Cognition and Decision making exam 1

3 elements of decision making

judgment, preference, and choice

epistemic rationality

believing only that for which you have strong evidence

mnemonic: “system” requires evidence

instrumental rationality

acting only in ways that are in alignment with our goals

mnemonic: instrumental means physical action

descriptive claims

about what is the case (describing reality)

e.g. shannon said you shouldn’t text in class

normative claims

about what should be the case

e.g. shannon should tell you not to text in class

cognitive illusions approach

a focus on the systemic errors in human decision making and the conditions under which they arise

fast and frugal approach

focuses on the adaptivity of human decision making— how mental shortcuts balance cognitive costs and overall accuracy

cognitive reflection test (CRT)

a measure of the ability/disposition to reflect on a question and resist reporting the first response that comes to mind.

• even among all the possible wrong answers, intuitive answers dominated

• even when the right answer was ultimately given, the intuitive wrong answer was often considered first.

• people who gave wrong answers judged the problems to be easier than people who gave the right answers.

wason selection task

• with negation, people did much better on this task due to the matching strategy- picking the cards named in the rule

  • when people used the matching strategy (resulting in the correct answer) on the negated task, they justified their choice by saying it was just the correct answer

  • when people used the matching strategy (resulting in the wrong answer) on the affirmative task, they didn’t know what to say

→ choose the cards first, justify the choices second

dual process theory

cognitive behavior is driven by two forms of processing:

type 1: fast and intuitive

type 2: slow and deliberative

• can produce corrections of type 1 outputs or justification for them

problems for dual process theory

interaction problem: when do type 2 processes turn on, and why?

1. parallel competitive models: type 1 and type 2 processes are both engaged from the start, and type 1 outputs the response before type 2 does. additional processing occurs if responses conflict.

2. default intervention (serial) models: type 1 but not type 2 processes are engaged from the start. type 1 processes output responses, and then type 2 processing may occur if type 1 outputs are suspect.

3. hybrid models: multiple type 1 processes engage from the start, potentially yielding conflicting outputs. type 2 processing occurs if type 1 outputs conflict.

cluster problem: do conventional attributes always cluster together?

not always:

1. nonconscious + slow: sleeping on a problem

2. nonconscious + intentional: skilled activities e.g. driving

3. intentional + uncontrollable: bat and ball problem/CRT tests

4. unintentional + controllable: stereotyping, mimicry

working memory is the single distinguishing feature between type 1 and 2.

dichotomy problem: even if we reduce the type 1 vs type 2 distinction to a distinction in working memory demands, that distinction isn’t all or nothing— “type 1… do post their products into working memory…”.

→ where do we draw the line? how do we dichotomize something that is a continiuos spectrum?

in early dual processing, the focus was on the style (quick, slow). recent research proposes mental heuristics to explain it.

incompatibility between intuitive and logical responses elicit activity in the _______.

anterior cingulate cortex (ACC)

global workshop theory

conscious states are a subset of working memory (non conscious e.g. driving automatically)

states are conscious only when in the spotlight of attention, globally broadcasting them to other systems.

overriding intuitive responses, intertemporal choice, and executive control is correlated with activation in which area of the brain?

prefrontal and frontal cortex regions

unimodel theory

there aren’t different types of processes, but just different degrees. there are underlying rules for both.

gaze heuristic

can be used both as a conscious and a nonconscious process.

1. nonconscious: adjusting speed of running to catch a ball

2. conscious: flying a plane for instrument free navigation

addition rule

if outcomes A and B are mutually exclusive (one OR the other):

P (A v B )= P(A) + P(B)

multiplication rule

if outcomes A and B are independent (doesn’t effect the probability of the other):

P (A ^ B) = P(A) * P(B)

law of large numbers

large samples will be representative of the population from which they are drawn

law of small numbers

the law of large numbers wrongly applied to small samples

gambler’s fallacy

the belief that if some outcome has occurred in the past, it is less likely to occur in the future, even if the outcomes are independent

representativeness heuristic

judging the probabilities of events based on how representative they are

e.g. robins are more representative of birds than penguins

the linda problem- conjunction rule and fallacy

conjunction rule: a conjunction cannot be more probable than one of its conjuncts.

conjunction fallacy: making that mistake

people ranked “is a bank teller and is active in the feminist movement” more likely than “is a bank teller”.

since a conjunction can be more representative than one of its constituents, instead of judging rational probability, people deploy the representativeness heuristic

the linda problem- pragmatic reasoning?

direct subtle test- the regular version

direct transparent test- each participant rates conjunct and conjunction and the relation is highlighted

e.g. linda is a bank teller and active in the feminist movement; linda is a bank teller whether or not she is active in the feminist movement.

