Langston, Cognitive Psychology, Notes 13 -- Reasoning and Decision Making

I.  Goals.
A.  Where we are/themes.
B.  Logic.
C.  Heuristics.
D.  Probability.

II.  Where we are/themes.  In this unit we'll turn our attention to some of the tasks that people think of when they think cognitive psychology.  How do you think and reason?  My main focus will be on problems in thinking (problems that arise due to the unfortunate interaction of normal cognitive activities).  There are three areas we'll consider:
A.  Logic:  How people fail to use valid logic when thinking (just a taste of this, but it fits nicely with the other areas where we've seen formal logic run into trouble as a model of cognition).
B.  Heuristics:  How little short-cut rules lead to problems when applied to reasoning.
C.  Probability:  How a lack of appreciation for simple concepts from probability can lead people to make bad decisions.
By the end of the unit, you should have some idea of the way people think, and how the way people think can lead to problems.

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III.  Logic.  We'll just consider one aspect of logic:  Conditional reasoning.
A.  The situation is this:  You have a hypothesis (an if-then statement) and you want to test it.  Here's an example from your text:  If there's fog, then the plane will be diverted.   How can we determine if this statement is true?  There are four tests we can perform:
1.  Present a situation where there's fog.
2.  Present a situation where there's no fog.
3.  Present a situation where the plane's been diverted.
4.  Present a situation where the plane has not been diverted.
For each of these tests, we could get a particular outcome and then determine whether or not the if-then statement is true.  Let's have some examples.  For each of the four situations described below, write T or F to indicate whether this evidence leads you to conclude that the hypothesis is true or false:
1.  Present a situation where there's fog and find that the plane is diverted.
2.  Present a situation where there's no fog and find that the plane is diverted.
3.  Present a situation where the plane's been diverted and find that there's no fog.
4.  Present a situation where the plane has not been diverted and find that there's no fog.
Here's the catch:  Only two of these tests involve valid logic (so only two of these tests can have any bearing on whether or not the if-then statement is true).  That means that the correct answer to two of the problems above is "I don't know."  You probably didn't write that.  So, go back now and identify which two will have no bearing on the if-then statement.
You probably had a hard time doing that.  The correct answers are:
1.  T
2.  I don't know
3.  I don't know
4.  T
Why do I say this?  There are technical reasons based on logic, and those are presented as clearly as I can present them in my research methods notes.  But, I think we can think our way through it.  In order for statement 2 to be a valid test I would have to assume that the only way a plane could be diverted is if there's fog.  That is obviously not true.  Lots of reasons could cause a plane to be diverted.  For statement 3, I would have to make the same assumption.  In reality, neither of those tests has any bearing on the if-then statement.  Contrast that with statement 1.  Is fog a sufficient reason to divert a plane?  Given the results of our test, the answer is yes.  In 4, we're also testing whether fog is sufficient to lead to a diverted plane.
To put it another way, in the if-then statement I said fog will cause the plane to be diverted, I didn't say the only way for the plane to be diverted was for there to be fog.
B.  Problems:  People aren't very good at conditional logic problems.  Part of the trouble comes from the seductive nature of the invalid logic.  For example, imagine I've provided the hypothesis

if you smoke, then you will get cancer

If someone says:  "That can't be true, my uncle got cancer and he never smoked" or that person says "That's not true, my uncle never smoked and he got cancer" those could both sound like good arguments if you're not thinking carefully.  But, again, I only said if you smoke, then you'll get cancer.  I didn't say the only was to get cancer was to smoke.  People who get cancer aren't really who I'm talking about, I'm talking about people who smoke.  One thing that contributes to making the invalid logic seductive is illicit conversion.  That happens when people reverse the if and then parts (so it would be something like "if you get cancer, then you smoked").  Obviously, once you turn the parts around, the "tests" presented above about our hypothetical uncle become valid.  The important thing to remember is that the order of the parts in the if and then are not arbitrary, and that order has to be maintained.
Confirmation bias is a special problem for conditional reasoning.  People are much more likely to attempt to confirm their hypotheses than they are to disconfirm them.  That leads to a lot of errors in conditional reasoning.  Try this problem:  There are four cards below.  If there's a letter on one side, there's a number on the other.  Which two should you choose to test "If there's a vowel on the front, then there's an even number on the back?"

