Sunday, September 7, 2014

Disproportionate Consequences

As I was climbing a long, narrow mountain ridge the other day, I got to thinking about what it is that makes me so nervous about height exposure. It occurred to me that the issue is that a minor error could lead to a major disaster. The phrase that came to mind was "disproportionate consequences."

Walking down a suburban sidewalk, if I were to trip or slip, or if the wind caused me to lose my balance, the worst that could happen is that I would fall and scrape my knee, or perhaps in freak circumstances bump my head. On a ridge, depending on how narrow it is and how steep the sides are, a similar error could easily be fatal. Relative to the typical consequences of an everyday error, the potential outcome is disproportionate.

A similar concern may drive some people's fear of flying. In our everyday experience, mechanical problems with vehicles are common but the consequences are usually very limited. The consequences of a mechanical problem with a jet in flight can be dire, hence the discomfort.

This notion is not limited to negative outcomes. It is also applicable to lotteries, early stage investing, meeting new people (particularly for introverts), and flyfishing. In economic terminology, we can characterize this situation as one where the value or cost of a discrete outcome possibility is substantially greater than the expected value or cost, where expected value is the product of the cost or value of an outcome times its probability of occurring. There is much to explore here, including the fact that humans generally seem to have different behavioral inclinations and emotional experiences in relation to such risk disparities; or that there seems to be no fully objective or purely rational means of determining the right course of action in the face of choices of this kind - which, given that sometimes the outcomes affect other people, makes me suspicious of any claims to universal ethical standards; or how this plays into the assessment and uncertainty surrounding the outcome value or cost and the probabilities of those outcomes.

What I'd like to consider, though, is a relatively simple deviation from the usual claim that we should maximize expected value or minimize expected cost (and excluding those relatively rare - usually emergency - situations where the primary outcomes both good and bad are both far from the expected value). In cases of disproportionately negative consequences, we might bias toward increasing expected cost in order to substantially reduce the probability of maximum cost; and for positive consequences, we might be willing to tolerate a lower (but not negative) expected value to increase the probability of a high value. I'll provide one example of each.

On that high mountain ridge, I can choose between walking erect along the top, or staying on the less exposed side and having to scramble a bit over rocks and deal with an uncomfortable but not dangerous sidehill. The latter requires considerably more effort, such that the expected cost is considerably higher than the former, but on the truly exposed sections of the ridge, it may be (depending, I suppose, on one's skills and emotional inclinations) the better choice. A fall would bring my expected value maximization strategy to an abrupt end.

In the field of entrepreneurship, I have often encountered founders who have a choice between a very solid but size-limited business opportunity and a highly risky but potentially industry-changing approach. If the company has venture capital investors, the investors will almost always show a preference for the risky strategy even though the expected value is probably lower. This might be counterintuitive (investors have numerous investments and would seem to be prime candidates for expected value maximization), but it is the better approach because the upside is unknowably large and they are seeking outsized overall returns.

The actual analysis in individual cases is complex. The point is that an expected value approach is increasingly suspect as the maximum cost or value deviates from the expected cost or value.

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