|> Skills||> Self-Test|
Effective decision making involves more than just identifying logicial fallacies when listening to a debate. Here are a few questions where you can test your skill. Most of the questions are multiple-choice. To select your choice, click the radio button to the left of your preferred answer.
Questions 2 through 7 are adapted from Judgement in Decision Making by Max Bazerman (New York: John Wiley & Sons, 1990). The very last question is from The Power of Logical Thinking by Marilyn Vos Savant (St. Martins Press, 1997).
Following the questions I have provided answers and explanations. Note: This is not computer-scored test so there is no button to press to calculate your results. You need to read the answer section below to understand why particular answers are considered better than others.
|a. Linda is a teacher in an elementary school|
|b. Linda works in a bookstore and takes yoga classes|
|c. Linda is active in the feminist movement|
|d. Linda is a psychiatric social worker|
|e. Linda is a member of the League of Women Voters|
|f. Linda is a bank teller|
|g. Linda is an insurance salesperson|
|h. Linda is a bank teller who is active in the feminist movement.|
It is claimed that when a particular analyst predicts a rise in the market, the market always rises. You are to check that claim. Examine the information about the following four events (cards):
Card 1 Prediction:
Card 2 Prediction:
Card 3 Outcome:
Rise in the market
Card 4 Outcome:
Fall in the market
You currently see the predictions (cards 1 and 2) or outcomes (cards 3 and 4) associated with four events. You are seeing one side of a card. On the other side of cards 1 and 2 is the actual outcome, while on the other side of cards 3 and 4 is the prediction that the analyst made. Evidence about the claim is potentially available by turning over the card(s). Which cards would you turn over for the evidence that you need to check the analyst's claim?
A company has recently acquired a firm which has had financial difficulties. The new owner is considering refurbishing two old factories. $10,000,000 has been raised for the project. Here are the alternatives. Indicate which you would choose:
Last question. Be very careful of this one. It has fooled many people who have phD's in math!
Suppose you're on a game show, and you're given a choice of three doors. Behind one door is a car and behind the others are goats. You pick a door--say number 1--and the host, who knows what's behind the doors, opens another door--say number 3--in order to reveal a goat. He says to you, "Do you want to pick door number 2?" In order to win the car, is it to your advantage to switch your choice of doors?
If you carefully compare questions 1 and 8, you will see that the situation and alternatives are exactly identical. Only the wording differs.
In question 1, choice "a" is described as a situation where half the jobs are lost. In question 8, choice "a" is described as a situation where half the jobs are saved.
When thinking of a situation as a potential loss, people are willing to take greater risks. But if alternatives are viewed as gains, then people tend to avoid risk. Thus, many people will answer "b" for question 1, but "a" for question 8. Yet the odds and stakes in both questions are identical; it is illogical to answer them differently.
The consequence of this human tendency is this: People can often be manipulated to make a particular choice by someone who is skillful in "how they ask the question".
If you answered questions 1 and 8 the same way (both "a" or both "b") then give yourself one point.
If you chose "a" and were fairly confident about that, score -1 (minus one). The correct answer is "b".
When trying to solve this problem, people typically try to think up words that begin with "r"; then they try to think up words that have "r" as the third letter. Typically it is easier to think of words that begin with a given letter, so they can recall more of those words. Thus they suppose that there are more words that start with "r".
There are various errors that people make because they base their judgement on recall rather than statistical fact. For example, a person can easily assume that airline travel is more risky than automobile travel, merely because they have seen more airline accidents reported on the news. (But as we all know, statistics reveal that per km traveled, airline travel is safer.)
If you chose "a" you were wrong. How many jobs do you suppose that there are in this world managing arts organizations? Even if Mark preferred such a job, the odds of him actually finding one are very low. Consulting jobs, on the other hand, are much more common occupations for MBA graduates. (To answer this question correctly, you need to be careful not to let extraneous details deter you from considering the odds.)
If you chose "b", add one point to your score.
Answer "b" is correct.
Because the cars are identical, a very large sample should reveal that on average the drivers find no difference in the cars. In the small sample ("B"), there is greater chance of random variations due to the personalities or other quirks of the drivers. So even though the test with the small sample is run for more days, it will have more frequent swings from the norm.
People often make the mistake of making judgements based on anecdotes or a few isolated cases, while ignoring facts based on larger volumes of data.
If you chose "b", add one point to your score.