The correct two cards are "A" and "9."  Some data from your book (I'm guessing this is Wason & Johnson-Laird, 1972):  33% turn over only "A."  That shows a confirmation bias because A is a vowel, if there's an even number on the back, it confirms the rule.  An additional 46% turned over "A" and "2."  This is an error because 2 has no bearing on the situation (it is a sort of illicit conversion, I never said even numbers needed vowels on the other side).  However, choosing 2 does fit a confirmation bias.  It's like people think something along the lines of "If there's a vowel on the other side of 2, that will prove it true."  The right combination is "A" and "9."  Only 4% did this.  Turning over 9 could serve to prove the hypothesis false, people rarely seek negative evidence.

CogLab:  We'll look at our data from the Wason selection task.

There is a way to make people do this task correctly.  In fact, I can present you with a problem that 100% of you will get correct, and I could guarantee that even without providing you with all of the information you've already seen.  The rule is:  If you're under 21 then you can't be drinking alcohol.  Here are four people at a party:

 Bob 18 yrs. old Carol drinking a Coke Jerry 43 yrs. old Emily drinking beer

You're the vice squad.  If you know an age, you can check the beverage.  If you know the beverage, you can check the age (the beverages are exactly as listed, with no secret ingredients).  Who do you need to check to see if the rule is being followed at this party?
Everyone can tell immediately that it's Bob and Emily.  Why is this so easy when the other problems are so hard?  This problem has a context.  Additionally, this problem involves detecting cheaters.  As we'll see in the last unit, there's a reason from evolutionary psychology for why we should be particularly good at problems that involve detecting cheaters (even if we stink at all of the rest of the problems).  That might make a nice reaction paper discussion.
One last bit for this.  Confirmation bias can lead to all sorts of problems.  Some examples of how it can lead research awry are in my methods notes.  In the real world, confirmation bias can lead to the development and maintenance of prejudices.  In fact, the interaction between confirmation bias and the rules we discuss below can make it almost impossible to overcome prejudicial thinking.  For example, a lot of the early research on gender neutral pronouns demonstrated that when he was used as a generic pronoun it actually led to thoughts of men.  This was true even when the person being described was in a stereotypically feminine profession (for example, "if a schoolteacher wants to get ahead he should be friendly to parents") (MacKay & Fulkerson, 1979).  One problem this causes is that it plays into people's confirmation biases in situations where a pre-existing stereotype exists (engineer..he confirms people's expectations).  When you combine that with the fact that she has often been used as the generic pronoun for stereotypically feminine professions (like secretary) it can make it very hard to change people's stereotypes.  If that translates into behavior ("we need to hire a new girl for the office" biases against men and "let's get the best man for the job" biases against women) it could be a problem.  Add this bias for information that fits with the confirmation bias to the heuristics below, and there could be more trouble.

