Governance decision makers’ attitudes toward risk may vary widely. People who have strong preferences for risk assumption may turn out to be chronic gamblers. Such people get their “kicks” from accepting adverse-odds bets (long shots) with negative expected values. Even though the odds are against them, it is more intellectually satisfying to them to win “big” on rare occasions than to gain small sums more frequently on favorable-odds bets. Risk preferrers are likely to lose (on net balance) over the long run. Luckily for society (and themselves), they are in the minority. It is theoretically possible for a decision maker to be essentially risk-neutral, having neither preference for nor aversion toward risk. However, this is such a “razor’s edge” state that few people find themselves there.
The vast majority of all people who regard themselves as rational thinkers are risk-averse, and the more extreme of them are risk avoiders (they expect bad things to happen to them each morning as soon as they get out of bed). A normally risk-averse decision maker likely would not accept an even-odds bet on a two-possibility event (50 percent chance each way) because the loss of the sum at risk would mean more to them (negatively) than would the gain of an identical sum would mean to them (positively). It is likely that most business decision makers, who tend to be a conservative lot, are risk averse. This does not mean that they seek to avoid risk altogether (if so they would not behave as entrepreneurs); rather, they attempt to manage risk by seeking more information in order to diminish it, by attempting to take offsetting positions, or by attempting to insure against the risk.
If it were practical to specify personal utility functions for decision makers, it would be possible to include the decision maker’s attitude toward risk as an argument (i.e., one of the independent variables) in the function. We might find the risk preferrer to “consume” risky items under conditions of increasing marginal utility, the risk-indifferent decision maker to exhibit a linear risk utility function, and one who is averse to risk to experience diminishing marginal utility with respect to risk.
The conditions under which a decision maker realizes satisfaction (i.e., utility) with respect to income (whether monetary or “in kind”) are thought to influence his attitude toward risk. For decision maker A, utility increases at a constant rate as income increases. Decision maker B’s utility increases at a decreasing rate (the utility function, though positively sloped, is concave downward). This illustrates the so-called principle of diminishing marginal utility, and is thought to be descriptive of typical human behavior with respect to the receipt of income. Decision maker C realizes additional utility at an increasing rate as income increases (i.e., the curve is concave upward). Although this utility pattern is thought to be atypical of human behavior except in the very early stages of consumption, it would illustrate a phenomenon of increasing marginal utility. In all three cases, the utility function is extended into graphic quadrant III (negative values for both income and utility) for purpose of illustration. Although utility is hardly measurable, and certainly not comparable from one decision maker to another, I shall indulge in the heroic assumption of the same numeric scale on the vertical axis of all three graphs.
Suppose that these three decision makers are all presented with an investment opportunity that requires a capital outlay of $1 million, and which can be expected to result in only two possible outcomes, success yielding a $5 million return, or failure yielding a zero return. Although the three decision makers might estimate widely divergent probabilities of success and failure, for purposes of argument let us for the moment suppose that all three accept a conventional wisdom that 80 percent of such ventures are doomed to failure, but 20 percent succeed. The expected value of such an investment opportunity may be computed as follows:
EV = ($5 mil – $1 mil) x .2 + ($0 mil – $1 mil) x .8
EV = $4 million x .2 – $1 million x .8
EV = $800 thousand – $800 thousand = $0.
The expected value of the decision alternative not to invest (which will require no capital outlay and yield no return) is also $0. On the basis of expected value of the returns, it would appear that all three decision makers should be indifferent between the decision to invest and not to invest (indeed, since the expected value of the opportunity is $0, why bother?).
However, an examination of their expected utilities (a probability weighted average of the utilities which they would realize) reveals a different story. The expected utility for decision maker A may be computed as
EUA = 400 x .2 – 100 x .8 = 0 units of utility, which is the same utility realized from not investing. In this case, the conclusion is identical to that reached by examining the expected value of the opportunity.
Decision maker B realizes additional utility under conditions of diminishing marginal utility. The expected utility may be computed as
EUB = 270 x .2 – 150 x .8 = -66 units of utility.
Decision maker B would suffer an absolute loss of utility if the investment were undertaken, and would therefore prefer to realize a utility of zero from not investing.
The expected utility for decision maker C, who realizes additional income under conditions of increasing marginal utility, may be computed as
EUC = 650 x .2 – 70 x .8 = 74 units of utility.
Decision maker C would enjoy a net of 74 units of utility from undertaking the investment compared with zero units from not investing, and therefore can be expected to proceed with this “long shot.”
Although there is no direct linkage here between marginal utility and risk, there is a rather strong presumption that decision maker B’s diminishing marginal utility implies that he is risk averse, while decision maker C’s increasing marginal utility leads to a preference for risk. Decision maker A’s constant marginal utility function results in indifference with respect to risk.
Several important governance implications follow from this analysis. One is that the expected value of a decision alternative is a good selection criterion only in the case of a decision maker who realizes increased satisfaction at an approximately constant rate. Alternately, if the marginal utility for a decision maker is approximately constant in the neighborhood of the EVs of the available decision alternatives, the EVs may serve as adequate selection criteria. For other decision makers who realize increased satisfaction at decreasing or increasing rates, it is necessary to consider the expected utilities of the decision alternatives.
Even slightly different assessed probabilities may change the decision picture significantly. Suppose that the probability of success decreases to 15 percent, while the probability of failure rises to 85 percent. The recomputed expected value and expected utilities are as follows:
EV = $4 mil x .15 – $1 mil x .85 = -$.250 mil
EUA = 400 x .15 – 100 x .85 = -25 units of utility
EUB = 270 x .15 – 150 x .85 = -87 units of utility
EUC = 650 x .15 – 70 x .85 = 38 units of utility
In this case, the expected value is negative and decision makers A and B would rationally choose not to invest. But decision maker C would realize positive utility from the investment, even though the expected value of the venture is negative! Such a decision maker who experiences increasing marginal utility of income strongly enough to induce him to accept an adverse-odds venture with a negative expected value is surely a gambler.
If the probability of success rises to 25 percent while the probability of failure of the venture falls to 75 percent, the computed expected values become:
EV = $4 mil x .25 – $1 mil x .75 = $.250 mil
EUA = 400 x .25 – 100 x .75 = 25 units of utility
EUB = 270 x .25 – 150 x .75 = -65 units of utility
EUC = 650 x .25 – 70 x .75 = 110 units of utility
Under these probability circumstances, the expected value of the venture is positive, but decision maker B is still so risk averse due to diminishing marginal utility as to be unwilling to undertake it. This is because the prospect of losing $1 million in case of failure means so much more than the prospect of gaining $4 million in case of success of the venture. Decision maker B would hate losing $1 million more than the enjoyment of gaining $4 million. The reader should confirm that in order for risk-averse decision maker B to realize a positive expected utility from the venture, the probability of success would have to rise to 36 percent.
In the real world, three decision makers would likely experience not only different utility conditions, but may also come up with different assessments of the probabilities of success and failure of the decision alternatives before them. This means that two or more decision makers examining exactly the same decision opportunities may reach widely divergent conclusions about them. For example, suppose risk averse decision maker B assesses the probability of success of the venture at 36 percent, which would yield a positive expected utility, while risk preferring decision maker C assesses the probability of success at only 9 percent, which would yield a negative expected utility. Under these circumstances We might witness the irony of the risk adverse decision maker undertaking the venture while the risk preferrer rejects it.
This series is a lot of parts that I am quasi-using pieces of for a academic research paper stance so bear with me if it gets too esoteric. Or read the other governance articles available within the SharePoint Security category within the main site (available through the parent menu).