Lecture 15: How We Decide Flashcards
what types of decisions do we make?
lower stakes: ice cream flavor
higher stakes: stock market, investments
decisions about other people: tinder, relationships
how SHOULD we decide? (ideally)
use the expected value formula
expected value formula
expected value: odds of gain * value of gain
what were the two game examples given for expected value and should we play them or not and why?
- coin flipping: Would you pay $4 to play a coin flipping game where you win $18 if you guess right about the coin flip (H or T)
–> YES play: expected value = (1/2) * 18 = 9 > 4 - dice rolling: Would you pay $4 to play a dice rolling game where you win $18 if you guess the dice side right?
–> NO play: expected value = (1/6) * 18 = 3 < 4
ideally the expected value should be ___ than the amount you pay for you to play the game
expected value should be greater than the amount you pay to have a higher chance of gaining a positive profit
why do we not follow the expected value formula?
we make 2 types of errors in the expected value formula:
1. errors of odds
2. errors of value
explain the example given by the lottery and why people play it despite it not being supported by the expected value formula
lottery: Ie. ticket for a lottery: a game where you pay $1 and you pick 6 numbers between 1-75. If you get 5 right, you win $1,000,000
–> expected value = $1 million / 18 million = ~$0.05 < 1
people actually BELIEVE they have a chance of winning
a lot of the work and study about decision making was done by which two people?
Daniel Kahneman and Amos Tversky
what are heuristics?
cognitive shortcuts that (usually) work
Shortcuts that we take for problems that are too complicated/messy for us to solve exactly, but often times an approximation is good enough
however for the questions proposed in class, often times simply relying on our heuristics gives us the WRONG answer
examples of sample size neglect
- babies in hospitals
- kidney cancer
what principle explains the sample size neglect?
the law of small numbers
what is the law of small numbers?
when you have a small number of observations, there is a greater chance of weird and extreme results
explain the babies in hospital sample size neglect example
Question 1: “400 babies are born each day in a large hospital, and 40 babies are born each day in a small hospital. For any day in which more than 60% of the births at a hospital are girls, that hospital hands out free girl scout cookies.” Which hospital will have more free-cookie days?
400
40
same
→ most people in the world are probably thinking the answer is the “same” (C)
The prob of having a boy and a girl is the same and that is true for a small or large hospital
However answer (C) is WRONG; answer (B) is right (the smaller hospital)
Explanation: smaller samples are more prone to extreme things happening to them
As the hospital size gets bigger and bigger, it will converge closer and closer to the expected 50-50 split between boys and girls
However a smaller hospital is more likely to have extreme days (aka 70-30 split or 20-80 split another day)
base rate neglect
Failing to take into account the underlying odds of something being the case
What IS the same for the babies in hospital example?
the thing that IS the same between the two hospitals is that they are equally likely to have more boy days or more girl days (but the smaller hospital is more likely to have more extreme days)
explain the kidney cancer sample size neglect example
The counties in the US with the lowest incidence of kidney cancer had the following properties
Rural
Sparsely populated
Religious
→ HOWEVER… it was also true that the counties with the highest incidence of kidney cancer is ALSO
Rural
Sparsely populated
Religious
→ the reason for this is the key word “sparsely populated” since in smaller sample sizes, there are more extreme cases on both ends of the spectrum
give 2 examples of base rate neglect
- Ron trumpeter or farmer
- Ron 6’7’’ tall NBA player or teacher
explain the Ron trumpeter or farmer base rate neglect example
Ron is an opera buff who enjoys touring art museums when on vacation. Growing up, he loved listening to classical music and playing chess with friends and family. Which is more likely?
Ron plays trumpet in a major symphony orchestra
Ron is a farmer
Answer: It is more probable that Ron is a farmer since there are way more farmers than people who plays trumpets in a major symphony orchestra (aka there are very few people who have this job)
Trumpeters in major symphony orchestras: ~300
Farmers: ~2,000,000
explain the Ron NBA starter or teacher base rate neglect example
Ron is 6ft 7in tall. Which is more likely?
Ron starts for an NBA team
Ron is a teacher
Answer: it is much more likely that he is a teacher than an NBA starter since there are a lot less NBA starters than there are teachers
NBA starters: 150
Teachers: ~3,200,000
what are we tempted to make the base rate neglect error?
representativeness heuristic
give 2 examples of the availability bias and one of the availability heuristic
availability bias:
1. Are there more English words with “r” as the first letter, or with “r” as the third letter?
2. risk of airplane, car, and bathtub
availability heuristic: Which is more likely? A dog on a lease or a pig on a lease?
representativeness heuristic
representativeness heuristic: which of these given options is more representative of this information?
- if it seems like “X”, then it must be “X” (if it looks like a duck and quacks like a duck, then it’s probably a duck” type of thinking)
Ie. the description seems more representative of a classical musician than a farmer
Ie. the description of 6’7’’ seems more representative of an NBA starter than a teacher
availability heuristic
what is more cognitively accessible (easier for me to think of) to me?
difference between availability heuristic vs availability bias
When the availability heuristic is helpful and accurate → call it availability heuristic
When it is NOT helpful and instead misleading → call it availability bias