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IV.  Heuristics.  Outside of logic, what other thinking generalities can we uncover?  There are two basic ways to work out the solutions to problems.  the algorithmic method is to use a set of rules to methodically arrive at a conclusion.  The best way to see this is to multiply 365 by 48.  You go step by step through the problem applying the rules for multiplication.  You'll always arrive at the right answer (provided your math is correct).  Unfortunately, this is impractical in a lot of real-world tasks.  Instead, people tend to rely on a set of rough-and-ready rules that can apply to a variety of situations.  These rules are called heuristics.  Provided that the information going into the application of a heuristic is correct, the shortcuts will produce relatively sound answers.  Unfortunately, the information going into heuristics is frequently incorrect (often due to confirmation biases), making the results suspect as well.  Let's consider some examples of heuristics (I'm also lumping in other characteristic modes of thinking).
A.  Representativeness:  The more something resembles your prototype of its population, the more likely you are to assign it to that population.  This can lead you to make some errors in reasoning.  A simple example from the book:  Which of these sequences is more likely to have been produced by flipping a coin six times in a row, HHHTTT or HHTHTT?  Most people choose the second one, but they're equally likely.  People choose one on the basis of which one looks more random, not on the basis of probability.
This example is related to a tip that will help you really appreciate the odds of winning the lottery.  Imagine playing 1, 2, 3, 4, 5, 6.  Does that seem like a really unlikely combination?  If you think to yourself "there's no way that combination could win," you've got a chance to save yourself some money playing the lottery.  All combinations are equally likely.  For example, in the UK lottery with 49 numbers and you pick six, there are 13,983,816 combinations, each has a 1/13,983,816 chance of winning.  If you think choosing a sequence that looks more random increases your chances, you're fooling yourself.  Whenever I play keno (which I do for the fun of tormenting my fellow players and not from the expectation that I'll win), I like to choose "unlikely" looking sequences.  It makes people crazy to see me throwing my money away.  All the while they're trying to come up with a "random" sequence that has a better chance (or falling back on a belief in magic and trying to read the keno vibes in the air).
Here are some tips based on other people's faulty thinking that will help you maximize your expected value in a lottery play (which is not entirely dependent on the odds).  The idea is to pick numbers nobody else would pick so if you should be so fortunate as to win you won't share your prize.  First, a lot of people think of 1, 2, 3, 4, 5, 6 as a good choice because "nobody else will think of it."  It's representative of a choice nobody will play.  Therefore, it's a bad choice to make.  Another strategy that's representative of "numbers other people don't pick" is to choose all numbers higher than 31 (numbers under 32 are possible birthdays, which a lot of people play).  But, since a lot of people do this, and there are usually fewer numbers over 31, you're actually hurting yourself.  One last thing (it's not really representativeness, but it's related to the lottery):  Avoid any strategy with "due" numbers (as in "42 hasn't come up in 10 draws so it's due").  If there's any possible bias in the system it's that a slight physical defect in one of the balls or the mechanism helps or hurts a particular number.  If 42 comes up 10 draws in a row, there's a reasonable chance that the 42 ball is defective and more likely to be picked, so go with it.  If it never comes up, the chances are it's defective the other way, so you would be insane to pick it because it's "due."  Your best case scenario when a ball never comes up is that it's just a result of random chance, which is the way it's supposed to work anyway.  (Lottery information from Eastaway, R., & Wyndham, J., 1998, Why do buses come in threes:  The hidden mathematics of everyday life).
The representativeness heuristic can be a large factor in perpetuating stereotypes.  Combine it with confirmation biases and you will notice examples which are representative of the stereotype, store those away, and use them for further processing.  Think about astrology.  Cancers (like me) are supposed to be moody and crabby.  If you know this, you might take note of my behavior when it seems representative of the cancer stereotype, and thereby reinforce your belief in the accuracy of astrology.  Behavior in non-cancers that is representative of cancers is less likely to be noted, and so unlikely to shake your belief in astrology.  This is one of the problems with heuristics.  Once a little bias gets into the system, the results aren't likely to be very successful.
B.  Availability:  If I ask you how likely something is, you try to think of an example.  The easier it is to think of an example, the more likely you say it is.  For example, what's the probability of a batter reaching first base by getting a hit?  By having the catcher drop a third strike?  You should feel availability taking over by trying to think of an example of each and using the ease of getting an example to make your estimate.
Your book's example:  Are there more words in English that start with 'k' or that have 'k' as the third letter?  You'll start trying to think of words, and conclude that starting with 'k' is more common.  That's because you organize your mental lexicon around first letters and not third letters.  So, it's easier to search that way and you get more results.  As you probably guessed, there are more with 'k' in the third letter.  Anything that affects the ease with which you think of something will affect availability (maybe as an exercise you should try thinking of influences now):
1.  Frequency:  More frequent = more available.  Again, if you put in confirmation biases then what you encode more frequently may not reflect the population, making your estimate inaccurate.
2.  Familiarity:  More familiar stuff is easier to recall and so more available.
3.  Vividness:  More vivid stuff is easier to recall, so more available.  This is one reason why flying seems more dangerous than driving.  Vivid plane crash stories are easy to retrieve, so it seems like a crash is more likely (also plane crashes get more coverage, so frequency and familiarity come into play).
4.  Recency:  More recent stuff is easier to retrieve.

Demonstration:  I have a powerful example of the way availability can make something really simple seem remarkable.

C.  The simulation heuristic:  Ease of simulation will affect people's judgments.  The example in your book describes two men who are on flights at the same time, are equally delayed getting to the airport (in the same car), and both arrive 1/2 hour after their planes were supposed to leave.  However, when they arrive they find that Mr. Crane's flight left on time, but Mr. Tees' flight was delayed, and left just five minutes before they arrived.  Who's more annoyed?  Most people think Mr. Tees is more annoyed.  The reason is that it's easier to simulate how they could have been just five minutes earlier than a half hour earlier.  Some influences:
1.  Undoing:  When people simulate undoing an event, it's more common for them to file down an unusual detail to make it more typical (called a downhill change) than it is to add a new detail (an uphill change).  It's easier to make an event more like the typical script than to make it less like that script.
2.  Hindsight:  Once you know the outcome, it's easier to simulate how that outcome happened.  That makes it seem more likely, and can even make you change how you remember your predictions.  For example, if someone on a game show decides to go for it and misses, you might re-simulate and decide that it was obvious they should have stayed.

