10 – Reasoning

Motion Judgment

Problem Solving

Decision Making

Motion Judgment

Nearly every day, people observe objects roll, fall, and slide.

Yet many people hold striking false beliefs about these kinds of motion.

Falling Bomb Question

A horizontally-flying plane drops a bomb.

Choose the bomb’s trajectory.

 

 

 

    A B Ccorrect answer C

 

common error A

 

one explanation of error Bombs appear to drop vertically.

 

(McCloskey, 1983)

Pendulum Question

When the pendulum bob is at its highest point, the string breaks.

Choose the bob’s trajectory.

 

 

A B C D

correct answer A  common error D

 one explanation of error Memories of jumping off swing?

Marble Question

Two identical marbles are released simultaneously.

The ramps are identical except for one section that is a dip or a hill.

Which marble wins?

“hill” marble

“dip” marble

tie

Modal Answer

Tie “because each ramp has fast downhill & slow uphill”  

(continued)

Correct Answer

Dip

Speed is greater at lower elevation, regardless of slope.

Example

slow

medium

fast

Dip vs. Hill

Dip vs. Flat

Tip for instructor: R. click on icon and select “Packager shell…”

DipHillRaceDemo.exe

Simpend.exe

Experiment

Ss observed computer animations of motion for commonly-held false beliefs.

For each scenario, Ss saw two animations: true motion and false belief.

Results

Ss rated the “false belief” version as unnatural

(e.g., Kaiser, Proffitt, Whelan, & Hecht, 1992)

Summary of Motion Judgment

In one sense, people have poor understanding of motion.

Examples

Falling Bomb Question

Broken Pendulum Question

Marble Question

However, people understand motion at some level.

Examples

Animations of false beliefs look unnatural.

People can perform complicated tasks that require understanding of motion

(e.g., catch fly ball)

Problem Solving

Many problems require an insight – a sudden realization of the solution.

Examples

Archimedes: “Eureka”

Chimp suddenly realizes how to get banana

Köhler (1927)

Not all problems require insight (e.g., add fractions)

To what extent can people improve their

chance of solving insight problems?

Examples of Problems used in Insight Studies

Interpret the following:

1. oholene hole in one

2. point ______ range point blank range

Find a fourth word that relates to the first three words.

 

1. off top tail spin

2. ache sweet burn heart

3. arm coal peach pit

4. tug gravy show boat

Bridge Crossing Problem

Four men must cross a bridge that can hold only two men at a time.

It is too dark to cross without a flashlight, and they have only 1 flashlight.

The men walk at different speeds. Here are the bridge crossing times for each man:

Mr. One 1 min

Mr. Two 2 min

Mr. Five 5 min

Mr. Ten 10 min

How can all four men cross the bridge in 17 minutes?

 Solution

1 and 2 over (2 min)

1 returns (1 min)

5 and 10 over (10 min)

2 returns (2 min)

1 and 2 over (2 min)

Demo

This shape is divided into 3 congruent parts.

This shape is divided into 4 congruent parts.

Can you divide this shape into 5 congruent parts?

For each problem, use bottles A, B, and C to produce the goal amount.

Volume

Problem A B C Goal Solution

1 5 20 7 8 B – A – C

2 2 15 4 9 B – A – C

3 4 17 11 15 A + C

Problem 3 is harder if … Ss first solve Problems 1 and 2

Thus, one’s mind set can impede ability to solve problem.

(Luchins, 1941)

When stuck on a problem, why does taking a break sometimes help?

Hypothesis 1

During the break, your mind makes progress outside your awareness.

Hypothesis 2

The break disrupts your mind set and allows for a fresh start

Evidence supports #2

(e.g., Smith & Blankenship, 1989; 1991)

Demo

The sequence 2, 4, 8 conforms to a rule.Your job is to figure out the rule. To do so, suggest a sequence, and I will tell you if it conforms to the rule.

Rule Numbers increase. Results Ss seek data confirming their belief (confirmation bias) 

Lesson Seek disconfirming evidence.

(Wason, 1960)

Many psychology researchers seek confirmation.

Common psychology paper

If our Theory is true, we should find Result R.

We found Result R.

Therefore, our Theory is true. Invalid

What can be concluded?

