What are the odds?

Reckoning policy

Imagine a worthy cause in international affairs — a beleaguered country invaded by an aggressive neighbor, say. Rate this country’s cause on a scale of worthiness, with 0 percent being utterly unworthy and 100 percent obliging even the hard-hearted to provide a helping hand.

Now consider the form assistance might take, perhaps deployment of troops. Rate the chances of this policy succeeding, with 0 percent signifying no chance and 100 percent a slam dunk.

Multiply the two numbers. What do you get?

Nonsense, maybe. Moral worth cannot be reduced to a number. And predictions are just fancy guesses.

But you might get a way of rationally ranking policy options. Resources are limited. Choices have to be made. How to compare?

Aiding a worthy cause could have a high payoff. But if the chances of achieving that payoff are low, then a decision to commit the aid might be a bad one.

Conversely, assisting a dubious cause might have a low payoff. But if the likelihood of success is high, the policy might be worth pursuing.

Should the United States defend Taiwan against Chinese attack?

Here's how to decide.

First, estimate the value to the United States of a free Taiwan. This would be mostly in the realm of trade. Let's call it $30 billion per year.

Second, estimate the value to the United States of a Taiwan absorbed by China. Taiwan's trade would still be worth something, say $5 billion per year.

Third, estimate the chances of Taiwan remaining independent if the United States came to its aid. This might be a toss-up, so let's say 50 percent.

Fourth, estimate the chances of Taiwan remaining independent if the United States did not come to its aid. Let's put this at 10 percent.

Fifth and finally, estimate the cost of an American military operation to defend Taiwan. Call this $100 billion. Spread it over 10 years, a reasonable time horizon for such an undertaking, and you get $10 billion per year.

Now work out the expected value of the two policy choices.

If the United States defended Taiwan, it would have a 50 percent chance of succeeding and thereby receiving $30 billion dollars per year. It would have a 50 percent chance of failing and thereby receiving $5 billion per year. The cost for either outcome would be $10 billion per year.

The arithmetic:

($30b x .50) + ($5b x .50) - $10b = $7.5b per year.

If the US chose not to defend Taiwan, there would be no outlay for defense, and the expected return per year would simply be the sum of the expected outcomes of Taiwan defending itself.

($30b x .10) + ($5b x .90) = $7.5b per year.

Put no faith in these particular numbers. They were pulled out of the air. The fact that they turned out the same is quite accidental.

Needless to say, they tell only part of the story. They don't include opportunity costs. Would defending Taiwan weaken America elsewhere? They don't include collateral benefits. Would defending Taiwan strengthen America elsewhere?

More profoundly, they don't include non-economic values. Do Americans consider Taiwan's freedom worth defending in its own right?

These are perfectly legitimate objections to the exercise above. Perhaps this exercise really is nonsense.

But it's hard to argue that thinking carefully about costs, benefits and risks is a bad idea. We do it in many other fields. We do it every time we listen to a weather forecast and decide whether to carry an umbrella. Investors do it when choosing this stock or that. Venture capitalists do it with a vengeance, reckoning that they need but one investment out of twenty to pay off, since that payoff will be very large. Analysis of cost, benefit and risk is the lifeblood of the insurance industry.

Dwight Eisenhower, who spent a long time planning for D-Day, offered various reflections on the value of plans. The most succinct was, “Plans are useless, but planning is essential."

Ike knew what he was talking about.