57% violated conjunction rule

indirect tests- separate tests rate conjunct and conjunction

i.e. test 1: linda is a bank teller and is active in the feminist movement.

test 2: linda is a bank teller.

the general placement of the respective rankings stayed the same

the linda problem- semantic inference?

german speakers were asked to describe the linda problem and that the word “probability” had to be paraphrased.

there were various paraphrases for the word. perhaps people are understanding it differently?

the linda problem- evidence assessment?

are people estimating the degree of evidential support rather than estimating probability?

a piece of evidence can give more support to H1 than H2, even if H1 is a subset of H2.

• raises the probability that Linda is a feminist bank teller

• lowers the probability that Linda is a bank teller

cannot increase the probability of the conjunction to such an extent that it becomes more probable than the conjunct, but increases probability of the conjunction more than it increases the probability of the conjunct.

availability heuristic

estimating the probabilities of events based on how easily you can or could bring examples of those events to mind (whether it be from speed or the number of examples)

attribute substitution

replace difficult questions by subbing in heuristics that come more readily to mind.

• occurs if the substituted attribute is relevant and “good enough” to solve the problem

anchoring and adjustment heuristic

start from the initial value, assess whether it is too low or too high, and adjust it

issues with anchoring and adjustment

problem 1: anchoring and adjustment is still active when initial value is irrelevant.

e.g. spin a wheel designed to land on 10 or 65, and then guess what % of the countries in the UN are from Africa.

→ if you landed on 10, the average guess is 25%

→ if you landed on 65, the average guess. is 45%

e.g. estimate the answer within 5 seconds:

8×7×6×5×4×3×2×=2,250?

1×2×3×4×5×6×7×8=512?

thin rationality

th(in)

focuses on (in)ternal consistency

e.g. whether one’s actions align with their goals

broad rationality

asks whether the goals themselves are reasonable

normative theories / descriptive theories

normative theory:

theories that tell us what we ought to do based on rational decision making

• what “should be the norm”

descriptive theory:

how things actually happen and how people actually act in the real world

expected value theory

multiply the value of each possible outcome by the probability of that outcome. add the products together.

• we assume that the probabilities are fixed and known

• we assume that people prefer higher values over lower values

normative decision rule

rational people should choose the actions or options with the highest expected value/utility

st. petersburg paradox

flip a coin until it lands on tails.

if it lands on tails, you get the content of the pot, which starts at $2. if it lands on heads, you x2 the pot and flip again.

• ( ½ × 2) + (( ½ × ½ ) x 4) + (( ½ × ½ x ½ ) x 8) …

1 + 1 + 1 + 1…

the EV of this problem is ∞

law of diminishing marginal utility

the more money you have, the less any additional dollar means to you

expected utility theory

replaces objective value in EVT with subjective utility.

• assumes a utility function that maps an amount of money to an amount of utility. (calculating the real “value” of money based on its utility/value to the individual person)

utility of each possible outcome x probability of occurrence

axioms of choice

1. completeness- for every set of options, you must have a preference between those options or else be indifferent

2. continuity- if you prefer a > b > c, then there is some arrangement where you are indifferent between (a & c) and b

e.g. having salad for sure = 1/3 chance of pizza and 2/3 chance of celery

3. independence of irrelevant alternatives- the introduction of new options must not alter existing rankings

e.g. if you prefer pizza to salad, introducing chocolate should not make you want to suddenly prefer salad

4. transitivity- preferences must be consistently rank ordered

e.g. if you prefer pizza to salad, salad over celery, you must prefer pizza to celery

axioms of choice counterexamples

completeness:

• sophie’s choice (which child will be chosen to get killed? which child is preferred?)

