Friday, November 15, 2002

Straight Thinking 101, Part 4

Decisions in a World of Uncertainty, Risk and Debate

Over the past couple of days, I have been busy, so pardon the delay. But, note the newly uploaded web site.

In many decision-making situations, what the facts are is an open question, often hotly contested by highly articulate adsvocates and spin-doctors. Thus, we are forced to act in the face of uncertainties, risk and probabilities.

Operations Research offers a framework for making such decisions, based on Game Theory: playing a “game” with Nature as the opponent.

For instance, let us again consider the situation of Acts 27, from a decision-making perspective:

NATURE: The relevant environmental factor was the weather. We can identify at least three plausible states of Nature, given that it was late in the year, so the first winter-storms could have come at any time.

(1) Continued adverse winds until the first winter storm closed down sailing for the winter. (This would have locked the ship up in Fair Havens, regardless of intent.)
(2) A day or two of good sailing wind, as that would suffice to get the ship within striking-distance of the more commodious harbour, Phoenix.
(3) Initially favourable winds, but as a precursor to the first winter storm – what happened in the event.

DECISION-MAKER: This would have mainly been the Centurion, as influenced by the Experts (Ship Owner and Kubernete/steersman), the majority and Paul. Here, there were two options:

(A) Sail for Phoenix, if the winds became favourable. (The majority opinion.)
(B) Stay put in Fair Havens. (Paul’s alternative.)

We know that in the event, we had the match A-3, leading to disaster. However, this is after the fact. How can one decide wisely before the event?

Basically, we can set up a so-called “payoff table” showing what outcomes would be likely from A or B if Nature went to states 1, 2, or 3:

A: In state 1, there would be no opportunity to sail before the winter weather set in. If 2 ocurred, then the ship would have been in a better, and probably safer, harbour. Of course, as happened, we ended with A-3, a disaster.

B: Safe, but not comfortable, and the ship could possibly have been subject to damage.

The next step in deciding is to assess the likelihood or prudence of the outcomes, and to decide on the best alternative. Here, if one knows the probabilities attaching to states 1, 2 or 3 it would be helpful in quantifying the options. (One way to do this, is to ask the experts to indicate how often out of say six seasons the weather would play out as 1, 2 or 3.) But, the usual case is that such “subjective probabilities” are at best educated guesses, and the down-side vulnerabilities may exceed the upside benefits.

In that case, we should assess the range of opportunities and threats, and if possible, estimate what is more or less likely to happen. Then, we could weight the potential benefits and potential costs, to give an expectation, by summing up benefit/cost x probability. (For instance, if we bet $100 on a six on a die, for $1,000, we can expect, on average, to gain $1,000 if we get a 6, with a 1/6 chance, but stand to lose five chances out of six, so we expect to gain: 1/6 x $1000 + 5/6 x (-$100) = $ 83 per throw. One may lose most of the time, but on average, one would gain. That is how businessmen and investors make a living. Profit is often based on returns to the risk of enterprise.)

However, in some cases, like Russian roulette, even though the chance of a negative downside is 1/6: one bullet and five empty chambers when one pulls the trigger; the loss is so high that we would probably decide to minimize our exposure to a catastrophic outcome. (In yet other cases, the outcome is a mixed bag, so it may be wise to see how to minimize regret: the “if I had only known . . .” on either the upside or the downside.)

In the case in Acts 27, Paul’s initial advice was probably prudent, even if the gentle South Wind had lasted long enough, as the potential loss was so serious – as the Apostle pointed out.

Where does this leave us?

(I) We have defined a framework for decisions under risk/uncertainty. (NB: “risk” is used when we can assign probabilities to potential states of nature, and “uncertainty” is used when we don’t know enough to assess such odds.) Basically, the rule is: decide in light of options and the likely range of outcomes given environmental factors and trends.

(II) We see that good information is the basis for good decisions, and that probability, or at least a set of scenarios outlining options and outcomes is better than nothing.

(III) Finally, it is often wise to postpone final decision until there is sufficient information to make a clear decision, or at least till it is evident that the likely cost of further delay and investigation outweighs the likely benefit.
But, as the case of the ship in Acts 27 shows, often we do not think through the implications and likely outcomes of our decisions, and decide based on what the powerful want to hear, or who is popular, or what tickles our itching ears with what we want to hear. Or, we may be unduly influenced by personal interests or factional agendas.

Shipwreck has too often followed.

This brings us to the next point, for next time: “sustainability” in decision-making, and the prospects for sound development of our region.

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