1. Belief Irrationality

2. Outline Perception of Information
Framing effect, Anchoring bias, Availability bias
Optimism and Overconfidence
Representativeness
Belief Updating
Cognitive conservatism and Confirmation bias

3. Perception of information
Psychologists believe that the human mind is limited in its ability to focus and process all the incoming information.
Framing effect. This consists in analyzing problems without paying attention to their wider context or even in an extremely isolated way.
Tversky and Kahneman (1981, 1986) showed that decision makers may display changing preferences and make radically different choices depending on the way in which the same, logically identical problem was presented to them.

4. Perception of information
One version of the framing bias is the so-called money illusion.
Another instance of framing is mental accounting in which individual aspects of financial decisions are perceived in isolation (Thaler, 1985, 1990, 1999).
What may be especially important is separate accounting for profit and loss because decision makers usually have different preferences depending on whether they relate to gains or losses.

5. Perception of information
Diagnostic Question. p.A1-12
Psychologists have found that when faced with the preceding question, the majority of people choose the risk-free A over risky B, but choose the risky D over the risk-free C.
Aversion to a sure loss: Instead of accepting sure losses, people are prone to accepting risky, actuarially unfair prospects. (Psychological studies have demonstrated that many people would choose D over C even if the expected loss in D were more than $7,500.)

6. Perception of information
Let compare the choice (A,D) with (B, C), it results that (B, C) dominates (A,D). (B,C) provides more gains and smaller losses than (A,D).
This is called the “Narrowing framing bias”. People who engage in narrow framing ignore their overall return-risk profile.
Decision problems are often framed opaquely rather than transparently, and opaque framing often induce people to make the wrong decision.

7. Perception of information
Framing effects pertain to the manner people describe the information involved in decision tasks. It means that how the tasks are framed can affect decisions.
Think another question: would you be willing to take a 25 percent chance of winning $7,500, but a 75 percent chance of losing $2,500?
Note this question is an alternative frame of the second decision in p. A1-12: The alternative frame is between C (a risk-free $0) and D (25% of a $7,500 gain, and 75% of $2,500 loss).

8. Perception of information
When framed in this alternative form, most people answer no, judging the potential gain of $7,500 does not justify the 75% chance of losing $2,500. The point is most people accept the risk when the problem is framed to highlight the sure loss and refuse to accept the risk when the problem is framed to ignore the sure loss.

9. Perception of information
Anchoring bias. When people try to estimate a parameter or quantity, they start their thought process by adopting a value that is sometimes completely arbitrary (Kahneman and Tversky (1974)). There is overwhelming empirical evidence to suggest that people become very strongly attached to the initial value (the “anchor”) and are not able to adjust their final estimates correctly.
Diagnostic Question (p. A1-10).The first question is intended to provide a context for the way people think about the second question.

10. Perception of information
The issue here is whether people arrive at their prediction of the year of Attila’s European defeat by beginning with X (anchored number) and adjusting up or down.
Discussion. A regression of prediction year on the last three digits of telephone number has a slope coefficient that is about 0.75, which is significant at the 5 percent level.
Another experiment. In the experiment, subjects were asked to estimate the percentage of African countries in the United Nations.

11. Perception of information
First, respondents were requested to spin a “wheel of fortune” to generate a number between 0 and 100.
Next, they had to say whether they believe the percentage of African countries in the UN is lower or higher than the randomly selected number. Then they were asked to estimate the actual percentage of Africa’s representatives among all UN members as precisely as possible.
It turned out that the initial, totally arbitrary anchor value significantly influenced participants’ responses.

12. Perception of information
Availability bias. The tendency to overestimate probabilities or frequency of events we can remember easily (Tversky and Kahneman, 1973; Taylor, 1982).
Trying to estimate the probability of an event, people often rely on their memory and search for relevant information from the past. But memory might be selective and our consciousness is most responsive to signals that can be remembered most easily. We usually attach too much importance to information that is readily available, extreme, and often repeated, for example, in the media.

13. Excessive Optimism
Excessive optimism. People overestimate how frequently they will experience favorable outcome and underestimate how frequently they will experience unfavorable outcome.
Diagnostic Question. p. A1-1
This diagnostic question was designed to provide insight into the judgments that people form about risks they confront. People rate how likely they are to experience particular events relative to other people who are similar to them. Are they prone to particular biases?

14. Excessive Optimism
Discussion. A rating of 7 means that a person feels that an event is as likely to happen to them as to anyone else in similar circumstances.
It was found that typically the average rating for the unfavorable events is below 7, while the average rating for the favorable event is above 7.
While this kind of belief may be true for some people, it can not be true for everyone.

