We all must MAKE DECISIONS -- every day. Some more than others. In Business, in profit or nonprofit management, in The Military, as parents, etsettery.

Since undecidably when, humans have sought for some GUIDANCE in MAKING DECISIONS. The most frequent mode, likely, is prayer. Since the 18th century, mathematicians have given some thought to this problem.

One such guide was by, not PROBABILIY, but "expectation". I'll explain. Suppose in a fair lottery, 1000 tickets are sold. Fairness suggests that each ticket has 1/1000th probability of being the winning ticket. Suppose the Prize is $500. Then the expectation equals probability times value, or (1/1000 x $500) = $500/1000 = 50¢. (To make any money, the ticket price must be greater than the expectation -- here 50¢. The great philosopher, Voltaire, discovered a town lottery giving much more prize money than total cost of tickets. Borrowing from friends, Voltaire bought all the tickets and claimed the Prize. Investing it shrewdly, he was "fixed for life", and could devote his time to philosophy and writing.)

Confusing probabiliity with expectation played a role in "The Vietnam Conflict". Former GM "Whiz Kid", X Y, turned Secretary of Defense, assured us of a South Vietnam victory because "there are nine times as many ROKs [S. Vietnam Regular] as xxxx" (implying a probability edge). But some wag asked, "What if those nine ROKs won't fight, and that one XXX fights like hell?"

Not probability, but expectation as a decision-guide can be useful in cases similar to the following.

The probability of a fire in your neighborhood may be very small. But, if it occurred, the COST to you could be VERY GREAT. Not only property, but your "dear ones". So the negative expectation of not ensuring against fire is so much greater than the COST OF A PREMIUM that ENSURING is best.

However, the great Swiss mathematician, Daniel Bernoulli (x-y), discovered a "paradox" about expectation. Consider a game in which one is offered two choices:

1. Toss a "fair coin" (head on one side, tail on another), to receive $1 for each HEAD result, but game ends with a TAIL result.
2. The other choice is an outright sum of money, say, $50,000.

What's the paradox? Well, RANDOMNESS DOES NOT RULE OUT AN "ENDLESS" RUN OF HEADS. So, THE EXPECTATION OF THE GAME IS INFINITE. However, vastly more people asked would take the second choice. Deciding against the greater expectation.

This set off mathematicians and economists, since that time, toward consideration of other GUIDES. At least 6 economists have won Nobel Prizes in Economics for writing on this problem. For example, Herbert Simon (Nobelist, 1978), suggested "satisficing" your decisions. Thus, a young woman may not continue to look for the "Prince Charming of her dreams", but marry the "best" of her current suitors. (She satisfice on "what's out there".) Similarly, an potential investor with a "nest egg" may not continue to look for the "chance of a lifetime", but satisfice on the "best" of the current offerings.

Of all the DECISION-GUIDES so far, only EXPECTATION uses an arithmetical measure (PROBABILITY) to RANGE OVER THE POSSIBILITIES.

You will now learn another such one -- ASSERBILITY -- which RELATES TO LOGICAL ASSERTIONS THE WAY PROBABILITY relatES TO EVENTS. And, like PROBABILITY, ASSERBILITY is A MEASURE FOR DECISIONMAKING UNDER CONDITIONS OF UNCERTANTY! That is, two persons, given the same data and proceeding correctly, will ARRIVE AT THE SAME CONCLUSION! (We can prove this by AUTOMATING THE PROCEDURE, as a COMPUTER PROGRAM or a CALCULATOR PROCEDURE.)

Given this, you may sometimes be less BEDEVILED BY DECISIONS.