Many decision situations, even under certainty, involve tradeoffs between multiple attributes of different options. For example, a choice of a contraceptive method might involve such attributes as effectiveness, cost, convenience, side effects, and acceptability to one's religious beliefs.

Multi-attribute utility theory (MAUT) is a theory that underlies a set of methods for making these choices. All of the methods include:

1. Define the alternatives and relevant attributes
2. Evaluate each alternative on each attribute. Remove dominated alternatives.
3. Assign relative weights to the attributes
4. Combine the attribute weights and evaluations to yield an overall evaluation of each alternative
5. Perform sensitivity analysis and make a decision

Let's look at each in turn, considering a particular method called SMARTER (Simple Multi-Attribute Rating Technique with Rank weights, by Barron and Barrett):

I'm not going to say much about this, although there is a good-sized literature on methods for coming up with attributes, often involving a hierarchical breakdown of values that are relevant to the decision. Here, we'll assume that we know the alternatives and attributes we care about.

There are a number of ways to do this, analogous with the utility assessment methods we discussed last session. SMARTER uses a direct rating of the attribute on a scale from 0-100 for each alternative.

At this point, if there is any alternative that are worse than another alternative on all attributes, it should be discarded from the set of options. These alternatives are called "dominated" alternatives, and you'd never want to choose one.

Again, there are many ways to do this. Most start by trying to determine the rank order of the attributes. But there's a problem with just asking people to rank the attributes. Imagine that 'effectiveness' is the most important attribute, but that all of the alternatives are highly effective and don't differ much from each other. Effectiveness in itself may be important, but as a criterion for making this choice, it's not important. In short, direct rankings are not sensitive to the range of the attributes.

The preferred alternative (and the one used in SMARTER) is swing weighting. In a swing weighting procedure, you rank the attributes by asking the question "If I were faced with an alternative that had the worst values of all of the attributes, and I could swing one attribute from worst to best, which would I swing?" This is the most important attribute, and you do this repeatedly to determine the second-most important, third-most important, etc.

How do you go from ranks to weights? Early techniques tended to use direct ratings of attribute importance, standardizing them so that the sum of the attribute weights was 1. More recent techniques take advantage of the fact that most of the weighting information that you really care about is in the ranks already, and simply derive weights from ranks using either "rank sum weights" (Weight = (Reversed Rank)/(Sum of Ranks), where a reversed rank means that the first-ranked attribute in a set of X attributes is given reversed rank of X, the second-ranked of X-1, etc.) or

"rank order centroid" weights (Weight = (Sum of Reciprocal Ranks) / (# of ranks)). SMARTER uses rank order centroid ("ROC" weights, not to be confused with "receiver operating curves" from diagnostic tests!) weights; Alan will explain why they're probably better than rank sum weights.

This part is easy. The overall evaluation of an alternative is the sum of each of its attribute evaluations, multiplied by that attribute's weight. The alternative with the highest evaluation is the one that you should choose.

An important question about the results of an MAUT procedure is: How sensitive is this recommendation to the numbers I put in? If I changed the ranks of some attributes, would I still get the same recommendation? If I changed my evaluation of some attributes for some alternatives, would I get the same recommendation?

Sensitivity analysis of MAUT proceeds by doing exactly those kinds of things: considering places in the analysis where values might not be exact, and varying them to see what happens to the final recommendation. If the final recommendation is insensitive to these changes, it's said to be "robust".

A popular use of MAUT is in health-related quality-of-life instruments (HRQL). Hodder, Edwards, Brickley, & Shepherd (1997) perform an MAUT to assess outcomes of cancer treatments.

We won't have time in this course to really cover this, but one attribute of particular interest has been time. How should we evaluate an option that has benefits (or risks) that aren't realized until years later? How should we evaluate outcomes that consist of a series of different health states over time?

The normative economic viewpoint is that any good received later is less valuable than the same good received sooner; this is referred to as discounting. For example, you should prefer $100 today to $100 in a year. In fact, if you're not going to receive your money for a year, you should probably ask for around $103 in a year to equal $100 today. After all, you could invest $100 today and have $103 by the end of the year. Discounting is rational because the future is uncertain -- you may not be in a position in a year to use the $100.

The same might be said of health states. If you knew you were due to have a month of poor health, would you prefer to have it now or a year from now?

Of course, there is a normative/descriptive gap here, just as we're seen in other aspects of decision making. Assume that there's no interest-bearing savings allowed. Given a choice between $100 now and $105 a month from now, most people would take the $100 now. But given a choice between $100 12 months from now and $105 13 months from now, most people prefer the $105. This is bad news for the idea of a constant discount rate.

Worse, consider how you'd prefer to arrange 3 consecutive Friday nights: dinner at your favorite restaurant, dinner at a restaurant you don't like very much, and dinner at home. What does discounting predict? Does it match with your decision?

Gretchen Chapman (my predecessor here) and her colleagues have done excellent work comparing the way people discount money and health. I've included one of her articles (with Arthur) as well as an article about the public policy ramifications of discounting time on whether the elderly should be given treatment priority over those younger. These are in the optional readings, so read them if you're interested in this area.