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Analogical Reasoning

Psychology 355: Cognitive Psychology

Instructor: John Miyamoto

05/23/2018: Lecture 09-3

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Outline of the Analogical Reasoning Topic

• What are analogies? Why are they useful in problem solving?

• Structural definition of an analogy

• Discovery of analogies: What are the cognitive processes during

discovery of useful analogies?

• Influence of analogies on decisions

Psych 355, Miyamoto, Spr '18 2 Examples of Analogical Reasoning

Psych 355, Miyamoto, Spr '18 3

Examples of Analogical Reasoning

• Is the current international political instability analogous

to the political situation that preceded World War I?

• Is a successful business analogous to a successful football team?

• Is the mutilated checkerboard problem analogous

to the Russian marriage problem?

• Is the structure of an atom analogous to the structure

of the solar system?

• "pony" is to "horse" as ____ is to "cow"

"bird" is to "air" as "fish" is to _____.

Why Are We Interested in Analogical Reasoning?


Why Are We Interested In Analogical Reasoning?

• Seeing useful analogies is one of the basic mechanisms

of problem solving.

• Analogies influence decisions.

♦ Is the current instability in Ukraine and Crimea analogous to the German

annexation of Austria in 1938?

♦ Maureen Dowd writing in the New York Times (January 17, 2010) about

President Obama’s reluctance to support gay marriage:

“Obama sees himself as such a huge change that he can be

cautious about other societal changes. But what he doesn’t

realize is that legalizing gay marriage is like electing a black

president. Before you do it, it seems inconceivable. Once

it’s done, you can’t remember what all the fuss was about.”

[Italics added to the quotation]

Structure of an Analogy


The Structure of an Analogy

• Source (Base Problem): Typically,

a well understood problem or system

to which an analogy is made.

♦ E.g., structure of the solar system

Example: The structure of an atom is analogous to the structure of the solar system.

• Target (Test Problem): Typically, a less understood problem or

system about which we can learn by analogy to the source. • E.g., structure of the atom

• Representation: The structure of the source and the target.

• Mapping: A correspondence between the source structure

and the target structure

Main Steps in the Mental Construction of an Analogy

Source Target

Atom Solar System


Main Steps in the Mental Construction of an Analogy

• Create representations of the source and target.

• Noticing: Noticing that a potential analogy exists.

• Mapping: Constructing a correspondence between

the representations of the source and the target.

• Application: Applying the mapping from source to target,

i.e., drawing inferences about the target based

on what is known about the source.

Dunker’s Radiation Problem - Outline


Dunker's Radiation Problem - Outline

• Doctor must kill a tumor in a patient's stomach.

Surgery is not possible.

• There is a ray that can kill the tumor.

• In high dosages it will kill the tumor, but it will also kill

healthy tissue in front of the tumor.

• In low dosages, it won't harm the healthy tissue, but it also won't kill

the tumor.

• Question: How can the doctor kill the tumor without killing

the healthy tissue?

The Convergence Solution

Convergence Solution for the Radiation Problem

• Beam the ray at the tumor from many

different angles.

• All rays should have low intensity, but the

combination of rays at point of intersection

(at the tumor) will have high intensity. ----------------------------------

• The convergence solution respects the constraint

that the ray cannot be high intensity.

• Gick & Holyoak (1983): With no other hints, about 10% of subjects

(University of Michigan undergrads) produced the convergence

solution.

Psych 355, Miyamoto, Spr '18 8 Analogical Transfer


Analogical Transfer

• Analogical transfer – seeing analogies and using the analogies to solve

a new problem.

• Gick and Holyoak studied whether exposure to analogous problems

and their solutions would help people solve the radiation problem.

♦ Train subjects on one problem. (Referred to as the "base problem.")

♦ Test subjects on another problem that is analogous to the first problem.

(Referred to as the "target" or "test" problem.)

Gick & Holyoak on Analogical Transfer – Basic Idea


Gick & Holyoak's Study of Analogical Transfer

Step 1: Train subjects to solve (or at least think about)

one or more base problems (source for an analogy).

Step 2: Subjects are asked to solve the Radiation Problem

(target problem).

Compare the following two measures:

♦ How many subjects (%) solve the target problem without seeing

the base problem first?

♦ How many subjects (%) solve the target problem after seeing

the base problem?

Base Problem: The Fortress Problem


Base Problem: Duncker's Fortress Problem

• A general needs to capture

a fortress with his army.

• An attack by his entire army

would capture the fortress, but

the roads are mined.

• Since the dictator needs to move his workers to and from the fortress,

the mines are set to let small bodies of men pass over them safely,

• Any large force would detonate the mines.

• How can the general attack the fortress with all of his army?

