Decision Making Final

Automatic thinking

An unconscious way of thinking

Controlled thinking

deliberate, active thinking, considering alternate explanations

Bounded rationality

the brain doesn't always make the best decision, heuristics and other things can influence our ability to decide

4 Criteria of Decision Making

1. Based on current assets

2. Based on possible consequences

3. Evaluated according to probability theory

4. Adaptive within the constrains of the probabilities and valued of the possible consequences

4 Ways People Make Decisions

1. By habit

2. By conformity

3. By culture

4. By authority

Probability theory

Choice is evaluated based on the expected value

Expected value equation

Probability*Value

Normative

how people should make decisions

Descriptive

how people actually make decisions

Perceived probability

People tend to OVERVALUE small probability events and UNDERVALUE high probability events

Sunk Cost effect

Taking past investments in a decision alternative into account, even when they should not affect decisions about the future

Example of sunk-cost effect

Suppose you have just spent $200 on a non-refundable ski lift ticket for the day. Once you arrive at the lift, the weather turns bad, so skiing will be very unpleasant. What do you do: stay and ski anyway in miserable conditions, or just give up the $200, and go home, where you will find more enjoyable activities? Why would you decide as you do?

Overinclusive thinking

Considering extraneous information while making a decision

Incomplete thinking

People tend to not consider all options and potential outcomes of those options

Example of Incomplete Thinking

Jurors who form an early impression that a defendant is innocent usually only evaluate the consequences of handing down an innocent world

Expected utility

How much the gamble is worth to the decision maker

Expected Value

How much the gamble will pay

Decision Trees

• Consider all possible decisions and all possible outcomes

• Squares are decisions to be made

• Circles represent different possible outcomes

Rationality of Considering only the Future

If you only consider the satisfaction of the future, you will choose the option that gives you the most enjoyment going forward.

The Lens Model

We make decisions about underlying criteria based on multiple cues.

(Weight)(Attribute) + (Weight)(Attribute) + (Weight)*(Attribute)

Linear Models

Decisions are made on scores from a criteria. An example would be TSA screening. Workers will observe any suspicious passengers if they reach 4+ points, they will be inspected. If they reach 6+ points, they will be referred to by law enforcment.

Ellsberg Paradox

Suppose you have an urn containing 30 red balls and 60 other balls that are either black or yellow. You don't know how many black or yellow balls there are, but that total number of black plus yellow is 60.

Choose:
A: Receive $100 if you draw a red ball
B: Receive $100 if you draw a black ball

Choose:
C: Receive $100 if you draw a red or yellow ball
D: Receive $100 if you draw a black or yellow ball

Heuristics

Quick and dirty mental shortcuts

Availability heuristic

People estimate the likelihood of an event based on how easily similar memories can be recalled

Overgeneralization

People tend to overgeneralize a particular to the whole: One bad cop means all cops are bad

Biased sampling from memory

Biased sampling from memory
Easier recall increases your estimate of the frequency
"_ _ _ E " vs. "_ _ _ _ E D"
Pink garbage truckBiased sampling from memory

Availability to the imagination

"In a room with 10 people, how many different groups of 2 can be formed?"

"How many different groups of 8 can be formed?"
The answer for both is 45, but we tend to think that there is more groups of 2 because two is a smaller number

Subadditivity

The actual probability of all events is less than the sum of estimated probabilities

Example of subadditivity

Physicians are presented a patient case and asked to estimate the probability of each of the following outcomes:

• Patient dies while at the hospital

• Discharged alive but dies within a year

• Lives more than 1 year but less than 10 years

• Lives more than 10 years

The average summed probability was 164%

Superadditivity

The probability of all events is greater than the sum of estimated probabilities of all possible events

Example of superadditivity

What is the probability of each of the following, given that the birthrate in Myanmar is not equal to that of Thailand:

• Birth rate in Myanmar is greater than in Thailand

• Birth rate in Myanmar is less than in Thai

Average response for each option averaged from 0.42 to 0.47, doesn't add up to 100%

Anchoring

People make an initial estimate of a situation, and base new estimates on this original estimated, given new information

Under Adjustment

People tend to stay close to the anchor and fail to sufficiently adjust based on new information

Example of underadjustment

Spin a "wheel of fortune" with numbers between 1% and 100% then ask participants whether the percentage of African nations were UN members in 1972 is greater or less than this percent
People who spun "10%" estimated 25%. People who spun "65%" estimated 45%.

Certainty equivalent

If I offer you a choice between a gamble of $1000 with a probability of 70%, or I offer you a value of "X" with 100% certainty, what is the minimum value that X would be to choose X over the gamble?

As X increases, people increasingly choose X

Preference Reversal

People will change their preference depending on how the options are presented, people will undervalue EV and make decisions based on probability

Judgment by similarity

Subjects are told that a man is unsociable, disinterested in politics, and devoted to working on his boat in his spare time. How likely is it that he is:

• An engineer?

• A lawyer?

