On rare events and the economics of small decisions

Ido Erev, Technion

Examples: Using safety devices, cheating in exams, selecting among websites, stopping at red lights, continue listening.

Why small:•Can be studied in the lab.•Can be predicted with simple models with high ENO (Erev, Roth, Slonim & Barron)•Can be important.

Are small decisions similar to large decisions?

According to the common assumption large decisions can be studied by focusing on the way people decide based on descriptions of the possible payoff distributions.

For example:

3000 with certainty

4000 with probability 0.8; 0 otherwise

We believe that this paradigm is a useful simulation of the last stage in large decisions, but it is not clear that it trigger tendencies that are similar to the tendencies that affect small decisions.

In many settings small decisions are made based on personal experience without explicit descriptions of the payoff distributions.

Experimental research highlights large differences between decisions from descriptions and from experience

Decisions from description: 4 fold risk pattern (Kahneman & Tversky)

Gain, large P S 3000 with certainty

R 4000 with p =0.8; 0

Gain, low P S 5 with certainty

R 5000 with p = .001; 0

Buying lotteries

Loss, large P S -3000 with certainty

R -4000 with p =0.8; 0

Loss, low P S -5 with certainty

R -5000 with p =.001; 0

Buying insurance

Experimental research highlights large differences between decisions from descriptions and from experience

Decisions from description: 4 fold risk pattern (Kahneman & Tversky)

Decisions from experience: reversed 4 fold risk pattern(Erev & Barron, 2003)

Gain, large P S 3000 with certainty

R 4000 with p =0.8; 0

S 9 with certainty

R 10 with p =0.9; 0

Gain, low P S 5 with certainty

R 5000 with p = .001; 0

Buying lotteries

S 3 with certainty

R 32 with p = 0.1; 0

Learned helplessness

Loss, large P S -3000 with certainty

R -4000 with p =0.8; 0

S -9 with certainty

R -10 with p =0.9; 0

Loss, low P S -5 with certainty

R -5000 with p =.001; 0

Buying insurance

S -3 with certainty

R -32 with p =0.1; 0

It wont happen to me

This pattern can be explained with the assertion that rare events are overweighted when they are presented, but are forgotten when they are not (in decisions from experience).

In decisions from experience people deviate from maximization in the direction of the alternative that leads to better outcome most of the time.

This pattern was observed in a wide set of paradigms:

•Search paradigm (Fujikawa & Oda, 2004; Barron & Erev, 2003)•Sampling and a single choice (Hertwig et al., 2004; Ert et al., 2004)•Signal detection (Erev, 1998)•The joint effect of description and experience (Yechiam et al., 2005)

Relatively simple models allow useful prediction of behavior (Erev & Barron, 2005)

Pessimistic interpretation

In natural decision problems people rely on descriptions and experience. Thus, the two biases are likely to cancel each other out. So, the experimental examples are interesting, but can be ignored when decisions outside the laboratory are considered.

Under an optimistic interpretation the coexistence of the two biases magnifies the importance of the behavioral approach. It suggests that understanding of the conditions under which the two biases occur can be very useful.

Gentle enforcement of safety rules (Erev & Rodansky, 2004)

Enforcement is necessaryWorkers like enforcement programsProbability is more important than magnitudeLarge punishments are too costly; therefore, gentle enforcement can be optimal

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אוגוסט -אוקטובר-03נובמבר-03דצמבר-03ינואר-04פברואר-04מרץ-04אפריל-04מאי-04ספטמבר

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Consider a situation in which a rule enforcement unit has limited capacity. For example, it can punish, on average, only M violators. Assume further that the number of potential violators (subjects of the rule) is N>M, the cost of obeying the rule is C > 0, that the fine for violators (when punished) is F > C, and that (F)(M/N) < C.

i.e. N = 100 students, M = 10 fines, F = Fine of $7, C = cost of obeying $5.

This “game” has at least two Nash equilibria. In the first, no agent violates the rule. In the second equilibrium all the agents violate the rule.

Relative value of violation

Proportion of violators

C-F(M/N)

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Cheating in exams (Erev, Ingram, Raz & Shany, 2005)

Under a gentle solution, the enforcement unit can employ a gentle ZT policy that use moderate fines (C < F < C(N/M)). Under this solution the unit declares that the first M violators will be punished. Given this declaration no one will be motivated to be the first violator. As a result “no violation” is the unique equilibrium of the game.

A field experimentTo evaluate this solution, we used it to try to reduce cheating during university exams. The experiment was conducted during final semester exams of undergraduate courses. Traditionally, instructions for exam proctors included the following points: (1) The student’s ID should be collected at the beginning of the exam, (2) A map of students’ seating should be prepared.

To facilitate the implementation of gentle ZT in the experimental condition we simply changed the second instruction to proctors: (2e) “A map of the students seating should be prepared 50 minutes after the beginning of the exam.”

Other examples

Two-stage lottery promotion (Haruvy & Erev, 2006) The effect of rare terrorist attacks (Yechiam et al., 2005).The effect of immediate feedback on the decision to practice.The value of free sampling (Ert et al., 2006).Risk attitude in time saving decisions (Munichor et al., 2006).

In summary, Paris Hilton and Amnon Rapoport are correct, but small decisions can be interesting.

Reinforcement learning among cognitive strategies (RELACS)Erev & Barron (2005)

Basic idea:

The optimal strategy in decisions from experience is situation specific:

Slow best reply (Stochastic fictitious play) (9) or (100, .1; 0)Fast best reply (11) or (10)Best reply to pattern

People learn among the reasonable strategies

The Equivalent Number of Observations of Descriptive modelsIdo Erev, Al Roth, Bob Slonim and Greg Barron

Assume that you are asked to predict behavior in a new environment (e.g., the proportion of violations of safety rules given a new rule enforcement policy).

Learning models can be used to drive ex ante prediction. This prediction can be described as the modeler’s prior opinion.

When observations concerning behavior in the new situations are available, the prior opinion can be revised.

We show that the optimal revision is given by the rule:

RevPred = W(Prior) + (1-w)(Obseved)

Where W = ENO/(ENO + n)ENO is the model equivalent number of observationsAnd n is the number of observations of behavior in the new situations