Rationality and Probabilistic Reasoning Flashcards
What is rational
people are rational to the extent that the normative and descriptive theories of rationality agree
what is the problem with formal logic
logic deals with certainty but human reasoning deals with uncertainty because the world is fundamentally uncertain
what is an intuitive statistician (Simon, 1955)
people have evolved in an uncertain world so they should be able to reason probabilistically so can be called intuitive statisticians
we are able to reason as accurately as possible given the limited amount of information that is often available to us
what is bounded rationality (Simon, 1955)
people are rational, sensible and justified in their decision making within the bounds or limitations on rationality
these limitations are our own cognitive capacity (to keep information in mind) and external forces like available time and access to information
What is the right normative theory for judgement under uncertainty
probabilistic reasoning
specifies the way in which we should think about evaluating evidence and making judgements (particularly high level reasoning where we are making judgements about the world) where p≠1
for independent or linked events
what evidence is there that people do not reason probabilistically
failures in simple tasks
base rate neglect
how have we been so successful in the world if we cannot reason probabilistically
heuristics provide a solution to bounded rationality
these produce biases in reasoning but are often accurate
what arguments are there against very biassed humans
system 1 vs system 2
reasoning with frequencies
what are the results of the three-card trick (Bar-Hillel & Falk, 1982)
three cards one red, one white, and one red and white are placed in a hat, one is taken out at random and placed on a table
the side facing up is red, what is the probability that the other side is also red?
the answer is 2/3 but only 6% of people get this right
what is the monty hall problem (Granberg & Brown, 1995)
a prize is hidden behind one door (out of ABC)
you pick door A
you’re told the prize is not behind door C
should you switch to door B
Intuition that there is no reason to switch to B when in fact you should
what did Casscells et al.’s (1978) medical diagnosis study show
“If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a
positive result actually has the disease, assuming that you know nothing about the person’s symptoms or signs?”
18% of medical students correctly answer <5% while 45% (the majority) answer >90%
this is because people only use part of the information and ignore the overall base rate
What is base rate neglect (Kahneman & Tversky, 1973)
people are insensitive to prior probability
particiapnts given the information that psychologists have administered personality tests to 30 engineers and 70 lawyers, who are all successful
then given a description of Tom, a 30 YO man, married with no children, high ability and motivation who wants to be successful and is well liked - asked how likely it is that he is an engineer
most people answer 50% despite told that 30% were engineers
this tells us that despite the description being uninformative it influences people’s decision more than base rate probability
what are Kahneman & Tversky’s (1974) heuristics and biases
we often lack information to assess probabilities
the information necessary is very complex, so even if we had access to it we couldn’t work them out
instead we substitute difficult calculations with simpler ones
heuristics are rules of thumb which help us to arrive at quick useful answers which are often accurate but are not guaranteed to be so
we have a limited number of heuristic principles which reduce the complex tasks of assessing probabilities to simpler judgemental operations
this means that they lead to severe and systematic errors when misapplied
these biases are cognitive illusions that reveal the heuristic strategies people are using
what is the availability heuristic
we are often need to judge the frequency of an event
this is a difficult question that we do not have all the sufficient information about to answer
instead we ask a simpler question: how easy is it to bring examples to mind (how available are they in memory)
this enables us to answer the question but brings errors
e.g
of participants who were asked which are more frequent, words beginning with r or those with r as the third letter, 69% incorrectly answered begin with -
how we access the mental lexicon means that we can access words based on the first letter more easily than the third
What is the representativeness heuristic (Tversky & Khanman, 1983)
problems where we do not have access to information of likely category membership
instead of answering how likely is A to be from category B we answer how representative is A of B based on our accessible knowledge
participants were given a description of Linda as a 31 YO, single, outspoken, bright, phiosophy major, concerned with issues of discrimination and social justice and then asked whether it was more likely that linda is a bank teller or a bank teller and a feminist
85% answer bank teller and feminist
this is because of the conjunction fallacy where individuals believe the conjunction of descriptions to be more likely than any component in the description