The manager's thinking is incorrect. There are a couple of situations that may exist here:
a) There is nothing wrong with the sales directors. It is the lousy work environment and incompetent manager that is taking perfectly good candidates and making it impossible for them to do their jobs well. The manager apparently doesn't see the error of his ways and is about to ruin his fifth candidate.
b) The other possibility is that there is no systemic cause of the sales directors' poor performance. In that case, each selection can be thought of as a random selection (because the candidates will become available at random as they graduate or leave other jobs). The outcome of one random selection is not dependent on previous events.
Regardless of which of situations "a" or "b" are true, the manager's thinking is incorrect: there is no greater likelihood of the next candidate being better.
If you recognized this, add one point to your score.
The more specific your guess is, the less likely it is to be correct.
For example, if it is true that "Linda is a bank teller who is active in the feminist movement", it is also true that "Linda is a bank teller". If you are right on the more specific item, you are guaranteed with 100% probability to be right on the more general item. The reverse, however, provides no such guarantee.
Obviously then, you should rate "bank teller" as more likely than "feminist bank teller". But when people answer this question, they often fall into the "conjunction fallacy"; they mistakenly pick the most descriptive items as being the most likely.
If you rated "h" as more likely than "f", subtract 1 point from your score. Ignore the rest of the items.
You need to see the other side of cards 1 and 4.
Remember, that the analyst only claims to be right when he predicts a rise in the market. He makes no claim about his accuracy in predicting a fall in the market.
If the claim is correct, the other side of card 1 must be a "rise" in the market. If not, his claim is disproved.
The opposite side of card 2 is irrelevant, because he makes no claim about his accuracy on predicting a "fall".
The opposite side of card 3 is irrelevant. If he had predicted a rise and the rise occurred, he would be correct. But if he had predicted a fall and the rise occurred, his claim would still be correct. (Remember again, that he makes no claim about his accuracy in predicting a fall.)
The opposite of card 4 is important. If he had predicted a rise when this fall occurred, that would prove that his claim was false.
Most people in answering this question fail to check card 4. They seek only evidence to confirm the claim, but do not seek evidence to disprove it.
That is a common human error. People often seek to confirm beliefs (and especially if they hold those beliefs personally!) but they don't often think to check for disconfirming evidence.
Add 1 point to your score if you chose cards 1 and 4.
You don't need to score this item. (See the answer to #1.)
There is an advantage to switching.
This is counter-intuitive. After the door is opened, there are two doors remaining. Because you tend to think of this as a new, random choice, you might suppose that the odds are 50/50 of the prize being behind either door.
However, if you enumerate all the possibilities, you will see that the odds are not 50/50.
Consider the chart below. The first three rows show the three possible placements of the prize. You have chosen door #1 as the first choice. Once one of the goats behind door 2 or 3 is revealed, you switch to the whichever of doors 2 or 3 is unopened. As you will see, the "switch" strategy would cause you to win in two out of three cases:
|Door 1||Door 2||Door 3||Result of switching|
Now consider the following chart. Again we show the three possible placements of the prize. But this time you follow a different strategy. The host opens one of doors 2 or 3, but you don't care. You have chosen door #1 initially, and you choose to stick with that choice. As you see below, this would cause you to win in one out of three cases:
|Door 1||Door 2||Door 3||Result of staying|
The two tables indicate that it is a better strategy to switch (because the odds of winning are better). Exactly why is hard to explain, but in essence the host has given you some information when he opened the door. Thus, the second choice is not an independent random event as you may have originally supposed.
When the author of this particular puzzle (Marilyn Vos Savant) revealed the answer, she got a large volume of letters telling her that she was wrong. Many people's intuition on the matter was so strong that they simply wouldn't accept her explanations.
As a last resort to convince her skeptical readers, she published a challenge for people to try it themselves as an experiment. She suggests that you might test this quite simply as follows: Get someone to act as the host with three playing cards (for example, two jokers for the goats and an ace for the prize). Try this a hundred times following each strategy and add up the results.
She reported that many school teachers took up the challenge, having their students try the experiment as an in-class exercise. The results: exactly as she had predicted!
Give yourself 1 point if you got this right!
A perfect score on the above test is 6. The worst possible score is -2 (minus 2).
The score itself doesn't tell you whether you are smart or stupid. Very intelligent people can make mistakes if they don't know what mistakes to avoid. Sometimes even when people are very familiar with logic and statistics, they don't put this information to practice in daily decision making (and hence they tend to make the same errors).
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