Other Base Problems – Red Adair & Arrow Diagram


Other Base Problems

• Red Adair Problem: (Red Adair was famous for being

able to put out burning oil wells)

♦ Need to put out a burning oil well

but can't deliver enough water from

any one position.

♦ Convergence Solution: Direct streams

of water at the well from many directions.

• Arrow Diagram: In some conditions,

subjects were given an arrow diagram

to see if that would be helpful.

Three Conditions in the Experiment on Analogical Transfer


Gick & Holyoak: Study of Analogical Transfer


Target Problem: The Radiation Problem

Three Experimental Conditions

1. Subjects are not shown the base problem.

Subject attempt to solve the target problem.

♦ This condition tests for the rate of spontaneous solutions to the target problem.

Same Slide with Condition 2 Added








2. Subjects are shown the base problem.


♦ This condition tests for the rate of spontaneous use of the analogy of the base

problem when attempting to solve the target problem.

Same Slide with Condition 3 Added








2. Subjects are shown the base problem.


3. Subjects are shown the base problem plus a hint that

the base problem may be useful when working on the

next problem.. Subject attempt to solve the target problem.

♦ This condition tests for the rate of using the analogy when the subjects

are informed that it may be useful.

Results of Gick & Holyoak's Study

Summary of Results (Gick & Holyoak, 1980, 1983)


• These results show that noticing the analogy is a separate step from

constructing the analogy. (Condition 3 is better than Condition 2.)

Same Slide with Emphasis Rectangles

% Solutions Three Conditions

10% 1. Control: No base problem, no hint

30% 2. Base problem, no hint

75% 3. Base problem + hint

Summary of Results (Gick & Holyoak, 1980, 1983)


• These results show that noticing the analogy is a separate step from

constructing the analogy. (Condition 3 is much better than Condition 2.)

Noticing Analogies: Effects of Superficial Similarities

% Solutions Three Conditions

10% 1. Control: No base problem, no hint

30% 2. Base problem, no hint

75% 3. Base problem + hint


Noticing Analogies: The Effects of Superficial Similarities

How to increase the rate at which people notice an analogy?

Hypothesis: People are more likely to notice an analogy

if the base and target problem share superficial features.

♦ Evidence for this is given by the Lightbulb Problem (next).

Lightbulb Problem – Standard Version


Effect of Superficial Features

Lightbulb Problem (Fragile Glass Version; see Goldstein, pp. 352)

Ruth must repair an expensive lightbulb. The filament is broken.

A high intensity laser can repair the filament, but it will break the

glass.

Solution: Beam many low intensity lasers at the filament from

many different directions.

Holyoak & Koh (1987):

• Subjects who were only given the Lightbulb Problem

solved it 10% of the time.

• Subjects who were first saw the Radiation Problem and

its solution solved the Lightbulb Problem 81% of the time.

♦ Excellent transfer! Recall that the Fortress Problem transferred

to the Radiation Problem 30% of the time.

Comparing Effects of Superficial Features & Structural Features


Effects of Superficial Features versus Structural Features

• Subjects first saw the Radiation Problem and its solution.

They then tried to solve a version of the Lightbulb Problem.

Lightbulb Problem (Fragile Glass Version) – shares

both superficial & structural features with the Radiation Problem:


A high intensity laser can repair the filament, but it will break the glass.

(Same as scenario on preceding slide.)

Lightbulb Problem (Insufficient Intensity Version) – shares

superficial BUT NOT structural features with the Radiation Problem:


A high intensity laser can repair the filament, but she doesn’t have one.

She only has low intensity lasers available to her.

Solution for both versions: Beam many low intensity lasers at the

filament from many different directions.

Results for Two Versions of the Lightbulb Problem


Results: Superficial Features versus Structural Features

Subjects first saw the Radiation Problem and its solution.

They then tried to solve one version of the Lightbulb Problem.

Lightbulb Problem (Fragile Glass Version) –

shares both superficial & structural features with the Radiation Problem:

Lightbulb Problem (Insufficient Intensity Version) –

shares superficial BUT NOT structural features with the Radiation Problem:

Results:

% Solution Version

69% Fragile Glass Version

33% Insufficient Intensity Version

Comparison of Features for Different Problems

Superficial Similarities

+

Structural Similarities

Analogical Transfer

Comparison of Features Among the Problems


Superficial Feature Structural Feature

Problem Medium of

Action

Why One Strong

Beam/Attack

Not Possible

Analogical

Transfer

Successful?

Radiation Problem X-ray beam

One strong x-ray beam will

injure the intervening

tissue.

