain fairly
weak and (to many people) reasonable assumptions, any rational decision maker
acts as if he/she has a utility function and makes decisions by maximizing
expected utility.  This utility function assigns a numeric value to every
possible condition.  If the only condition you are considering is wealth in
dollars, then most people tend to have a concave (negative second derivative)
utility function.  This is the technical definition of being "risk averse."

As an example, suppose there is a person named Charlie who has the following
concave utility function:

  A B C   D

A = Lose $1000; B = Lose $500; C = No change; D = Gain $1000.
The vertical axis is utility, the horizontal axis is wealth.

Now imagine that Charlie must choose between two actions whose anticipated
outcomes may be summarized as follows:

1. A certainty of losing $500.  (B certain.)
2. A 50% chance of gaining $1000 and a 50% chance of losing $1000.  (Either A
   or D occurs, with equal probability.)

A quick glance at the graph verifies that the average of the utilities of A
and D is equal to the utility of B.  Thus Charlie has no preference between a
guarantee of losing $500 and a fair gamble of $1000.  Now, suppose we add a
third possibility:

3. A certainty of losing $Z, where Z < 500.

Charlie obviously prefers (3) to (1), and he is indifferent between (1) and
(2), so Charlie prefers a CERTAINTY of losing any amount of money less than
$500 to a 50/50 chance of gaining or losing $1000.  This is why we say that a
person with a concave utility function is risk averse -- he will actually pay
to avoid a fair gamble.