What if they are told that he was selected from a group that was:

• 70% lawyers and 30% engineers?

• 30% lawyers and 70% engineers?

Result: Subjects judged that he was an engineer, regardless of whether scenario A or B was presented

People ignore the base rates

Similarity heuristic

Category membership judgments are often based on similarity to known categories

Contrast Model

We tend to judge similarity of an instance to a category by looking for matches or mismatches between attributes of an instance and attributes of a category

If we know someone is famous, a good public speaker, and deceptive, we will assume he is a politician

Stereotypes are an example of this.

Bayes' Rule

How we can take both similarity and probability into account

P(A|B) = P(B|A)P(A)/P(B)

Conjunction probability error

Cognitive bias that occurs when people overestimate the likelihood of two events happening at the same time. This is statistically illogical because the probability of two things happening at the same time cannot be greater than the probability of one of the events happening on its own

Story Model

1. Evidence accumulation through story construction

2. Representation of the decision alternatives by learning verdict category attributes

3. Reaching a decision through classification of the story into the best fitting verdict category

How the jurors construct the story determines their verdict:

Coverage - does it account for all the evidence?

Coherence - no internal contradictions, story makes sense

Uniqueness - is it the only story that fits?

Judging by scenarios

Narrative stories include not just actual narratives of what happened, but also narratives of what WOULD have happened if other conditions had occurred

Example of judging by scenarios

A woman works in a mall in a high crime area, and gets assaulted after work.

Story 1: If there had been more guards, she would not have been assaulted

Story 2: If there had been more guards, she would have been assaulted anyway because the crime rate is so hate

Create a story of what WOULD have happened if things were different

Illusion of Control

The perception that one can control events that are entirely up to chance

Endowment effect

People are willing to pay less money to buy an object than they would demand in payment to sell the same object

The hot hand fallacy

The perception that one who is winning is likely to continue winning, even when the events are random.

Example of the hot hand fallacy

Does a basketball player have a better chance of making his next shot after making the last 2 or 3?

91% said yes

The Gambler's Fallacy

The false perception that the outcome of a current random events is dependent on the outcomes of preceding random events

A random event is more likely to occur because it has not happened for a period of time

Texas sharpshooter fallacy

A rifleman shoots a bunch of holes in the side of a barn. He draws a target around the cluster and says he's a good shot

Correcting for multiple comparisons

If there are 10 different diseases, and the probability that a town has more than a certain threshold number of any one of them is 0.05, then what is the probability that there will be an above-threshold number of one or more diseases?

1-p(none) = (1-0.95^10) = 40%

Disjunction

In a situation in which events have the same probability, this is the case in which one or more of the events happens.

The disjunctive probability fallacy

People tend to underestimate the probability of a disjunction

Opposite of the conjuction fallacy

Regression to the mean

The probability of some great event happening twice is lower than a less great event happening after that

Example of regression to the mean

Sons of tall fathers tend to be taller than other people, but shorter than their fathers

The two envelope problem

Suppose you and a friend are given an envelope. Each envelope has some money in it, and one envelope has exactly twice as much money as the other. You are each allowed to open your envelope and look inside to see how much money there is, but neither of you is allowed to tell the other how much money is in the envelope. You are given the option of exchanging envelopes once or keeping the original. Do you exchange or do you keep?

Probability Theory: 0.52x + 0.51/2x = 1.25x

By switching, you expect on average to increase your gain, but the other person should want to switch envelopes for exactly the same reason!

Should you continue switching envelopes indefintely?

The monty hall problem

Game Show: 3 doors: behind one door is a new car, and behind the other two doors are goats. You choose one door at random. After you state your choice, Monty opens one of the other two doors that you DIDN'T pick to reveal a goat. The door monty opens always has a goat behind it, then you get to switch.

If you pick door #1, then the combined probability that the car is behind doors two or 3 is ⅔

If Monty opens door 3, then the combined probability of ⅔ falls all on door two.

Probabilities:

• Door 1: ⅓

• Door 2: ⅔

• Door 3: 0

Evaluation heuristics

Good things satiate and bad things escalate

Duration neglect

People are insensitive to the duration of an unpleasant experience

Diversification bias

People underestimate how similar desires will be on different occasions

Students ask to choose in advance a snack that they will get in 3 weeks.

Later, students wished they had chosen a cookie for each week

Non-regressive prediction

People tend to overestimate how good they will feel about good consequences and overestimate how bad they will feel about bad consequences

Bounded self-control

People overestimate their ability to resist their own visceral desires in future situations (people plan to avoid drug use but do it when they get the opportunity)

Emotion

This factor allows quick and dirty responses that allow a response before we have the details of what we are responding to

Delay discounting

People tend to discount the future value of something

Example of delay discounting

$500 right now or $1000 in a year

Future value needs to be a certain amount larger than the immediate reward

V = 1/(1+kT)

Iowa gambling task

Players sample from any one of 4 card decks

Decks A and B have a higher rewards but also have higher punishments (average loss)

Decks C and D have lower rewards but smaller losses (average gain)

Individuals with brain damage similar to Phineas Gage (parts of the frontal lobe) consistently picked A and B, while normal individuals learn to choose C and D.