Radiation problem

is the source

problem

Fortress Problem Attack

by troops

One strong attacking army

will detonate mines on

roads.

poor

Lightbulb Problem (Insufficient Intensity

Version)

Laser beam High intensity laser

not available poor

Lightbulb Problem (Fragile Glass

Version)


will break the glass. good

Same Slide with Emphasis Rectangles

Superficial Feature Structural Feature

Problem Medium of

Action

Why One Strong

Beam/Line of Attack

Not Possible

Analogical

Transfer

Successful?

Radiation Problem X-ray beam

One strong x-ray beam will

injure the intervening

tissue.

Radiation problem

is the source

problem

Fortress Problem Attack

by troops

One strong attacking army

will detonate mines on

roads.

poor

Lightbulb Problem (Insufficient Intensity

Version)


not available poor

Lightbulb Problem (Fragile Glass

Version)


will break the glass. good

Comparison of Features Among the Problems

Psych 355, Miyamoto, Spr '18 23 What Influences the Likelihood of Analogical Transfer?

What Influences the Likelihood of Analogical Transfer?



+ Structural Similarities

Analogical Transfer

Schema Induction in Problem Solving

The relationship depicted on this slide needs to be modified.

See diagram below that includes the effect of schema induction.



A problem schema is an abstraction of the similarities

between many problem solutions. It is a general description

of how problems of a given kind can be solved.

• Does having a good problem schema makes it more likely

that one will see an analogy?

Experiment on Schema Induction + Results

Schema induction is not discussed in Goldstein, but it is an important concept

in the study of analogical reasoning.

• Gick and Holyoak (1983) introduced idea of schema induction

in analogical reasoning.

• Gentner and Goldin-Meadow (2003) developed similar idea

of analogical encoding (discussed in Goldstein, pp. 353 - 354).



Gick and Holyoak (1983):

♦ Subjects read the fortress story and the "Red Adair" story.

♦ Subjects were asked to write a brief summary describing

as clearly as possible the ways in which the stories were similar.

♦ Subjects' problem summaries were rated by independent raters

for quality of the description of the convergence schema.

♦ Subjects then attempted to solve the radiation problem.

RESULTS: % Successful Solutions

Rated Quality of Schema to the Radiation Problem

"good" 91%

"intermediate" 40%

"poor" 30%

• Having a good problem schema correlates with seeing the analogy

between the source problems and the target problem.

Summary re Schema Induction

What Influences the Likelihood of Analogical Transfer?



+ Structural Similarities

+ Induction of a

Problem Schema

Analogical Transfer

Summary re Analogical Transfer


Summary re Analogical Transfer

• Noticing that a potential analogy exists is more difficult than

applying an analogy once it has been noticed.

• Superficial features and deeper structural relationships influence

the likelihood of noticing an analogy.

• Discovering a schema for an analogy is promoted by seeing

multiple examples of the base problem.

♦ Examples: Gick and Holyoak (1983) described in preceding slides;

Gentner and Goldin-Meadow (2003) as discussed in Goldstein, pp. 353 -

354.

• Possibly end lecture here?

Gilovich – Superficial Associations Influence Judgment


Gilovich – Superficial Associations Influence Judgment

Gilovich, T. (1981). Seeing the past in the present: The effect of associations to familiar events on

judgments and decisions. Journal of Personality and Social Psychology, 40, 797-808.

• Basic argument: Superficial associations to past experience

influence judgment.

• Experiment:

♦ Subjects were 20 male sportswriters

(the Oakland Tribune; the San Jose Mercury News; the Merced Sun Star; the Palo Alto Time).

♦ Subjects read a description of a hypothetical player.

♦ Subjects predicted the future success of college players in pro football on

a 9-point scale from:

1 = fails to make a pro team to 9 = star/superstar

Example of a Player Description and Experimental Results

FYI: The Gilovich study was not discussed on the Goldstein textbook.


Example of a Player Description in Gilovich’s Study

Gilovich – Superficial Features Influence Policy Analogies

Results: Average Ratings of Tim B's Chances in Pro Football Rating

Award named for famous player who played the SAME position. 6.44

Award named for famous player who played DIFFERENT position. 4.80

Offensive Guard: Tim B. 6'3". 260 lbs. 5.0 speed in the 40. Good strength and

body control. Has a quick, strong charge that enables him to move opponents off

the line of scrimmage. Will need to learn to pass block since his college ran the Veer.

Tim won the award for football excellence.

FYI: Drew Pearson was a famous wide receiver (different position).

Gene Upshaw was a famous offensive guard (same position).


Do Superficial Features Affect Availability of Analogies?

Gilovich, T. (1981). Seeing the past in the present: The effect of associations to familiar events on

judgments and decisions. Journal of Personality and Social Psychology, 40, 797-808.

• Basic structure of the scenarios:

Country A is threatening to invade

its peaceful neighbor, Country B.

