Module 10 (Reasoning + Decision Making)

Reasoning

Means from going to premises to conclusions

Premises

Existing beliefs

Conclusions

New beliefs

Prescriptivism

This is the right way + everything else is wrong

Descriptivist

No right/wrong; Here’s how to do it

Deduction

Logically certain reasoning

Ex.

If an animal has liver, they have stomach

Rat has a liver, so they have stomachs

Induction

Probable reasoning, not definitive

Ex.

Squirrels like nuts

Badgers are similar to squirrels

Badgers prob like nuts

2 Rules of Deduction

1. Modus Ponens

2. Modus Tollens

Modus Ponens

If A then B; If A is true then B is true

Antecedent → A (1st one)

Consequent → B (2nd one)

2 Rules of Deduction

Modus Tollens

If a conditional statement is true, and the consequent is false, then the antecedent must be false

Wason Selection Task Def

Each of these 4 cards has a letter on one side + a # on the other

Task is to eval the rule; If there is a vowel on 1 side, there is an even number on the other side

Which card do we turn?

Also did the same thing for a real life situation

Wason Selection Task Results

Ppl fail the task with the cards but got it in the real life scenario

So ppl are not pure logic when they reason

Is deduction useful in real life?

Not rly

Degree of Belief

The degree to which we ought to believe a proposition; Can quantify

Ex. If a coin always landed on heads, prob a 2 sided coin

Is induction probabilistic reasoning?

Yes

Bayes Rule

A model for induction; Basis for doing reasoning with probability by looking at how strongly to believe H as a function of

• Degree to which H fits the evidence AND

• The prior prob of H

Normative

p(A)

The probability that A is true; Degree of belief in A that is always between 0 + 1

Ex. I think she is a lawyer → p(.9) she’s a lawyer

p(~A) = 1-p(A)

Probability she is a lawyer = probability that is false

Conjunction Rule

A + B both being true probability is less than probability of A or B

So probability of A and B MUST BE less than or equal to A OR B

Disjunction Rule

All probability is less than 1

p (A | B) = p (A and B)/p (B)

Probability of A given B (if) is true

Like a hypothetical (idk if B is true, but if it is, what would the probability of A be?)

Only care about probability of A

Likelihood

The degree to which H fits the evidence

Prior Probability

How likely it was before evidence/considering data

Ex. Prob it will rain generally

Posterior Probability

Probability of H, given the data, D

Calculated by Bayes Rule

Is posterior always det by both the prior + likelihood?

Nope, could just be one

Normative

Method that objectively gives you the right answer

Bayesian Inference

What does it mean if ppl are bayesian?

They form beliefs in a way thats optimal given the info available to them

What does it mean if ppl are not bayesian?

Ppl are irrational, which means they form in a way thats incoherent or internally inconsistent

Rational Self Interest

Econimists assume ppl are Bayesian bc they think ppl make optimal use of their info

Cog Illusions

Ppl exhibited fallacies of reasoning

Conjunction Fallacies

Ppl are more likely to give higher ranking to a series of events leading to one thing rather than just the 1 thing → not possible

Heuristic

An approx strat for solving a prob thats easier in some way than the optimal procedure

Representativeness Heuristic

Ppl est probabilities by using “representativeness”

Ex. Linda sounds more like a feminist bank teller than just a bank teller

Base Rate Fallacy

When ppl ignore the prior + only consider likelihood

Ex. There was a taxi accident, witnesses saw blue taxi (85% taxi green, 15% blue); Witness usually say green even tho they saw blue

Gambler’s Fallacy

Tails is “due”

Explained via heuristic

Law of Small Numbers

Small samples should reflect properties of longer series

Hot Hand Fallacy

The coin is “hot” (hot streak), so p(H) > .5

Explained via heuristic

Heuristics + Biases

Ppl dont reason using normative strats but instead via this

Prescriptivists

Think heuristics are defective

Bayesian Cog Sci

Idea that mind approx optimal in its use of info

Are ppl Bayseian?

Unsure

Perhaps perception is but cog isnt

Decision Making

The process of identifying + choosing among possible options to solve a prob or achieve a goal

Expected Value Theory

Suggests that individuals should choose the option with the highest expected value

Need to look at the long run

Poor Man’s Dilemma

Poor man sells ticket for 4k even tho he could win 10k bc he needs to live

Expected Utility Theory

Helps individuals choose between uncertain prospects by comparing their expected utility values

Says poor man dilemma is irrational (bc 4k feels great aka selling at lower price, compared to 0 which would feel awful or 10k, but 10k wouldnt be much dif than 4k)

Risk Aversion

Flatting of curve

Ex. 4k not much dif than 10k

Expected Utility

Takes the total wealth of decision maker in consideration

The utility weighted by the probability of experiencing it

Are ppl rational choosers?

No, bc we make inconsistent choices

Reference Point

Ppl behav inconsistent regarding this (0 point)

Loss Aversion

Where they treat neg outcomes dif than pos outcomes

Prospect Theory

Suggests that losses have a greater impact on individuals than gains

Choice Consistency

Like if you say you have a strict pref of apple to pear, can assume apple utility > pear utility

Intransitive

Cant be proven to make decisions as if theyre maximizing something or working toward certain goal

Picking something you dont pref

Rational Decision Maker

Consistent in decision making to achieve something

Temporal Discounting

Value of something gets lower as time continues; Can lead to pref reversal

Ex. Marshmallow task

Multiple Selves

Human choosers are more like a combo of hot, impulsive, self + a cold patient self that are always competing for control → lead to irrational choices

Exponential Discounting

Theres a constant rate of change in utility

Satisficing/Bounded Rationality

Choose the first option that is good enough or decide based on only 1 feature