• we don’t have a preference for every possible combo of good available for sale at costco compared to all other combos

continuity:

• a > b > c, but

a= eating a nice meal

b= scratching your finger

c= destruction of the world

there is no scenario where b = the chance of a nice meal or the destruction of the world.

• you would not take a gamble of a chance of a nice meal or the destruction of the world over getting a scratch

independence of irrelevant alternatives:

a) subscription A ($59)

b) subscription A + B ($125)

later, add c) subscription B ($125)

now, option B seems more appealing

transitivity:

• the game that people would prefer to play (thus, more value) vs the game they would sell for more money was different— the values/preferences flipped

• prefer apples > bananas, bananas > cherries, cherries > apples

problem of uncertain odds

a flaw with EUT is that without certain probabilities, there is no way to calculate the rational decision.

to combat this:

• maximax- maximize the maximum gain

• minimax- minimize the maximum loss

problem of unreasonable assumptions

EUT unreasonably assumes perfect info (such as uncertain odds), and including of your own preferences, as well as perfect calculation and infinite time to reason

• in the real world, this is unrealisitic

principle of invariance

according to EUT, the choice between options relies only on expected utility. it should not matter how the options are presented.

framing effects

influences preferences between choices even when the choices are equivalent in expected value.

• framing choices in terms of gain leads people to be risk averse, taking the sure gain over the gamble

• framing choices in terms of loss leads people to be risk seeking, taking the gamble over the sure loss

framing effects are an issue because even if the expected value is the same and should result in the same preference, the framing of the question influences preference.

certainty effects

outcomes that are certain are overweighted relative to outcomes that are merely probable

possibility effects

possible but improbable outcomes are overweighted:
the shift from impossibility to possibility results in greater gain in desirability than a proportional shift from one probability to another

0 → 0.1% vs. 50% → 50.1

possibility effects lead to a reversal in normal attitudes towards risk

• with low odds for gains, people suddenly become risk seeking

  • a) 100% gain $5

  • b) 0.01% gain $5000

  • same EV

• with low odds for losses, people suddenly become risk averse

  • a) 100% lose $5

  • b) 0.01% lose $5000

why are certainty/possibility effects a problem for EUT?

EUT depends only on the utilities of outcomes x their probabilities.

preferences should not depend on how close those probabilities are to 0 and 1.

prospect theory

(subjective value) x (decision weight)

1. editing phase- preliminary analysis that yields a simpler representation

• coding- outcomes are framed in terms of gains and losses relative to a natural reference point (e.g. current wealth, goal wealth)

• simplification- outcomes are rounded, events of extremely low probability are discarded, and events of extremely high probability are treated as certain.

2. evaluation phase- edited prospects are evaluated and the prospect of the highest value is chosen.

value function

under prospect theory, outcomes are evaluated not in terms of wealth but in terms of gains or losses relative to a reference point. (s shape curve)

• when making a decision, we are attuned to changes rather than absolute values.

• value judgments are just like perceptual judgments

e.g. $1mill → $5 mill YAY!

$9 mill → 5mill BOO!

loss aversion

the displeasure of losses is greater than the pleasure of equal sized gains

weighting function

people overweight small probabilities and underweight moderate-large probabilities

• decision weights are not probabilities

• they do not obey the axioms (rationality). they don’t reflect personal belief.

• instead, they are a measure of how the chance of an event impacts the desirability of a choice

conditional probability

the probability of an event given some other event

standard probability

the odds that evidence is seen given that the hypothesis is true

p(E|H)

inverse probability

the odds that the hypothesis is true given that some evidence is seen

p(H|E)

bayes: given that i’ve seen evidence, how much should i update my beliefs?

what does it depend on?

priors and likelihood

base rate neglect

cognitive bias where people underemphasize the general prevalence of an event (base rate of occurrence) when making a probability judgment, focusing more on specific info.

how to combat base rate neglect

phrasing problems using natural frequencies instead of probabilities helps bayes be more intuitive