Inductive Reasoning
Psyc 494
Talia Ben-Zeev
Inductive Reasoning
• Reasoning from a set of statements to a general
conclusion with some but not a complete degree of
certainty
The oldest living woman in the world lives in Transylvania
Olga is the oldest woman in the world
Olga lives currently in Transylvania (deductive)
The oldest living woman in the world tomorrow will live
in Transylvania (inductive)
Problems with inductive
reasoning
1. Evaluating a conclusion is often hard
Often when Jane turns around in class, Bob is
looking at her.
Bob keeps asking Jane to Play Tennis with him.
Bob has stopped dating Susan.
Therefore, Bob has a crush on Jane
2. Coming up with a conclusion is often hard
The first number in the series is 1.
The second number in the series is 3.
The third number in the series is 7.
The loose view of reasoning
Rips (1990)
Goodman’s (1955) New Riddle of Induction:
“Let grue be the color of an object at time t if
and only if the object is green and t is before the
beginning of the year 2,000, or the object is blue
and t is on or after the beginning of the year
2,000.”
All emeralds so far observed have been green
The first emerald to be observed after the beginning
of the year 2,000 will be green
All emeralds so far observed have been grue
The first emerald to be observed after the beginning
of the year 2,000 will be grue
Analogical Reasoning
Gick & Holyoak (1980)
The Tumor Problem
A doctor is seeing a patient with an inoperable
stomach tumor. The doctor knows that there are
rays that can destroy the tumor, but a ray with
sufficient intensity that would destroy the
unhealthy tissue, would also destroy the healthy
tissue surrounding the tumor. What would be a
way to destroy the tumor without causing
damage to the healthy tissue that surrounds it?
Analogical Reasoning
Gick & Holyoak (cont)
The Attack-Dispersion Problem
A general who is planning to conquer a fortress.
The general’s problem is that the roads leading
to the fortress are mined such that they explode
when a large group of soldiers passes over them,
but they do not explode if the group of soldiers
is small enough. The general decides to solve
the problem of attacking the fortress with a
sufficently large enough army by sending a large
number of small troops along the different roads
that lead to the fortress, and having these troops
meet at the fortress.
Analogical Reasoning
Gick & Holyoak: Exp 4
Both groups: received the attack dispersion
problem first and two distractor problems
(for “recall) , then were asked to solve the
tumor problem
Group 1: Hint (92%)
Group 2: No Hint (20%)
Danger: Confirmation Bias
• Wason’s 2-4-6 Task
You are provided with a set of three
numbers,{2, 4, 6}. These numbers conform
to a rule. Your task is to discover the rule
by creating new triples. I will respond
“yes” if your triple conforms to the rule and
“no” if it does not..
Confirmation Bias vs.
Positive Test Strategy
C
Wason‟s 2-4-6 Task
H
Klayman and Ha:
Positive test strategy
C H
H
C
Are People Rational?
The Monty Hall Dilemma
“Suppose you‟re on a game show, and you‟re
given a choice of three doors. Behind one door is
a car; behind the others, goats. You pick a door --
say, No. 1 -- and the host, who knows what‟s
behind the doors, opens another door -- say, No. 3
-- which has a goat. He then says to you, „Do you
want to pick door No. 2?‟ Is it to your advantage
to switch your choice?” (Vos Savant, 1990)
? ?
mental models
According to Johnson-Laird et al.,(1999), creating the necessary
exhaustive set of models exceeds working memory demands.
Instead, people create the following models:
Door 1 (prize)
Door 2 (prize)
Door 3 (prize)
Working Memory and
Mental Models
The collapsing sets hypothesis:
Increasing working memory demands can facilitate making a
correct probabilistic choice
3 choices: P(initial choice) P(choice2) P(choice3)
3 mental models .33 .33 .33
100 choices: P(initial choice) P(remaining choices)
2 collapsed
.01 .99
mental models
Experiment 1
Participants were divided into a 3 and a 100 choice conditions, which
involved choosing a box with a cash prize
? choice
choice
Results: Incorrect (Stay) Correct (Switch)
3 boxes 15 1
100 boxes 8 8
Experiment 1: Correct
Probability estimates
without understanding
Median judged probability of winning
People who stayed People who switched
.50 The only subject who
3 boxes switched did not report an
12 ss = .50, 2 ss = .66, 1 subject = .67 estimate
.50 .50
100 boxes
6 ss = .50, 1 subject = .01 4 ss = .50, 2 ss = .99, 1 subject failed to report
Experiment 2: Increasing
memory load facilitates
correct responses
The number of boxes were varied from 5 through 10
Contrast B S.E. Wald df Sig
Model 15.67 5 .008
5 vs -1.68 .77 4.69 1 .03
6,7,8,9,10
6 vs. -1.08 .55 3.87 1 .05
7,8,9,10
7 vs. 8,9,10 -1.23 .57 4.66 1 .03
8 vs. 9,10 -.16 .55 .09 1 .77
9 vs. 10 -.51 .60 .73 1 .39
10 vs. 1.33 .47 8.20 1 .004
5,6,7,8,9
9 vs. 1.03 .53 3.75 1 .05
5,6,7,8
8 vs. 5,6,7 1.50 .57 6.80 1 .009
7 vs. 5,6 .57 .68 .70 1 .40
Why don‟t most people
switch?
According to regret theory, people tend to stay
because errors of commission are perceived as
being worse than errors of omission (Gilovich et.
al., 1995). People would regret having had the
prize and then giving it up, rather than not having
the prize in the first place.
Experiment 3: Mitigating the
effects of regret
Will helping people to collapse sets, by making the
partioning of choices more salient (having two separate
tables), overcome the effects of potential regret?
Step 1:
Host chooses a box
and moves it to
other table
Step 2:
stay or switch?
Experiment 3: Mitigating the
effects of regret
incorrect (stay) correct (switch)
3 boxes
16 16
100 boxes
7 22
Conclusion: The
paradoxical effects of
increasing memory load
i. The probability of switching on the Monty Hall dilemma increased with the
number of options presented up to an asymptote at a value close to the
capacity of working memory.
ii. Despite this difference in choice, judgments of the probability of the
prize’s location were unaffected by the number of presented options.
iii. Mitigating the effects of regret, further supported the collapsing-sets
hypothesis.
Working memory limitations can be an advantage in inducing people to
make a correct probabilistic choice.
Are People Rational?