Problem Solving

A.P. Psychology - Chapter 8

• Can you solve the following problems:• In the Thompson family there are five brothers, and

each brother has one sister. If you count Mrs. Thompson, how many females are in the Thompson family.

• Fifteen percent of the people in Topeka have unlisted telephone numbers. You select 200 names at random from the Topeka phone book. How many of these can you expect to have unlisted phone numbers?

Answers to the Questions

• #1 There are 2 females ~ Mrs. Thompson & her one daughter, who is the sister to each of her brothers.

• #2 None ~ you won’t find any unlisted phone numbers in the phone book.

Types of Problems• Problems of Inducing Structure

• Require people to discover the relations between numbers, words, symbols or ideas

» Analogy problems» Series completion problems

• Problems of Arrangement• Require people to arrange the parts of a problem in a

way that satisfies some criterion – usually there are many ways, but only a few form a solution

• Problems of Transformation• Require people to carry out a sequence of

transformations in order to reach a specific goal

Problems of Inducing Structure

• What word completes the analogy?– Merchant: Sell ::

Customer : ________– Lawyer : Client ::

Doctor : __________

• What number or letter completes each series?– 1 2 8 3 4 6 5 6

__– A B M C D M __

Problems of Arrangement

• The String Problem

• Two strings have from the ceiling but are too far apart to allow a person to hold one and walk to the other. On the table are a book of matches, a screwdriver, a few pieces of cotton. How could the strings be tied together?

• Insight• Sudden discovery of the correct solution following incorrect

attempts based primarily on trial & error• Often helps to solve Arrangement Problems

Problems of Transformation

Barriers to Effective Problem Solving

• Irrelevant Information– Many problems include

information that is irrelevant to solving the problem

– Leads people astray

• Functional Fixedness– The tendency to perceive

an item only in terms of its most common use

• Ex. In the string problem, people see a screwdriver in terms of its most common use, not as a possible weight.

• Mental Set– Exists when people

persist in using problem-solving strategies that have worked in the past

• Unnecessary Constraints

Approaches to Problem Solving

• Working Backward• Search for Analogies• Forming Sub-goals

– Use intermediate steps• Change Representation of the Problem

– Change how you see the problem• Algorithms

– Methodical, step-by-step procedure for trying all possible alternatives in searching for a solution

– Ex. Anagram IHCRA – you would list out all the possible arrangements of the letters

• Heuristics– A guiding principle or “rule of thumb” used in solving

problems or making decisions

Try some more problemsThe Tower of Hanoi – move rings from peg A to peg C. You can only move the top ring

on a peg and you can’t place a larger ring above a smaller one

Try some more problems

• The water lilies on the surface of a small pond double in area every 24 hours. From the time the first water lily appears until the pond is completely covered takes 60 days. On what day is half of the pond covered with lilies?

• A teacher had 23 pupils in his class. All but 7 went on a museum trip and thus were away for the day. How many students remained in class that day?

Decision Making

• Evaluating alternatives & making choices among those alternatives

• Herbert Simon– Theory of Bounded Rationality

• People tend to use simple strategies & focus only on a few facets of available options resulting in “irrational” decisions

Selecting an Alternative

• Additive Strategy• List personally

important attributes then rate choices based on each

• Elimination by Aspects

• Gradually eliminate less attractive alternatives

• When any alternative fails to satisfy criterion, it is eliminated

Which Strategy Do We Use?

• John Payne (1976)• When there are few options with few attributes to

evaluate by additive strategies• More options & more factors elimination by aspects

• We adapt out approach to the demands of the task

• Tversky & Shafir (1992)• We delay our decisions when alternatives are not

dramatically different• We struggle with conflict & so seek out additional info

Risky Decision Making

• Making choices under conditions of uncertainty• Strategies

– Expected value – extrinsic reward– Subjective utility- intrinsic worth– Subjective probability – personal estimates of worth

Heuristics in Judgements of Probability

• Amos Tversky & Daniel Kahneman– Availability Heuristic

• Estimated probability based on the ease with which relevant instances come to mind

– EX. Divorce Rate based off of how many of your friends are divorced

– Representativeness Heuristic• Estimated probability based on how similar the event is

to the typical prototype of that event– EX. Flipping a coin 6 times

» 1. T T T T T T» 2. H T T H T H

Pitfalls in Reasoning about Decisions

• Gamblers Fallacy• Odds of a chance event

increase if an event has not happened recently

• Law of Small Numbers• Misleading results tend to

happen in smaller samples – small samples lead to flukes

• Misplaced faith in small numbers explains why people are often willing to draw general conclusions based on a few individual cases

» Chance of getting all “heads” flipping a coin 5 times is much better than 100 times

Pitfalls in Reasoning about Decisions

• Overestimating the Improbable

• Overestimation of the dramatic, vivid – but infrequent events

• Confirmation Bias• Seeking info that supports

your decisions while ignoring disconfirming info

• Belief Perseverance• Hanging onto beliefs in the

face of contradictory evidence

Actual Mortality Rates for Causes of Death

Asthma 2,000

Accidental Falls 6,021

Tuberculosis 400

Suicide 11,300

Tornados 25