Decision Theory
Page 7
Modal (Most Likely Outcome) Criterion
The modal criterion presumes that the state of nature deemed most likely to occur will in effect occur, thus excluding all other potential states from further consideration in the decision process. In other words, the decision is made under the assumption that only one particular state of nature will take place. The selection of which state will presumably occur is usually made on a purely subjective basis, often impulsively, possibly due to a lack of reliable information. The term "modal" refers to the mode of the underlying probability distribution, which in practice is seldom estimated. The modal criterion describes an all too common informal approach to decision making that is decidedly nonrational.
Let's assume that ACME's managers, perhaps because of habit, were inclined to use the modal decision criterion. They would then act in the following manner:
Modal decision rule
1. Select the state Sj most likely to occur. This can be done judgmentally.
2. Obtain a new payoff matrix by discarding the remaining columns of S.
3. Determine the best payoff (max for positive flows, min for negative flows) in the sole surviving column.
The action alternative Ai corresponding to this payoff is the modal-criterion decision.
Using ACME's original decision matrix and assuming state M as the most likely outcome:
Critique of Modal Criterion
We've been criticizing all decision rules that leave out available problem information as irrational, and here comes the modal criterion and does precisely that. In real life, however, things are usually a bit more complicated and irrational impulses may not be apparent. The payoffs in the decision matrix are not, in general, given a priori: they represent data that must be collected. This means time and effort (hence, additional costs) must be expended in collecting the data. Some decision makers may see no point in collecting payoff data for states of nature deemed unlikely to occur from the modal perspective. So the decision matrix they infer may actually be just the column vector for the modal state. The danger of this approach should be clear: decisions are being made from a position of ignorance.
Decide for yourself
The modal decision for the matrix below is A1. Would you forgo an 80% chance of getting $100 just because the mode points to a $1 gain?