Our results suggest that our theory is true. Invalid

Our theory predicts the results. Valid

Our results are consistent with our theory. Valid

Our results are consistent with many theories. Valid and Honest

9 Dots Problem

Connect the dots by drawing 4 straight lines without lifting your pen.

HintDon’t assume that each line segment starts and ends on a dot.

Solution

Cake Problem

A round cake must be divided into eight pieces.

Only 3 straight slices of a knife are allowed.

The pieces of cake cannot be moved between slices.

 

Hint

Do not assume that slices must be perpendicular to table.

 

 

 Solution

Elevator Problem

Ten-year-old Suzy lives on the 16th floor of an apartment building.

When she goes to school, she takes the elevator from the 16th floor to the 1st floor.

When she returns, she takes the elevator from the 1st floor to the 8th floor,

and then she climbs the stairs from the 8th floor to the 16th floor.

Why doesn’t she ride the elevator all the way to the 16th floor?

 

Solution

She’s too short.

Poisoned Drink Problem

Mr. Sip and Mr. Gulp enter a diner.

Each orders a cola with ice.

Mr. Sip slowly sips his drink, but Mr. Gulp quickly gulps his drink.

Later, Mr. Sip dies because the drink was poisoned.

But Mr. Gulp is fine even though the drinks were identical.

How can this be?

 

Solution

Poison is in the ice

 

 

Manhole Cover Problem

Why are round manholes safer than other shapes?

 

SolutionA round manhole cover will not fall through  

 

Overview of Previous Problems

Avoid false assumptions.

9 dots problem

cake slicing problem

Act out the problem.

elevator problem

poisoned drink problem

manhole cover problem

blank

Decision-MakingWhy do people sometimes make irrational decisions?

Example

You spent $500 for a weekend trip to the Bahamas.

The cost is NOT refundable.

On the day before you leave, you become very ill.

You’re so ill, you’d be less miserable if you stayed home.

You decide to go so you “don’t waste the money.”

 

(continued)

sunk cost fallacy

completing an action that is not worthwhile because of prior investment

aka “throwing good money after bad”

Another example 

Congress spends $100B to build X (rocket, jet fighter, etc.)

After $100B is spend, price increases to $500B.

Congress agrees because it doesn’t want to waste the first $100B

(e.g., Arkes & Ayton, 1999)

Question

A disease threatens an island with 600 people.

If nothing is done, all 600 people will die.

You have two options. Subject Group 1 Option A: 200 live

Option B: 1/3 chance 600 live 2/3 chance 0 live

 Subject Group 2 Option A: 400 die

Option B: 1/3 chance 0 die 2/3 chance 600 die

 

Results

Group 1: most chose A (no risk)

Group 2: most chose B (risk)

(continued)

Why?

When contemplating a gain, Ss are risk-averse

When contemplating a loss, Ss are risk-seeking.

More generally, this finding is an example of a

framing effect phrasing or format of options affects person’s preference

(Tversky & Kahneman, 1981)

Experiment

Group 1

  “You’ve been given $300. Now choose option A or B”

A. You receive another $100

  B. Coin flip You receive another $200 or nothing more

  

Group 2

“You’ve been given $500. Now choose option A or B”

A. You lose $100

  B. Coin flip You lose $200 or lose nothing

   

Results

Group 1 prefers A(no risk)

Group 2 prefers B (risk)

(Tversky & Kahneman, 1987)

 

Why do more Ss avoid a “sure thing” when options are framed as losses?

loss aversion people would rather avoid loss than acquire gain

Example

Not losing $10 is better than finding $10

Experiment

Chinese factory workers were offered weekly bonus of 80 yuan if they met target.

Two groups:

Gain Frame “You’ll receive your bonus at the end of the week if you meet target.”

Loss Frame “You’ve already received bonus, but you’ll lose it if you don’t meet target.”

The bonus system continued for many weeks.

Results Productivity was greater when bonus was framed as a Loss

(Hossain & List, 2009)

In Flossmoor, a wealthy suburb [of Chicago] where the average income is $117,000 a

year, a monthly average of $4.48 is spent on the lottery per household. In Possen, a

poor suburb where average household income is $33,000, the monthly average is

$91.82.

 

Washington Post

November 12, 1995

 

Is gambling foolish?

Objectively, a gamble is irrational if expected value < cost.