Demonstration:  I have a few simulation examples.

D.  And the rest:  Here are some more influences on thinking.
1.  Anchoring and adjustment.  Do the multiplication problems in the demonstration.

Demonstration:  There will be a multiplication problem to perform, but you will only have a short amount of time to do it.  One half do the first problem.  The other half do the second problem.  Compare answers.
Another:  You get one of two lotteries.  The first is to draw a red marble from a bag with 50% red and 50% white.  The second is to draw seven reds in a row from a bag with 90% red and 10% white (we'll replace the marble drawn each time to keep the odds the same on each draw).  Which gives you the best chance of winning?

Anchoring and adjustment is related to the fact that people start from the first part of the problem (the anchor) and then make adjustments from that when heuristics take over.  If the anchor is low, people tend to guess low.  If the anchor is high, people tend to guess high.
2.  Set/fixedness:  We have a lot of experience with the world, and this usually influences our behavior, even when it's better if it doesn't.  Set:  An example of this is the classic 9-dot problem.  If you ask people to solve it, they usually get stuck because they don't think outside of their set, but that's what the solution requires
Fixedness:  We come up with a solution that works and keep applying it in the face of simpler solutions.
Functional fixedness:  We can't stop thinking of an object in its usual function, and that hinders finding the solution.

Demonstration:  One for each above.
For set, connect the nine dots below by drawing four straight lines.

For fixedness your job is to do some jug problems.  Basically, you're given three jugs of various sizes and you're supposed to get a particular amount using those jugs.  Solve each of the problems in the table below (from Myers, 1995):

 Problem Jug A Jug B Jug C Target Amount 1 21 127 3 100 2 14 46 5 22 3 18 43 10 5 4 7 42 6 23 5 20 57 4 29 6 23 49 3 20 7 15 39 3 18

For functional fixedness imagine this situation:  You're in a plane and it crashes in the desert.  You're miles from help, and you have no food and water.  All you have is a parachute, a pocket mirror, a compass, and a map.  What's your most important asset?

3.  Confidence:  We usually have very poor calibration of comprehension (knowledge about how well we did on a task).  This applies to decisions as well.  You can test that by answering this question:  “Hirsute probably means ‘really hairy’ or ‘habitually late.’”  (Choose one.)  Generally, people are more confident of their answers to these questions than they are correct.  The more confident, the more they overestimate their ability.
4.  Belief:  If I get you to state a belief first, it’s a lot harder to get you to change your mind.  So, if I say to you “it’s much safer to be in the back of a plane if there’s a crash, why do you think that is?,” you can probably make something up to account for it.  Then, if I give you opposite evidence, it will be really hard to persuade you to change your mind.  Better yet, if I tell you that my evidence was just made up, you’ll still cling to your incorrect belief based on that information.
5.  Framing:  How you ask the question will impact how people feel about it.  So, if I tell you that 10% of people who eat a particular kind of Sushi keel over and die, or I tell you 90% come through unharmed, you’ll think it’s more dangerous in the 10% die case (I’ve framed the problem negatively).

CogLab:  We'll look at our results from the decision making demonstration.

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V.  Probability.  One last thinking topic has to do with people's generally poor comprehension of the laws of probability.  This generally leads to a lot of thinking errors.  (Most of this came from an excellent book called Using Statistical Reasoning in Everyday Life.  The book will be published by Wadsworth this summer.  Unfortunately, I don't currently know the author's name.  If you've ever wondered why you need to know anything about statistics, this book would be an excellent choice.  What is below is just a taste.)

CogLab:  We'll talk about the Monty Hall problem as an interesting example of probability.

A.  Conjunction.  How do you combine the probabilities of a bunch of independent events?  Try the example in the demonstration.

Demonstration:  Estimate your likelihood of avoiding all of the causes of death on the overhead.

Generally, people overestimate.  Even though each number is high (the odds of avoiding a car accident are 99%), their conjunction is not so high.  To compute correctly, multiply all together.  Note how anchoring and adjustment played into your estimate.  Others might also have been involved.  The lack of ability to correctly predict the probability of conjunctions can have implications for real life.  For example, there's a 90% chance I'll finish the paper on time, a 90% chance I'll finish the take-home test, and a 90% chance I'll get my chores done, what's the chance of getting all three done?  (It's not 90%.)

Demonstration:  Which fact about Mr. F seems more likely?  Try Linda the bank teller.

