# The point of utility measurement

Cost-utility analysis

Registry of published analyses (Harvard School of Public Health)

# The general idea

Compare two intervals:

A -------- B
C ---------------- D

1. Direct judgment.
Rate ratio or proportion (analog scale, attribute weights)
Rank order (dichotomous choice, "conjoint")

2. Find D' so that CD' matches AB.
CD is money, probability, time, or number of people

# Analog scale

Where does BB go on the following scale?
```
N -------------------- BBDD
100                    0
```
Doesn't force a difference of 10 to mean the same thing everywhere on the scale.

But could be seen as difference measurement, assigning numbers to differences between outcomes, e.g., A-B=?, B-C=?.

RATIO JUDGMENTS (RJ):
BBDD is times as bad as BB.

# PERSON TRADE-OFFS (PTO):

How many people would have to get outcome A for the total good (or bad) to be the same as if X many people got outcome B? e.g., "Curing how many people of headache is just as good as curing 100 people of cough?" Suppose the answer was 50 people. Then if U(cough)=-20 (relative to U(normal health=0)) we can infer that U(headache)=-40.

# STANDARD GAMBLES (SG):

Suppose you had to chose between:
Option 1: p (Down syndrome birth) = X
Option 2: Abortion for certain.

What would X have to be for you to be indifferent between the two options?

Suppose X would have to be .03. If we assume that you would be indifferent only when the expected utility of the two options is the same, then, on a scale where 0 = normal birth, and -100 = Down's syndrome birth, the expected utility of Option 1 is, (.03)(-100) = -3, so we can infer that the utility of Option 2 is also -3.

What would be the risk of BB so that you would have a hard time deciding whether to accept this risk or a 10/1000 risk of BBDD? /1000

# TIME TRADEOFF (TTO):

"How many days of headaches is just as bad as 10 days of cough?"

Suppose the answer was 5 days. Then if U(cough)=-20 (relative to U(normal health=0)) we can infer that U(headache)=-40.

# Why PTO doesn't measure of "social utility"

Some have argued that "social utility," measured by PTO, is different from "individual utility" measured by other methods, such as risk-risk tradeoff (RR). Here is an example of the trouble this can cause:
• In a population of 1000 who are at risk of some disease, we must choose between saving 10 lives or curing 100 people with the disease.
• PTO says that saving 10 lives is just as good as curing the disease in 90 people.
Therefore, we would do better by curing 100 people than by saving 10 lives.
• But, with RR, each person says that a 10/1000 risk of death is just as bad as a 110/1000 risk of the disease.
Therefore, we would do better by removing the risk of death, since a 100/1000 risk of the disease is not as bad as a 10/1000 risk of death.
• In sum, if we use the PTO to override individual judgment, we can wind up doing something that is worse for each person.
What good is "social utility" if it make things worse for each person?

# Biases

Diminishing sensitivity in direct rating (Varey & Kahneman)

Superadditivity: (x-y) + (y-z) > (x-z)
Explained by diminishing sensitivity

Ratio inconsistency: A/C less extreme than (A/B)(B/C)
Explained by Parducci's range-frequency theory

Certainty effect (avoided by RR)

Ratio bias: 10/1000 seems worse than 1/100.
Epstein (but also Piaget and Inhelder)
not avoided by RR :(

PVs for life in time tradeoff

# Consistency checks (Keeney & Raiffa)

"... if the consistency checks produce discrepancies with the previous preferences indicated by the decision maker, these discrepancies must be called to his attention and parts of the assessment procedure should be repeated to acquire consistent preferences. ...

Of course, if the respondent has strong, crisp, unalterable views on all questions and if these are inconsistent, then we would be in a mess, wouldn't we?

In practice, however, the respondent usually feels fuzzier about some of his answers than others..."

# Ratio consistency check (PTO and AS):

From your answers, we can conclude that being Both-blind is A% as bad as being Both-blind-Both-deaf, and being One-blind is C% as bad as being Both-blind. So the badness of being One-blind compared to Both-blind-Both-deaf should be C% of A% or CA%. But you said E%.

This would create a problem for the insurer. To determine the badness of being One-blind relative to Both-blind-Both-deaf, they would not know which answer to use. ...

Try to make your numerical answers consistent. Can you do this and still have them reflect your true opinions about the conditions? (If not, why not?)

# Another consistency check: Additivity

For another check, suppse we ask people for two comparisons. AB and BC are both compared to AC. The utilities of AB and BC should thus add to 1.
```1. A-----------B
A-------------------C

2.             B-------C
A-------------------C
```

For example, suppose question 1 is "How large is the difference (in percent) between no problems and being blind in one eye, compared to the difference between no problems and being blind?" Suppose question 2 is "How large is the difference between being blind in one eye and being blind, compared to the difference between no problems and being blind?" Then the sum of these answers should be 100%.

# Conjoint analysis

Simple way of doing it:
• Assume utility is a sum of utility on attributes.
• Ask for judgments of every combination of top and bottom.
• Measure the utility of each attribute by subtraction.
• Gives utility of each attribute relative to others.

Example (from Psych 353):
Study on attractiveness and relationships (Christine Kam)