15. Overconfidence
A lot of evidence suggests that decision makers are generally overconfident. This can be manifested in three basic ways: above-average effect, calibration effect, and illusion of control.
1. Above-average effect: When making assessments and constructing beliefs about reality, people consider their knowledge and skills to be above the average. They rate themselves better than the average man.
2. Calibration bias

16. Overconfidence Diagnostic Question. p. A1-4
These are 10 difficult questions. The point of the question is to establish low and high guesses that bracket the true answer 90 percent of the time (a range that you feel 90 percent confident that the right answer will lie between your low and high guess).
Discussion. A person scores a “hit” on a question when the true answer lies between the low and high guess. It was found that typically the most frequent number of hits, and the average number of hits, is about 4.

17. Overconfidence
When asked to provide information or make a forecast without being precise but estimating within a certain confidence range, people usually give answers which indicate that they are overconfident as to the precision of their knowledge.
When people set their intervals too narrowly, their hit rates would be small. When they set their intervals too widely, their hit rates would be large. People who are well-calibrated should expect to score nine hits for the 10 questions (since the confidence level is 90 percent).

18. Overconfidence
Overconfidence grows with the degree of difficulty of the tasks and if there are no prompt signals from the environment that confirm or negate previous information or previously made decisions.
Barber and Odean (2001) document overconfidence among investors and March and Shapira (1987), and Ben-David, Graham, and Harvey (2007) provide evidence on overconfidence among corporate managers.

19. Overconfidence
3. Overconfidence also manifests itself in the illusion of control. People are frequently convinced that their actions may positively affect totally random outcomes. Langer (1975) documents that lottery players place a higher value on the tickets for which they themselves picked the numbers than on the tickets filled in by the quick-pick lottery machine.
Diagnostic question (p. A1-6)

20. Overconfidence
Overconfidence is supported by the selective- attribution bias, which consists in people attributing successes (even random ones) to themselves and their capabilities while explaining failures by independent factors, such as bad luck, mistakes made by others, and so on (Langer and Roth, 1975; Miller and Ross, 1975; Fischhoff, 1982; Taylor and Brown, 1988).
Overconfidence is a bias pertains to how well people understand the limits of their knowledge, their own abilities, or both.

21. Representativeness
Representativeness heuristic. This is a mental shortcut where the probability of an event or a state is estimated through assessing the degree to which incoming information is similar to a specific remembered pattern (Kahneman and Tversky, 1973; Tversky and Kahneman, 1974; Grether, 1980).
Diagnostic Question. p. A1-5
Based on your friend’s descriptions about Linda, you rank the eight possibilities about Linda’s current interests and career.

22. Representativeness
Discussion. Typically people put activity in the women’s movement and psychiatric social worker as the most likely possibilities. The two situations that people judge to be least likely are insurance salesperson and bank teller.
Psychologists suggest that people consider each situation as a category and ask how representative Linda is of the category. This kind of judgments (heuristics) may result in systematic errors. For example, most people assign a higher likelihood to item 8 than they do to item 6.

23. Cognitive conservatism
There is a lot to suggest that we cannot properly update our forecasts in the light of new facts and that we often treat such facts in a selective manner.
Cognitive conservatism. Edwards (1968) proved that even though new information usually triggers a change in opinion in the direction predicted by the Bayes’s rule, the value of the change is far from satisfactory. People usually display excessive cognitive conservatism and are slow to react to new information.

24. Cognitive conservatism
Although representativeness bias may stem from such factors as overreaction to clear, descriptive signals conforming to a stereotype, cognitive conservatism occurs when such signals cannot be assigned to any specific pattern familiar to the decision maker. In such cases, the new information is likely to be underestimated, and the decision maker will focus on his initial assessments (Barberis and Thaler, 2003).

25. Confirmation bias
Confirmation Bias. This consists in a tendency to look for information confirming a previously adopted hypothesis while avoiding confrontation with facts that could contradict one’s current opinions or disturb a previously developed attitude toward a problem.
Diagnostic Question. p. A1-4
Select the minimum number of cards that will enable you to determine whether or not the hypothesis “Any card having a vowel on one side has an even number on the other side” is true.

26. Confirmation bias
Discussion. In this card test, most people turn over the card with the a, and some turn over the card with the 2 as well. Typically less than a third choose to turn over just the a and the 3.
The correct answer is to turn over only the a and 3. The efficient way of testing the validity of the hypothesis is to turn over only the cards that might falsify the hypothesis.

27. Confirmation bias
“a” card offers for both confirmation and falsification. “b” card offers no evidence. “2” allows for confirmation only. “3” allows for falsification only. Thus, the only two cards that offer the potential for falsification are the a and the 3.