Decision Making choice… maximizing utility framing effects

Value Round 1: Raise your hand if your birthday occurs in the first half of the year (jan-june 30th) Congratulations, you just won! You are entitled to one of our prizes: Prize A: $15 Prize B: $ 10 Which one do you choose? Duh! Prize A value > Price B value

Expected value Round 2: choose prize first Winners will be decided based on the last digit of their SSN: Prize C: $15 if your SSN digit matches the number that comes out for example, if ‘7’ comes out and your SSN ends in ‘7’ Prize D: $ 10 if your SSN digit is in the selected category (larger/smaller than 5) For example, if ‘7’ comes out, and your SSN ends in ‘5’, ‘6’, 7, 8 or 9 Which one do you choose to play? The "betting preferences" of people with regard to uncertain outcomes (gambles) can be described by a mathematical relation which takes into account the size of a payout (whether in money or other goods), the probability of occurrence, the different utility of the same payout to people with different assets or personal preferences, and risk aversion

Expected value Obviously, you chose prize D. Why? Expected value: Prize C = $15 x .1 = $1.5 Price D = $10 x .5 = $5.0 EV = Value x Probability The "betting preferences" of people with regard to uncertain outcomes (gambles) can be described by a mathematical relation which takes into account the size of a payout (whether in money or other goods), the probability of occurrence, the different utility of the same payout to people with different assets or personal preferences, and risk aversion

Expected Utility How desirable a bet is depends on: Expected value (size of Payout x Probability ) How much an individual values that payout (Saving a tree, $, etc.) This provides a single scale for the goodness of any particular choice Utility: how happy or satisfied something makes you (how desirable something is) Applying expected value and expected utility to decision-making requires knowing the probability of various outcomes. However, this is unknown in practice utility is a measure of the relative satisfaction from, or desirability of, consumption of various goods and services. rationality is precisely defined in terms of imputed utility-maximizing behavior under economic constraints The expected utility theory deals with the analysis of choices among risky projects In economics, game theory, and decision theory the expected utility theorem or expected utility hypothesis predicts that the "betting preferences" of people with regard to uncertain outcomes (gambles) can be described by a mathematical relation which takes into account the size of a payout (whether in money or other goods), the probability of occurrence, risk aversion, and the different utility of the same payout to people with different assets or personal preferences.

Utility theory: A Normative Theory of Choice Describes how people should make decisions In making a decision, you should: Assess how worthy each outcome is to you (subjective utility) Assess how likely each outcome is Compute the expected utility of each possible option Compare those expected utilities Select the choice with largest expected utility The basic idea here is that we have a single scale for the goodness of any particular choice…costs cause a lower rating on the scale, and benefits cause a higher rating on the scale. A simple enough and intuitively pleasing way to characterize choice.

Example: should you buy a lottery ticket? --Largest powerball jackpot ever = $195,000,000 !! --Probability of winning the powerball 1 in 10,000,000,000. --The expected value: .00000000001 x 195,000,000 = 2 lousy cents. Should you buy a ticket? Only if it costs 2c or less. Now you might ask yourself, is a lottery ticket worth a buck? Of course, this doesn’t take into account certain intangibles like the enjoyment we might get from the slightest delusion that we might actually win this thing! In this case, we will sort of gloss over some of the difficulties we’d encounter with regard to measuring the costs and benefits in all situations (for instance how do you compare the psychological benefit of a vacation with the monetary cost of the trip? It can be difficult to come up with a convincing scale for these things. In most of the situations we’ll consider, the costs and benefits will be relatively easy to specify… Just as in previous lectures, we will focus on some situations in which people depart from this normative model of choice…and we’ll try to draw some conclusions about the factors that play into people’s choices.

Utility theory: Criticism There are several problems with Utility theory: Probability outcomes are often unknown What is the probability that he will say ‘yes’ if I ask him out? It’s tricky to assess the expected utility of future outcomes How happy would I be to have chosen ‘Nova? Lots of evidence that people do not reason this way The basic idea here is that we have a single scale for the goodness of any particular choice…costs cause a lower rating on the scale, and benefits cause a higher rating on the scale. A simple enough and intuitively pleasing way to characterize choice.

Please make your selection... Option A. Winning $40 with probability .80 Option B. Getting $30 for sure Certainty Effect: People tend to prefer sure gains (risk averse for gains) Eva: $40 x .8 = $32 EVb: $30 x 1 = $30

Framing effects: Positive Frame Students in right side of class will answer: Imagine that the US is preparing for the outbreak of an unusual tropical disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. The estimates of the program’s effects are as follows: Program A: 200 people will be saved. Program B: 1/3 chance that 600 people will be saved. 2/3 chance that 0 people will be saved. Notice that because the expected values are the same, there isn’t necessarily a right answer in this situation. You could make arguments for or against the risky procedure in either case. The key point, then, is the dramatic reversal in people’s choices, based on the way that the question is worded. Are there similar effects in public policy or in public referendums?

Negative Frame Program C: Program D: Students in right side of class will answer Imagine that the US is preparing for the outbreak of an unusual tropical disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. The estimates of the program’s effects are as follows: Program C: 400 people will die. Program D: 1/3 chance that 0 people will die 2/3 chance that 600 people will die.

Positive Frame Negative Frame Program A: 200 people will be saved. Program B: 1/3 chance that 600 people will be saved. 2/3 chance that 0 people will be saved. Program C: 400 people will die. Program D: 1/3 chance that 0 people will die 2/3 chance that 600 people will die. 72% of subjects pick Program A when the problem is framed in terms of “lives saved.” With the positive frame, subjects are “risk averse.” Only 20% of subjects pick Program C when the problem is framed in terms of “deaths.” With the negative frame, subjects become “risk takers.”

Donating money & saving lives Each life is worth the same

How much money would you give to save Rokia To save people from the village where Rokia lives

} } A Hypothetical Value Function Value gains losses This graph shows the relationship between two variables…the perceived value or utility of a particular choice, and the overall cost or benefit associated with that choice. This graph just captures the idea that people may take losses more seriously than they take gains. This would be a departure from the normative model of expected value, because in that case, costs and benefits are counted equally. Notice that an equal size loss leads to a larger change in “value” than the same sized gain. Possible bonus? Going with this model, it is possible that subjects were willing to take a greater risk in the negatively framed situation, because they were more eager to avoid any losses. For the positively framed case, they may not have perceived as great a difference between the outcomes, so they went with the “sure thing.” - “The pain of a loss is greater than the pleasure of a gain.” - “ small loses hurt (proportionally more) than big losses”

Cash or Credit?? $1.30/gal 5 cent discount for cash... $1.25/gal losses Discount seems negligible, people use credit card. gains $1.25/gal 5 cent charge for credit... Surcharge is outrageous… people pay cash.

Framing effects are everywhere… What’s better? A basketball player who makes 75% of his free-throws, or one who misses 25% or his free-throws?

Summary Utility theory fails to describe how people make decisions: Frame effects Influence of justifications (minimize regret)