Multi-Perspective Utility Analysis

EXERCISE 45 Planning Conference

The original exercise refers to matrices and numerical inputs that are not reproduced here. You can follow the procedure using your own stated assumptions, but the source’s worked rankings cannot be recalculated from this excerpt alone.

The administrative staff of a nationwide hotel chain is selecting a site for the annual winter planning conference of its top managers. The choice of site depends on the recreational activities in which attendees can engage. Three sites are being considered: New York City (theaters and restaurants), Palm Beach, Florida (swimming and sunbathing), and Stowe, Vermont (skiing). The administrative staff has just been informed that the top managers attending the conference will be accompanied by their spouses and children. As a result, the staff, in selecting the site, must now take into account the recreational preferences—recreational utilities—of three different groups of people: attendees, spouses, and children. In other words, the staff must view the problem of site selection from three different perspectives.

Utility analysis handles multiple perspectives quite easily by analyzing each perspective separately (constructing a utility matrix for each) and then merging the results to rank the options. Because the options being weighed are the same for each, the matrices are identical in structure. Ensuring this uniformity of structure is critical to the process. Each matrix contains the same options and outcomes. For a given option, the probabilities describe the same weather events across stakeholder perspectives; probabilities may differ between sites. Only the utility values will vary because each matrix, as I said, views the problem from a distinctly different perspective (identified in the upper left-hand corner) with different self-interests in mind.

In the case of our “Planning Conference” problem, each matrix contains the same three options (New York City, Florida, Vermont). Because weather more than any other factor usually determines whether attendees at a conference are pleased with recreational activities, we will use weather as a class of outcomes and consider two outcomes: “warm-and-sunny” versus “cold-and-rainy.” Construct three utility-analysis matrices, one for each perspective. Do not include a “Rank” column in the matrix. (I’ll explain why momentarily.)

BEFORE CONTINUING, CONSTRUCT ONE MATRIX FOR EACH PERSPECTIVE.

Figure 16-1 in the source shows the matrix structure; it is not included here.

The utility analysis process for multiple perspectives is exactly the same as that followed in the preceding chapters: ask the Utility Question for each option-outcome combination, assign utility values, ask the Probability Question, enter the probability values, compute the expected values, add the expected values for each option, and enter the sums in the “Total EV” column.

The source supplies utility values for the matrices (Figure 16-2), but those values are not included here. The values were obtained by asking the Utility Question for each option-outcome, for example, “If the conference is held in New York City and the weather is warm and sunny, what is the utility from the perspective of the attendees’ enjoyment?” Choose and document utilities for your version of the exercise, then enter them in the matrices.

FIGURE 16-1

FIGURE 16-2

BEFORE CONTINUING, ENTER THE UTILITY VALUES IN THE MATRICES.

The source also supplies a weather forecast—the probabilities for the outcomes (Figure 16-3)—which is not reproduced here. Enter the probabilities in the matrices and calculate the expected values, add them for each option, and enter the sums in the “Total EV” columns.

BEFORE CONTINUING, ENTER THE PROBABILITIES AND COMPUTE TOTAL EXPECTED VALUES.

Figure 16-4 in the source shows the computations in each matrix.

The next step is to combine the option rankings in the three matrices. We do this by merging the expected values from each of the three matrices in a fourth, appropriately named, merged matrix (Figure 16-5). Construct a duplicate of this merged matrix and enter in each cell the total expected value from the perspective matrices.

BEFORE CONTINUING, CONSTRUCT A MERGED MATRIX AND ENTER TOTAL EXPECTED VALUES FROM THE PERSPECTIVE MATRICES.

Figure 16-6 in the source shows the merged matrix with total expected values.

We could, of course, just add the total expected values for each option and accept the one with the greatest expected value as the preferred choice. However, this method of merging preferences would be appropriate only if the administrative staff takes the Laplace approach (meaning it doesn’t have any basis to distinguish differences in the importance of the three perspectives) and values them equally.

FIGURE 16-3

FIGURE 16-4

FIGURE 16-5

But what if the staff considers the enjoyment of the managers to be many times more important than that of the spouses and children? In that event, we might weight the perspectives as follows: attendees .8, spouses .1, and children .1. Enter these weights at the top of the perspective columns in the merged matrix and add two columns (“Total Weighted EV” and “Rank”) to your merged matrix. Now multiply the total expected values of each perspective by its weight, add the resulting products, enter the sums in a “Total Weighted EV” column, and indicate the final rankings of the options in the “Rank” column.

FIGURE 16-6

BEFORE CONTINUING, ADD “TOTAL WEIGHTED EV” AND “RANK” COLUMNS TO THE MERGED MATRIX, COMPUTE TOTAL WEIGHTED EXPECTED VALUES, AND DETERMINE RANKINGS.

Figure 16-7 in the source shows the resulting merged matrix. With those weights and the source’s utility and probability inputs, New York City ranks first.

Different weightings can produce different results. Figure 16-8 shows three sample distributions of weight among the three groups. Figure 16-9 shows how the rankings of the options change when the spouses’ perspective is dominant and when the children’s is dominant.

This technique for utility analysis of multiple perspectives has wide application in problem-solving situations where conflicting interests render a choice among alternative courses of action difficult. The analysis makes the treatment of each party’s interests explicit, especially when those parties participate. It does not ensure an equitable result by itself. Before merging utilities, agree on comparable scales and examine how the chosen weights distribute influence. Test whether plausible changes to those choices alter the ranking.

FIGURE 16-7

FIGURE 16-8

FIGURE 16-9

FIGURE 16-10