Expected Value (EV) = average winnings if you played many, many times

= (probability of a win) (value of a win)

Example

A club sells 100 raffle tickets. Each ticket costs $1.

One ticket is chosen randomly, and the ticket holder wins $300. Everyone else loses.

What is the expected value of a raffle ticket?

EV = (.01)($300)

= $3

If EV < cost, you lose, on average.

If EV > cost, you win, on average.

Another way to measure whether a gamble is in your favor…

EVReturn = ----------- Cost

If return < 1, you lose, on average (because EV < cost)

If return > 1, you win, on average (because EV > cost)

 

Example. If return = .99, you will, on average, win 99¢ for every $1 you pay.

 

 

 Popular Gambles Approximate Return

 Lottery 0.01 - 0.5

Casino

Keno 0.4

Blackjack 0.99 (depends slightly on rules)

Are there gambles in which return exceeds 1?

stock market (historically)

But the EV measures the objective value of a win, not its subjective value

Example

Which would you prefer?

  A) 5% chance of $1 million (EV = $50,000)

  B) 1% chance of $10 million (EV = $100,000)

 

If man hates his job, and $1M is enough to retire, then A is better choice.

In other words, when measured subjectively, $1 M > (1/10) $10 M

When EV is measured subjectively, some low-return gambles are arguably rational…

 

Examples Subjective Value

raffle ticket charity

casino fun

lottery hope

Example

A $2 lottery ticket with EV = $1 may have additional subjective value of $2.

 

The End

Question

Four cards lie on a table.

Each has a letter on one side and a number on the other.

Someone makes the following claim:

If a card has a vowel on one side, it has an even number on other side.

To verify this claim, which card(s) must you turn over?

Correct Answer A and 7

Modal Answer A and 6

(Wason, 1968)

A B 6 7

A better approach…

If our Theory is true, we should find Result R.

We found not R (i.e., the opposite of R, not just a null result)

Therefore, our Theory is false. VALID

Even better:

Theory X predicts R and Theory Y predicts not R.

Our results disprove X and are consistent with Y.

Advice from J. R. Platt (1964):

Upon hearing of a theory, ask “what experiment could disprove it?”

Upon hearing of an experiment, ask “what theory does it disprove?”

Tumor Problem

A patient has a malignant tumor in his stomach.

The tumor can be destroyed by rays of radiation.

But the necessary intensity would kill surrounding tissue.

At lower intensities, the healthy tissue is spared.

How can these rays safely destroy the tumor? 

Fortress Problem

A general wishes to capture a fortress that is surrounded by a moat.

The moat is spanned by six bridges.

To succeed, 600 soldiers must cross the moat at the same time.

But each bridge holds only 100 soldiers.

How can it be done?

Solution to Tumor Problem

Experiment

Ss given tumor problem, but half first see fortress problem.

Fortress problem dramatically improves ability to solve tumor problem.

Finding demonstrates utility of appropriate analogy.

(Duncker, 1945)

Bookworm Problem

A set of encyclopedias sits on a shelf in the usual way.

It includes 26 volumes, one for each letter, in alphabetical order (as usual).

Each volume is 1 inch thick, including the covers.

A bookworm sits on the front cover of the A volume.

It then chews its way to the back cover of the Z volume.

How far did the bookworm travel? (The answer is NOT 26 inches.)

 Answer

24 inches

front cover of A back cover of Z

 

Another example of the sunk-cost fallacy

Company: We make fighter jets.

Congress: We’ll pay no more than $10B each.

Company: It’s a deal.

10 years later…

Company : We now need another $15B per jet.

Congress: Okay, we’ll agree so we don’t want waste our initial investment.

 

The sunk cost fallacy is also known as the Concorde effect, because the British and

the French continued to fund the development of the Concorde even after it became

apparent that there was no longer an economic case for the aircraft. The project was

regarded privately by the British government as a "commercial disaster" which

should never have been started, and was almost cancelled, but political and legal

issues ultimately made it impossible for either government to pull out.

 

(Arkes & Ayton, 1999)

 

By estimating EV, one can evaluate many kinds of risky ventures.

Example

Should you apply for a $1000 scholarship?

1. Estimate minimum probability of winning scholarship. 5%

2. Compute EV. (.05)($1000) = $50

3. Estimate cost (including the cost of your time). $30

Since EV > cost, applying is a good gamble