Basically, the conjunction between two events has to be smaller than the likelihood of either alone (or at the extreme the same size).  Most people use heuristics to estimate conjunctions (like representativeness for Mr. F) and overestimate the conjunction.  Use a Venn diagram to illustrate this.  We can also consider the story about Linda.  You know the rule now, but 85% of the people reading about Linda went for the conjunction fallacy.  Why?

CogLab:  We'll look at the results from our typical reasoning demonstration.

C.  The power of chance.  Now that you know the rule, try the stockbroker example.

Demonstration:  What are the odds of picking the direction of change in a stock price 10 weeks in a row?

If you use the correct conjunction rule, you might say the odds aren't too high.  But, if you imagine that the stock pickers are just flipping a coin, the odds are that one of them will get all 10 right.  In other words, it's very likely to happen just by chance.  The odds of one particular person getting it are low, the odds of someone getting it are not.  It's sort of like the lottery.  Your odds aren't so great.  But, the odds that someone will win are pretty high.  In other words, just because something is very improbable doesn't mean nobody will achieve it if enough people are in the game.  I guess the message is not to be too impressed with something that could have happened just by chance.
D.  Amazing coincidences.  The example above is related to amazing coincidences (like dreaming about being in a car crash and then crashing).  Or, the eerie similarities between identical twins raised apart.  Read the description in the demonstration.

Demonstration:  Description of the similarities between two women.

These women aren't twins.  They were randomly paired in a study by Wyatt, Posey, Welker, and Seamonds (1984).  They found that random pairs also produced a bunch of similarities when they were compared on a lot of dimensions.  The point is that the odds of a particular coincidence (like political leanings) might be low, but the odds of some coincidence out of the millions of possibilities are actually quite high.  It's not surprising if twins reared apart are similar in some way.
You could also relate this to fortune telling (segue back to Eastaway and Wyndham, 1998).  It would be impressive if a fortune-teller made a very specific prediction that came true ("you will meet an old friend on the street this week").  If a general prediction came true ("something interesting will happen this week"), that's not impressive.  It's especially not impressive given the heuristics and confirmation bias discussed above.  Let's consider a prediction.  In a room with 23 people, I predict two will have the same birthday.  If I'm proven correct, is that impressive?  Naive intuition might think it is (with 365 days to choose from, the odds of two out of 23 having the same birthday seem low).  However, the odds are actually 51%.  You can calculate them by using the conjunction rule.  Eastaway and Wyndham show it's easier to do this by calculating the odds of not having two birthdays the same.  For 23, it's 365/365 X 364/365 X 363/365 X ... X 343/365.  That's 49%.  So, there's a 51% chance of two birthdays being the same.  What would be more impressive is if I picked two people and said they would have the same birthday.  Then my odds are 1/365, which is a much more difficult prediction to get right by accident.  So, even though the situation feels similar, one is actually a lot more likely.
I mentioned the heuristics above, how do they come into play?  They help you take note of the amazing things that do happen and disregard the amazing things that don't happen.  They also help to determine what counts as amazing.  Eastaway and Wyndham (1998) point out that the odds of George Washington being born on February 22 and Queen Victoria being born on May 24 are 1 in 130,000.  In other words, those two birthdays happening are very unlikely.  But, it's not an impressive coincidence because you attach no significance to it.  A lot more on coincidences can be found at Skeptical Inquirer.  I think the section on Lincoln/Kennedy coincidences is particularly relevant for the discussion in this section.
E.  Certainty.  It's possible to know with relative certainty what someone will do in a situation.  This can be based on common reasoning errors and the heuristics above.  If people are relying on intuition to interpret how remarkable events are, then they will be easily tricked.

Demonstration:  I have a math problem for you to try.  I think you will all get the same sum, which I will tell you once you've had a chance to do the problem.

There's a common mistake that leads to this result.  This one's not 100% certain, but it's very likely.  You're probably not too impressed, however.  Let me do some magic tricks.

Demonstration:  I have a couple of magic tricks.

Were these impressive?  I won't spoil the show by telling you how they're done, I'll just let you know that they absolutely had to work out.  My point is this:  It shouldn't impress you when someone does something that had to come out the way it did.  Not having an appreciation of math (for my magic) or psychology (for most of the rest of this unit) can lead you to be overly impressed.  If there's time, I'll wrap up with a very impressive magic trick relying entirely on psychology.  Let's see if you can figure it out.

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Cognitive Psychology Notes 13
Will Langston