Wolfgang Kohler Problem solving

Initial state

Goal state

Seen as a process of moving through ‘problem space’ (Newell & Simon)

“Problem space”Initial state End state

Cat gets off washing (goal

state)Prod cat

Shout at cat

Don oven glove

Ignored

Approaches to problem space

• Algorithmic or heuristic

• Algorithms:

• Exhaustive search

• Following directions

• Means-end analysis (difference reduction)

• Local minima

Heuristics

• “Rules of thumb” for approaching problems

• A means of narrowing down the routes through problem space

• Heuristics come from

• Inbuilt biases

• Learning

Heuristic examples

• Where’s the best place in central Bath to find a taxi?

• How much cash do you need to take out when doing various activities?

Choice of approach• Many problems open to both

approaches

• “Where are my keys?!”

• Algorithmic approach, e.g., systematic search

• Heuristic approach, e.g., “Where do I tend to put them? Where are they really unlikely to be?”

Algorithm summary

• Better with well-defined problems

• ‘Solve 3x = 12 for x’ vs ‘Have a happy life’

• How to deal with vague problems?

• Should find solution if it exists

• May be time-consuming with large spaces

Problem-solving and mental set

• Studies identify difficulties solving problems owing to ‘mental set’

• Functional fixedness

• Negative set (Einstellung, ‘mind-set’)

Luchens (1942)

Problem Jug A size Jug B size Jug C size Target

1 21 127 3 100

2 14 163 25 99

3 18 43 10 5

4 9 42 6 21

5 20 59 4 31

6 23 49 3 20

7 15 39 3 18

8 28 76 3 25

9 18 48 3 22

10 14 36 8 6

Negative set

Negative set

1 2 3 4 5 6

Silveira (1971)You are given four separate pieces of chain that are each three links in length.! It costs £2 to open a link and £3 to close a link.! All links are closed at the beginning of the problem.! Your goal is to join all 12 links of chain into a single circle at a cost of no more than £15

Incubation

• Taking a break from a problem increases the likelihood of solving it

• Original explanation: subconscious thought

• Actually, incubation primarily due to (a) priming of more solution paths, and (b) forgetting dead-end solutions (Kaplan & Davidson, 1988)

Difficulties resulting from heuristics

• Tversky & Kahneman

• Looked at people’s abilities to solve various problems

• Elucidated various heuristic biases in problem-solving

The availability heuristic

• What proportion of Bath students are female?

• Is your estimate biased by the availability of information in your mind?

Availability heuristic

• “Judgements are biased by the ease with which relevant examples can be recalled”

• So personal experience of something can colour your judgements on that topic

• If your neighbour from country X is noisy, you are likely to make biased judgements about that country...

Availability heuristic

• Similarly, judgements are affected by:

• General knowledge

• Familiarity

• Salience/vividness

Simulation heuristic

• Mr Crane and Ms Tees were scheduled to leave the airport at the same time on different flights. The travelled to the airport in the same car but were caught in traffic. Mr Crane learns that his flight left on time. Ms Tees is told her flight was delayed, and just left five minutes ago. Who is more upset?

The Simulation heuristic

• A variation on the availability heuristic

• The extent to which something can be imagined affects the extent to which it is deemed likely to happen

• The mental image makes the notion ‘available’

Representativeness heuristic

• Tossing a coin - which sequence is most likely?

• HHHHTTTT

• HHTHTHTT

• Bias towards the second

Representativeness heuristic

• “Judgements of an event’s probability are influenced by how similar the event is to the population of events, or the process that produced it”

• So as coin toss is a 50:50 process, the more alternating sequence is favoured

Hospitals• In this area, women give birth at the

Royal United Hospital and Paulton hospital. The RUH has around 48 births a day, Paulton around 16.

• Obviously, 50% of all babies are girls, but on any given day, the percentage of girls seen at a hospital may be higher or lower than this.

• The two hospitals record how often they see more than 6o% girls in a day.

• Which hospital will have more days with over 60% girls?

Biases from representativeness h’stic

• Insensitivity to sample size

• Base-rate neglect

• Gambler’s fallacy

Use of heuristics

• People tend to be poor at apparently simple problems

• Tversky et al. therefore argue people are poor rational decision makers

Gigerenzer

• Argues that the errors seen in Kahneman/Tversky tasks shouldn’t be seen as errors

• Argues that the norms for evaluating judgements are too narrow and artificial

• Heuristics too vague as models of human thought

More generally

• In a situation where most people produce a ‘wrong’ answer, is this:

• A systematic failure of human problem-solving?

• A failure to understand the nature of human problem-solving?

• Over-emphasis on rationality?

Summary

• Problem solving described through problem space metaphor

• Much research on errors when moving through this space

• More recently, this has taken some criticism for not reflecting real nature of cognition