# Aspects of utility theory

Expected-utility: uncertain states

Multi-attribute: attributes, criteria, goals

Utilitarianism: people

Intertemporal choice: times

# Examples of choice over time

health behaviors (eating, exercise, smoking, etc.)

other preventive medicine (moles, exams)

(under)saving - individuals and governments

lack of planning (asteriods, global warming)

# One view

Discounting and health

# Normative theory: exponential discounting

u(t) = U0e-βt, or, if U0=1, r(t) = e-βt

Note: this is about decision utility.

# Reasons for discounting

Risk

Interest - everybody else does it

Pure time preference

Increasing standard of living

Changes in values (identity)

# Why discount lives

A. Save a life now, at T0, for \$100.

B. Invest the money. Wait until it doubles at time T1. Save 2 lives for \$200. (Assume no change in cost of lifesaving.)

C. At T1, invest the money, wait until T2, then save 4 lives.

Oops.

If we discount the lives at the rate of interest, this won't happen.
Thus, (1 life at T0) == (2 lives at T1) == (4 lives at T2).

u(t) = a/d(t+c)

# Summary of findings (descriptive)

• animals, people, short term, long term
• dynamic inconsistency
 A. one candy now vs. 3 in 24 hours. B. one candy in 24 hours vs. 3 in 48 hours. Same choice made at different times.
• both hypothetical (and long-term) and real choices
• excessive discounting (e.g., air conditioners)
• more discounting of smaller rewards
• less discounting for losses (dread?)
• health-money difference
• inflation interacts with delay, not p (Ostazewski, Green & Myerson)
• individual differences
• age
• "ego strength"

# Self control: Thaler's examples

1. Mr. and Mrs. J. have saved \$15,000 toward their dream vacation home. They hope to buy the home in five years. The money earns 10% in a money-market account. They just bought a new car for \$11,000, which they financed with a three-year car loan at 15%.

2. Mr. S. admires a \$125 cashmere sweater at the department store. He declines to buy it, feeling that it is too extravagant. Later that month he receives the same sweater from his wife for a birthday present. He is very happy. Mr. and Mrs. S. have only joint bank accounts.

# Ainslie's prescriptive theory

Extrapsychic devices.

Control of attention.

Control of emotion.

# Emotions

 future assimilation + certain savoring future assimilation + uncert. hope future assimilation - certain dread future assimilation - uncert. fear future contrast + certain impatience future contrast + uncert. fear? future contrast - certain ? future contrast - uncert. ? past assimilation + certain savoring past assimilation - certain horror? past contrast + certain missing past contrast - certain relief

+ and - refer to the event, not the emotion

# Heuristics (Loewenstein and Prelec)

2. preferring improvement over decline

A. dinner at a fancy French restaurant on Friday in 1 month vs.
B. dinner at the French restaurant on Friday in 2 months

A. dinner at the French restaurant on Friday in 1 month and dinner at a local Greek restaurant on Friday in 2 months, vs.
B. dinner at the French restaurant on Friday in 2 months and dinner at a local Greek restaurant on Friday in 1 month

A. dinner at the French restaurant on Friday in 1 month and dinner at home on Friday in 2 months
B. dinner at the French restaurant on Friday in 2 months dinner at home on Friday in 1 months

# Framing (Loewenstein and Prelec)

Subjects were asked when they would use two \$100 coupons to their favorite restaurants.

• No time constraint.
• 2 years
• 4 months

The 2-year group preferred longer delays than either of the other groups. They wanted to spread out the dinners over the whole interval. Of course, the first group had an even longer interval, but it was not brought to their attention.

# Framing (Loewenstein and Prelec)

Subjects were asked when they would use two \$100 coupons to their favorite restaurants.

• No time constraint.
• 2 years
• 4 months

The 2-year group preferred longer delays than either of the other groups. They wanted to spread out the dinners over the whole interval. Of course, the first group had an even longer interval, but it was not brought to their attention.

# Framing (Loewenstein and Prelec)

Subjects were asked when they would use two \$100 coupons to their favorite restaurants.

• No time constraint.
• 2 years
• 4 months

The 2-year group preferred longer delays than either of the other groups. They wanted to spread out the dinners over the whole interval. Of course, the first group had an even longer interval, but it was not brought to their attention.

# Framing (Loewenstein and Prelec)

Subjects were asked when they would use two \$100 coupons to their favorite restaurants.

• No time constraint.
• 2 years
• 4 months

The 2-year group preferred longer delays than either of the other groups. They wanted to spread out the dinners over the whole interval. Of course, the first group had an even longer interval, but it was not brought to their attention.