Neither country is strategically

important. Country B has asked

the U.S. for help.

• Question: Should the U.S. intervene

to help Country B?

Two Prototypes of American Military Intervention

FYI: This Gilovich study was not discussed

in the Goldstein textbook.


Question: Should the U.S. intervene to help Country B?

• Two prototypes of US military intervention

♦ World War II: Appeasement of Hitler leads to genocide & terrible war.

♦ Vietnam: Intervention leads to long, painful war.

• Research Question:

Can we manipulate the description of the situation

to make the WW II or Vietnam analogy more available?

Gilovich Experiment: Phrases Manipulated Across Conditions 1, 2 & 3

Phrases Manipulated Across Condition 1, 2 & 3


Phrase WW II Neutral Vietnam

The decision was made in

_____ (location).

Winston Churchill

Hall

Abraham

Lincoln Hall Dean Rusk Hall

The current U.S. president was

from _____, the same state as

_____.

New York; FDR Virginia; William

H. Harrison Texas; LBJ

The impending invasion was

referred to as a _____. blitzkrieg quickstrike quickstrike

A pact between Country A and

Country F was called a _____

nonaggression

pact pact pact

In an emergency, U.S. troops

stationed in Country D could be

flown to Country B in _____.

troop transports troop transports Chinook

helicopters

Minorities in Country A were

fleeing _____.

via boxcars on

freight trains to

Country G

to Country G

via small boats

up the coast to

Country G

Same Slide Without Emphasis Rectangles

Phrases Manipulated Across Condition 1, 2 & 3

Psych 355, Miyamoto, Spr '18 34 Dependent Variables (Ratings) & Results

Phrase WW II Neutral Vietnam

The decision was made in

_____ (location).

Winston Churchill

Hall

Abraham

Lincoln Hall Dean Rusk Hall

The current U.S. president was

from _____, the same state as

_____.

New York; FDR Virginia; William

H. Harrison Texas; LBJ

The impending invasion was

referred to as a _____. blitzkrieg quickstrike quickstrike

A pact between Country A and

Country F was called a _____

nonaggression

pact pact pact

In an emergency, U.S. troops

stationed in Country D could be

flown to Country B in _____.

troop transports troop transports Chinook

helicopters

Minorities in Country A were

fleeing _____.

via boxcars on

freight trains to

Country G

to Country G

via small boats

up the coast to

Country G


Results: Superficial Features Affect Availability of Analogies

• Subjects were 42 Stanford undergraduates who were enrolled in a

political science course.

♦ Rate: How successful would a US military intervention be in preventing a

takeover if a limited number of U.S. troops were sent to Country B.

♦ Rate: How likely is it that the crisis would turn into a major world problem

involving more countries than A, B, and the US.

♦ Rate your preferred policy on a scale from

1 = "hands off; appeal to U.N." to .....

9 = intervention.

• Results: Ratings were significantly more interventionist when scenario

contained WW II features than when it contained neutral or Vietnam

features. (Neutral & Vietnam conditions did not differ).

Interpretation of Results

Interpretation of Results

• Result: Non-relevant features that are associated with WW II or

Vietnam had an impact on subjects' judgments about what to do.

• Interpretation: The non-relevant features affected whether subjects

drew an analogy between WW II or Vietnam when deciding a course of

action.

♦ Note: The scenario never made a direct reference to “World War II”

or to “Vietnam.”

• Remember Gick & Holyoak found that superficial features

affect whether subjects notice an analogy.

Psych 355, Miyamoto, Spr '18 36 Ubiquity of Analogies in Real-World Problem Solving


Analogies in Real-World Problem Solving Contexts

"In-vivo" problem solving research = naturalistic studies of problem

solving, e.g., in a microbiology lab or a design engineering group.

• Finding: Scientists and engineers often use analogies in their

discussions.

• Question: Why are analogies often used by problem solvers

in real-world situations, but not by psychology subjects in cognitive

laboratory situations?

• True answer not known

♦ Notice that real-world problem solvers often have a lot of practice

looking for useful analogies in their area of expertise.

♦ Perhaps in the real world, many people use analogies but only a few people

discover the analogies. Applying an analogy is easier than discovering the

analogy.

Summary re Analogical Reasoning – END


Summary of Analogical Reasoning

• Analogies facilitate problem solving.

• Basic structure of an analogy: Source or base problem,

target problem, problem representation, noticing, mapping, application

• Subjects do not readily recognize the existence of analogies without

hints or suggestions. Subjects are influenced by superficial similarities,

but also by structural similarities.

• Schema induction facilitates analogical problem solving.

♦ Schema induction requires exposure to two or more instances of a problem

structure.

• Analogies occur often in the problem solving activities of scientists

when they are working on their research.

END

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