1. Decisions, Judgements, and Reasoning.
Cognitive Psychology
Chapter 11
Decisions, Judgements, and Reasoning.

2. Formal logic and reasoning
Chapter 11.2
2/17/2019
Formal logic and reasoning
Judgment
Psychophysics
Decisions I
Physical and Symbolic distance
Cognitive maps
Algorithms & Heuristics
Representiveness
The hot hand debate
Study Question.
• What is the symbolic distance effect and why is it important in understanding the notion of representation?

3. Decisions Psychophysics
Psychophysics: an experimental approach that attempts to relate psychological experience to physical stimuli.
Fechner and the difference threshold
Just Noticeable Difference (JND). The smallest difference between two similar stimuli that can be distinguished.

4. Decisions Psychophysics
Absolute Threshold: The critical level of intensity that gives rise to sensation.
Problems with determining the absolute threshold
The radar operator example
Bias versus sensitivity
Signal detection theory
Noise and noise plus signal
E.g., Library noise and library noise plus a gunshot
Library noise and library noise plus someone talking

5. Decisions Psychophysics Signal detection theory Sensitivity d }
Loudness
Library noises
Library noises plus
someone talking
Library noises plus
a gunshot

6. Decisions Psychophysics Signal detection theory b
Response Bias: Criteria setting
Brightness
Radar noise
radar noise
plus signal
Responds
Does not responds b

7. Decisions Psychophysics Signal detection theory b
Response Bias: Lax criterion
Brightness
Radar noise
radar noise
plus signal
Responds
Does not responds b
Correct rejection
rate = 50 %
Miss rate = 15 %
Hit rate = 85 %
False Alarm rate = 50 %

8. Decisions Psychophysics Signal detection theory
Response Bias: Lax criterion
Actual Events
Noise Signal+noise
Receiver Operator
Chooses
Noise
Signal
Correct
rejection
Miss
False Alarm
50%
Hits
85%

9. Decisions Psychophysics Signal detection theory b
Response Bias: Strict criterion
Brightness
Radar noise
radar noise
plus signal
Responds
Does not responds b
Correct rejection
rate = 85 %
Miss rate = 50 %
Hit rate = 50 %
False Alarm rate = 15 %

10. Decisions Psychophysics Signal detection theory
Response Bias: Lax criterion
Actual Events
Noise Signal+noise
Receiver Operator
Chooses
Noise
Signal
Correct
rejection
Miss
False Alarm
15%
Hits
50%

11. Decisions Psychophysics Signal detection theory b
Memory operating characteristics
Correct rejection
rate = 85 %
Miss rate = 50 %
Hit rate = 50 %
False Alarm rate = 50 %
Familiarity
New words
Old words
Responds
Does not responds b

12. Decisions The symbolic distance effect
Distance (discriminability) effect: The greater the difference (or distance) between the two stimuli being compared, the faster the dexision that that they differ.
Which line is longer?
vs.
Which dot is higher?
vs.

13. Decisions The symbolic distance effect
Distance (discriminability) effect
Distance
Near
Far RT

14. Decisions The symbolic distance effect
The Symbolic Distance (descriminability) effect: A distance (or discriminability) effect that is based on semantic or other long term memory knowledge.
E.g., Symbolic imagery effects
Which is larger a mouse or a horse?
Which is larger a donkey or a horse?
The effect mirrors (physical) distance effects
I.e., RT is a log function of perceived size discrepancy

15. Decisions The symbolic distance effect
The semantic congruity effect. Decisions are faster when the dimension being judged matches or is congruent with the implied semantic dimension
Which balloon is higher?
Which balloon is lower?
vs.
Which yo-yo is higher?
Which yo-yo is lower?
vs.

16. Decisions The symbolic distance effect Semantic congruity effect RT
Position
Balloon
Yo-yo RT
Lower
Higher

17. Decisions The symbolic distance effect Banks et al. (1976)
Distance and congruity
Number magnitude estimates
Which is larger? or 2
vs. 1 or 5
vs or 9

18. Decisions The symbolic distance effect Judging geographical distances
Holyoak’s work
People judge distances from their own perspective
E.g., Which are further apart?
Antigonish to Fredericton or
Sault Ste. Marie to Thunder Bay

19. Decisions The symbolic distance effect Judging geographical distances
Semantic / propositional intrusions
Which is further north, Edmundston, NB or Victoria, BC?

20. Decisions The symbolic distance effect Judging geographical distances
Which is further south: Detriot, MI, or Windsor, ON?

