Week 10: Reasoning Flashcards
Reasoning and Decision Making
Judgement:
estimating magnitudes/probabilities of some characteristic
Reasoning: drawing conclusions
Decisions: making choices between alternatives
Forming an opinion on a particular thing
Finding magnitude of certain characteristics
Taking available evidence that we have and concluding
Looking at available alternatives and choosing among them and acting in that certain way
Conclusions help us make decisions
Deductive Reasoning
Starts broad principles to make logical predictions about specific cases
Determining whether a conclusion logically follows from premises
Syllogistic reasoning
Two statements called premises
Third statement called conclusion
Categorical syllogism
Describe relation between two categories using. all, no, or some
Do not confuse “validity” with “truth”
Syllogism is valid if conclusion follows logically from its two premises
Truth refers to a relationship that holds in reality
Syllogisms can have validity but not the truth, and can have truth but not validity
Deductive
Situations where we start with broad principles and try to make a logical prediction about specific case
General to specific
Remember, don’t confuse validity with truth
Trying to determine if a syllogism is valid
Truth is what we usually think about
Categorical Syllogism
All men are mortal. (major premise)
Socrates is a man. (minor premise)
(therefore)
Socrates is mortal. (conclusion)
Logic and Eular
Assess syllogistic logic
Have category A represented by a circle, show a relationship with A and B by circle overlap
All A are B
No A are B
Some A are not B, Some A are B
Goal isn’t to find a way that sylllogism is true, but false
False makes it invalid
Abstract
All A are B (major)
All C are B (minor) therefore, All A are C (conclusion)
All A are not C in the diagram
True or False (valid)?
Concrete
All Liberals are human. (major premise)
All Conservatives are human. (minor premise)
(therefore)
All Liberals are Conservatives. (conclusion)
True or False (valid)?
Misinterpretation: All A are B = All B are A
Biggest error people make is that they feel like they can rearrange the equation
You can’t just flip it around
Form vs. Content
All dogs are animals. (major premise)
Some animals are pets. (minor premise)
(therefore)
Some dogs are pets. (conclusion)
True or False (valid)?
Dog category is independent from pet circle so syllogen is false
Don’t focus on content, focus on form of diagram
Using sharks make it easier to conceptualize
Belief bias: if content pushes you towards one interpretation, makes it hard to evaluate it logically
Reasoning Error
Belief bias (Henle, 1962): The tendency to think that a syllogism is valid if its conclusions are believable
Therefore, beware of syllogism’s conclusions that are true or agree with your beliefs
All of the students are tired
Some tired people are irritable
Some of the students are irritable
Atmosphere effect (Woodsworth & Sells, 1935): global impression or feel of the premises (e.g., same form)
All + All = All ?
All birds are mammals
All mammals sleep
All mammals are birds
Confirmation bias: the tendency to selectively look for information that conforms to our hypothesis and overlook information that argues against it
Reasoning Error
Some of the students are irritable is incorrect based on diagram
Atmosphere effect: idea that if the premises give a general feeling of particular form so that you have all As or Bs or Cs, that sort of gives the impression that it must be true
All + all = all
Since all mammals are not birds
Tendency that we have to prove that something is true due to expectation
What we want to do in logic and generally approaching things and we try to find ways that something is untrue
Conditional Syllogisms
A logical determination of whether the evidence supports, refutes, or is irrelevant to the stated relationship
Conditional clause (premise 1) – antecedent (if clause)
consequent (then clause)
Evidence (premise 2)
Conclusion?
Psyc 221
Psyc 221
First premise is the (if then) part
Second premise is the evidence support, refutes or is irrelevant to the first premise
Then you have to determine if you can reach some type of conclusion
Modus Ponens (97%)
Modus Tollens (60%)
The only time that you can come up with a valid conclusions is if you are affirming antiselent or denying the consequent
Example
Raining (antecedent)
Domique gets wet (consequent)
Evidence: it is raining
Conclusion: therefore, dominque gets wet (modus ponens)
Therefore its not raining (modus tollens)
Tricky since someone could just dump a bucket of water on her
Example 2
If i live in vancity
Then i live in BC
Evidence: i live in vancity
Conclusion: therefore, i live in BC
Or i do not live in BC, therefore, i do not live in vancouver
Or i live in BC, therefore, i do not live in vancouver
I dont live in vancouver, but i do live in BC
Wason Four Card Problem (1966)
To determine which cards needed to be flipped over to test the rule
One side had number and other had letter
If vowel then it was an even number
7 would go against the rule
E and 7 would need to be flipped
People have the most difficulty with this
Becomes easier when stated in terms that you can actually think of
Concrete terms will help
Agrees with the schema, a permission schema which agrees with the rules of society
Drinking is allowed to certain individuals in society
16 yr old would invalidate the question, drinking beer would also
Falsification principle:to test a rule, you must look for situations that falsify the rule
* Most participants fail to do this
* When problem is stated in concrete everyday terms, correct responses greatly increase
Wason Four Card Problem (1966)
To determine which cards needed to be flipped over to test the rule
One side had number and other had letter
If vowel then it was an even number
7 would go against the rule
E and 7 would need to be flipped
People have the most difficulty with this
Becomes easier when stated in terms that you can actually think of
Concrete terms will help
Agrees with the schema, a permission schema which agrees with the rules of society
Drinking is allowed to certain individuals in society
16 yr old would invalidate the question, drinking beer would also
Falsification principle:to test a rule, you must look for situations that falsify the rule
* Most participants fail to do this
* When problem is stated in concrete everyday terms, correct responses greatly increase
Permission schema: if A is satisfied, B can be carried out
* Used in the concrete versions * People are familiar with rules
Inductive Reasoning
Reasoning that is based on observation
* Generalizing from observations of specific cases to more general conclusion
* Reaching conclusions from evidence
* Conclusions are suggested only, with varying
degrees of certainty.