Certain areas of the brain activate to warn you of making a bad decision

Somatic marker hypothesis

Individuals experience a negative or unpleasant physiological response when contemplating certain potential choices

Cognition → Physiological response → Decision making

Weber's law

The Just Noticeable Difference between two stimuli is proportional to the intensity of the actual stimuli

A 100 watt bulb vs. a 2 watt bulb has the same difference than a 50 watt bulb and a 1 watt bulb.

Fechner's Law

A corollary of Weber's law: the physiological intensity is the logarithm of the physical intensity

The more money you have, the less value $100 has

Value

The quality of a thing by which its worth is estimate, the fair pricing of something

Personal value

Subjective value to the person making a decision

Framing effect

All options have the same EV, but the first is framed as a loss, the second is framed as a gain, so people tend to be more risk averse in gains and risk-seeking in losses.

Percent that prefers sure thing in gains MINUS percent that prefers sure thing in losses

Suppose you receive $400 and are given a choice between two options:

• Give back $100

• 50% chance of giving back $200

Suppose you receive $200 and are given a choice between two options:

• Receive $100 for sure

• 50% chance of receiving $200 more

Asian Disease Problem

The US is preparing for an outbreak of an unusual Asian disease that is expected to kill 600 people. Two alternatives are proposed:

A: 200 saved for sure
B: There is a 1 in 3 chance that 600 people are saved, and 2 in 3 chance that no one is saved.
Most people choose A.

Two other alternatives are proposed
C: 400 people will die for sure.
D: There is a 1 in 3 chance that nobody dies and a 2 in 3 chance that 600 people die.
78% choose D

Prospect theory

An individual views monetary consequences in terms of changes from a reference level, which is usually the individual's status quo. The values of outcomes for both negative and positive consequences of the choice then have the diminishing returns characteristic

The value function is steeper for losses than for gains

Probability graph shows that people overestimate the likelihood of infrequent events and underestimate the likelihood of more frequent events

Value function

V(x) =
x^a if x > 0
-λ(-x^a) if x < 0
Typically, a = 0.88 and λ = 2.25
A gain of $100 feels like +57.54
A loss of $100 feels like -129.47.

a has to do with risk

Decision-weight function

π(p): p^y/[p^y+ (1-p)^y]^1/y

Pseudocertainty effect

Adopting uncertain future events as the status quo from which prospects are evaluated
Choose A" or B"
A": With a probability of 0.75, fail at stage 1 of the gamble and receive nothing. If stage 2 is reached, win $45 with a probability of 0.8, otherwise nothing
B": With probability 0.75, fail at stage 1 of the gamble and receive nothing. If stage 2 is reached, win $30 for sure
People will be more likely to choose B", because the status quo has been changed once you add the 0.75 chance of making it to stage 2

Compensatory heuristics

Deficiencies in one category may be compensated for by another category

Non-compensatory heuristics

Require that an option be eliminated if a certain attribute is deficient

Decision by Dominance

Looking for alternatives that are better than any other alternatives for every attribute considered

Additive linear heuristic

The linear model approach. Each alternative gets assigned an overall score

Additive difference

Consider all possible pairs of alternatives and choose the best, like a bracket

Satisficing heuristic

Find the first alternative that is "good enough" on all attributes

Disjunctive heuristic

Find the alternatives that are "good enough" on at least one of the attributes considered

Lexicographic heuristic

Pick the best alternative(s) on one attribute. Then, consider all remaining attributes successively to pare down the list to one remaining alternative

Elimination by aspects

Like lexicographic, but set a minimum threshold for each attribute in turn and throw out the alternatives that don't meet the threshold. Repeat for remaining attributes

Recognition Heuristic

Name or brand recognition

Why would an insurance company want to offer rebate checks for safe driving?

Instead of flat out increasing rates, they increase the premium rate and then give you checks with a chance you get into an accident

Sensemaking

The division of departments to make sense of various pieces of data

Analysis of Competing Hypotheses

1. List hypotheses

2. Make a list of evidence and arguments for and against each hypothesis

3. Prepare a matrix: hypotheses across the top, evidence along the side.

4. Refine the matrix: Delete null evidence and arguments that don't support either hypothesis, or are invalid

5. Try to disprove conclusions

6. Analyze how sensitive your conclusions are to each piece evidence

7. Report your conclusions in terms of probability

8. Identify future milestones

Confirmation Bias

Pick a likely scenario, and then only look for confirming evidence

Persistence of Discredited Evidence

People tend to fail at discounting, discrediting evidence, treating it as though it were valid

Satisfaction of Search

Disengaging a search for additional objects or events after finding one instance of the searched-for object or event

Probability matching

Selecting options at frequencies that match payoff probabilities, instead of always selecting the option with the highest payoff probability