21. Decisions The symbolic distance effect Judging geographical distances
Which is further east: Florida or Chile?

22. Decisions The symbolic distance effect Judging geographical distances
Which is further south: Montréal or Paris?

23. Decisions The symbolic distance effect Judging geographical distances
Which is further west Reno or San Diego?

24. Decisions Algorithms and Heuristics
Reasoning under uncertainty: Inductive reasoning
Algorithms: A specific rule or solution procedure that is guaranteed to furnish the correct answer if it is followed.
E.g., finding a forgotten phone number
Heuristics: A strategy or approach that works under some circumstances, but is not guaranteed to produce the correct answer.
Kahneman and Tversky’s work
Behavioural decision work
Ups and downs of heuristics
Cf., Visual illusions

25. Decisions Algorithms and Heuristics The representativeness heuristic
E.g., Flip a coin 6 times, which is more likely
HHHHHH or HHTHTT
Which lottery ticket is most likely to win the next 6-49? or
The representativeness heuristic - samples are like the populations that they are pulled from.
The representativeness heuristic leads to a number of decision biases

26. Decisions Algorithms and Heuristics The representativeness heuristic
The 649 Controversy (Wed, March 19, 2008)
Too many second place winners?
Prize Payouts
Prize Matches Amount Winners
1st $3,500,
2nd 5 + Bonus $1,
3rd $2,
4th $ ,245
5th $ ,935
6th 2 + Bonus $ ,843
Lotto 6/49 - The winning numbers were….
Bonus 43

27. Decisions Algorithms and Heuristics The representativeness heuristic
The law of small numbers
Who is more likely to have days where more than 60% of the births are male? St. Martha’s or the IWK?
The Gambler’s fallacy
Superbowl ‘09 coin flip
• NFC had won 11 consecutive coin tosses
-> NFC won the coin toss
• Saints (NFC) won the coin toss for Super Bowl XLIV

28. Decisions Algorithms and Heuristics The representativeness heuristic
Ignoring base rates
John: Truck driver or classics professor at Dalhousie?
Cancer Screening example
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive results. 9.6% of women without breast cancer will also get positive results. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
--> Baysian probabilities

29. Decisions Algorithms and Heuristics The representativeness heuristic
The birthday bet
If you bet against the birthday bet, what is P(winning)?
Person 2 -> 364/365 = .99
Person 3 cannot have the same birthday as 1 or 2
& Person 2 cannot have the same birthday as 1
Multiplicative Rule: The joint probability of two independent events is the product of their individual probabilities
Person 3 -> 363/365 X .99 = .99
Person 4 -> 362/365 X .99 = .98
Person 5 -> 361/365 X .98 = .97
Person 6 -> 360/365 X .97 = .95

30. Decisions Algorithms and Heuristics The representativeness heuristic
The birthday bet
Person 10 -> 356/365 X .90 = .88
Person 15 -> 351/365 X .77 = .75
Person 20 -> 346/365 X .62 = .59
Person 25 -> 341/365 X .46 = .43
Person 30 -> 336/365 X .32 = .29
Person 35 -> 331/365 X .21 = .19
Person 40 -> 326/365 X .12 = .11
Person 45 -> 321/365 X .07 = .06
Person 50 -> 316/365 X .03 = .03

31. Decisions Algorithms and Heuristics The representativeness heuristic
Misperception of random events
Is the following a random sequence? (Gilovich, 1991)
OXXXOXXXOXXOOOXOOXXOO
“Maximally” indicative of randomness
Same number of X’s and O’s
Same number of X’s follow O’s as X’s following X’s
(and vice versa)
P(alteration) = .5
Most people expect P(alteration) =.7

32. Decisions Algorithms and Heuristics The representativeness heuristic
The hot hand in basketball
Study 1: 100 fans completed survey
91 % : a player has a better chance of making a shot after hitting the last two or three, a lower chance of hitting a shot if they have missed the last two or three
68 % for free throws
85 % believed that it was important to pass the ball to someone who had just made several shots in row.
Study 2: 76ers home games from season
Conditional probabilities
P(hit | 3 misses) P(hit | 2 misses) P(hit | 1 misses) P(hit) P(hit | 1 hit) P(hit | 2 hits) P(hit | 3 hits))
Julius Irving
Andrew Tony
Team

33. Decisions Algorithms and Heuristics The representativeness heuristic
The hot hand in basketball
Study 3: Free throws

34. Decisions Algorithms and Heuristics The representativeness heuristic
The hot hand in basketball
Study 4: Controlled shooting: Cornell varsity players
Determined 50 % range
Paid for hitting baskets and predicting hits and misses
14/26 had higher P(hit|miss) than P(hit|hit)
P(hit | 3 misses) P(hit | 2 misses) P(hit | 1 misses) P(hit) P(hit | 1 hit) P(hit | 2 hits) P(hit | 3 hits))
Mean

35. Decisions Algorithms and Heuristics The representativeness heuristic
The hot hand in basketball
Predicting:
Bet either “high” (5 cents for a hit, lose 4 cents for a miss)
Or “low” (2 cents for a hit, lose 1 cent for a miss)
Shooters and observers bet
Similar misconceptions (The clustering illusion)
Winning streaks as team momentum
Hitting slumps in baseball
Shooter & shot Obs. & shot Shooter & last shot Obs. & last shot
Correlation