* Strength of argument
* Representativeness of observations * Number of observations
* Quality of evidence
Used to make scientific discoveries
* Hypotheses and general conclusions
* Usedineverydaylife
* Make a prediction about what will happen based on observation about what has happened in the past
Inductive Reasoning
This is the opposite of deductive
Particular observation and determining the general conclusion
Based on evidence
We are trying to figure out what is being suggested
We still want as much certainty as possible and there are things that will strengthen the argument
You want a representatives sample
E.g., all crows are black in particular city
But if you only have the crows in one city, you cannot generalize all crows to the ones you have seen
Need higher amount of observations, the stronger the conclusion will be
Is there multiple sources that point to your conclusion
Such as articles with similar observations
Essentially what is used in science
Constantly looking at certain situations, taking these data points and taking hypothesis and determining general conclusions
Everyday, you have these expectations in the world that things will behave the way you expect, these are the inductions
Accounts of Reasoning/Decision Making
Normative: how things ought to go; what people should do
Descriptive: how things are; what people actually do (do)
Heuristic: a short cut; a strategy that risks error to gain efficiency (speed)
Algorithm: a guaranteed route to an outcome, which may be more tedious and effortful
Normative is how things should work in society
Descriptive is what people actually do
Heuristic is a short cut that allows us to reach a decision faster
Algorithm is sitting down and actually thinking about what we actually need but is very tedious
Kahneman and Tversky
pioneered the research on judgment under uncertainty
* emphasized the heuristics we use to process evidence and make judgments
* early work done at Hebrew University of Jerusalem
This work started in the 70s at University of Jearusalm
Proposed theory about decision making called prospect theory
Largely done in collab with Tversky
We typically rely on heuristics since we can’t get all the information and even if we could, it would take forever
Representative Heuristic
assume that each member of a category is representative of that category (like the prototype?), and has all its traits
* also assume the reverse—if something has a lot of the traits of a category, it probably belongs to that category
* be willing to draw conclusions from a quite small sample: “seen one, seen ‘em all”
Representative Heuristic
Argued that when we think about members of categories, we make the assumption that every member is like everyone else in the group
We also make the opposite as if something has alot of the traits of the category, it may be apart of it
If you have a situation where you are seeing something, you have a lot of info of that object since you are assuming that objects category therefore you know all the information about that item
Coin flip example: coin is random, assuming that this is random event and there are 2 possibilities, when things are random, we expect them to change
If you flip a coin 8 times, any of these 3 possibilities are equal due to chance
Each throw is independent
Gamblers Fallacy: feel like random events, the next thing should be a particular outcome
E.g., flipping a coin 4 times and 3 times it landed on heads, bet on last one, most will bet for a tails
People will think tails is more likely even though this isn’t true
Kahneman and Tversky (1973)
Talked to a bunch of students as samples in different groups
1 group: given a bunch of majors that they may be pursuing, what probability will students be in each category
Were given a prompt about a person
Asked questions about his similarity to other grads, likely a grad student, and a personality sketch of highschool and likelihood of being a student
More likely to be seen as comp sci or engineering student, likelihood highest as that as well
This proved that people were judging, people assumed his characteristics to people who were probably inclined with those majors
Even happened in the final group, even though things may have changed, people still said that he was more likely to be a comp sci/engineering student since he was similar to them
His test carried a lot of weight into the future
E.g., linda being judged as a feminist accountant doesn’t make sense since all accountants have the same category
This is the conjunction fallacy: 60% of being accountant 20% feminist, 12% of being feminist accountant
Probaility of conjoinment of 2 events is the multiplication of the two probabilities
Hospital birthrates: probabilities of which gender is born more
Large vs. small
10 births vs. 100 births
Any given day, fluctuations can happen so 10 is better and much more likely
Kahneman and Tversky (1973)
Likelihood judgments closely mirrored the similarity judgments rather than base rate
* How likely is it that Tom is a comp. sci. student versus humanities student?
* 95% pick comp. sci.
* base rate estimations by other subjects had humanities as 3 times more likely
* Even when based on projective tests that are unreliable, and things change from high school to grad. school
English
More r words or words with r as third letter?
Twice as many words with third r
Why do people think first one is right?
Fairly easy to generate words with r and harder to generate words with third r
Hence why we use availability heuristic