1 Regions of rationality: Maps for bounded agents (Decision Analysis, in press) Robin M. Hogarth ICREA & Universitat Pompeu Fabra, Barcelona & Natalia Karelaia H.E.C., Université de Lausanne

2 “Regions of rationality” The starting point: –“heuristics and biases” (Kahneman, Slovic, & Tversky, 1982) –simple decision rules can rival the predictive ability of complex algorithms (e.g., regression) (e.g., TTB: Gigerenzer, Todd, & the ABC Research Group, 1999; EW : Dawes & Corrigan, 1974). Idea: –Attention as a scarce resource (Simon, 1978) -> how much information to seek & how to combine the pieces to make decisions in different “regions”: identify decision rules that are appropriate to each region multiple-cue prediction (multi-attribute choice) cues are probabilistically related to the criterion

3 A theoretical approach… 1.Effectiveness of several heuristics: the probability that the best of m alternatives (with k cues) is identified; the environmental conditions favoring various heuristics, e.g.: differential weighting of cues inter-correlations of cues continuous/binary cues (c/b) noise in the environment interactions of these factors 2. Illustration: 20 “artificial” and 4 empirical environments

4 Models Single Variable (SV) models 1.Lexicographic – SVc 2.Lexicographic – SVb 3.DEBA (binary cues) Equal weight (EW) models 4. EWc 5. EWb Hybrid models 6.EW/DEBA 7.EW/SVb Domran (DR) models (lower benchmark) 8.DRc 9.DRb Multiple regression (MR) (upper benchmark) 10.MRc 11.MRb

5 Method Single Variable, continuous cues - SVc Choosing between A & B Y = criterion and X = cue Assume: Y and X are N(0,1), >0 = error,, N(0, ), Question:

6 Prob {SVc chooses the best b/w A & B}

7 Therefore, Prob {SVc chooses the best b/w A & B} pdf = probability density function

- z1 and z2 are bivariate N Prob {SVc chooses the best from A, B, & C}

9 SVc: generalizing to the case of m alternatives (m>3) where (m-1) between-alternative comparisons

10 Overall probability of correct choice by SVc Random sampling of m=3 from the underlying population of alternatives. Either A, B, or C is chosen -> overall probability is: 3 P{((X a >X b ) & (X a >X c ))&((Y a >Y b )&(Y a >Y c ))} integrated across : where,.

11 Overall probability of correct choice by SVc: generalizing to m>3 where

12 Other models: EWc & MRc Model: Error: VdVd di*di*

13 Models with binary cues - SVb where Therefore,

14 Models with binary cues - SVb choosing 1 of 2 where

15 Models with binary cues - DEBA & Hybrids Prob {a given alternative is chosen correctly}= the joint probability that the sequence of decisions (or eliminations) made at each stage is correct. Three key notions: 1.Appropriate model for each stage 2.Partial correlations: and partial st. deviations: 3. Probability theory to calculate sequence of correct eliminations

Illustration: 20 “artificial” environments -Choosing the best from 2, 3, and 4 alternatives -n=40 k

17 Low inter-cue corrHigh inter-cue corr 3 cues 5 cues High inter-cue corrLow inter-cue corr Choosing the best from 3

18 (1) Similarity of models’ performance –agreement between models (average between all pairs, A-D)=63% (vs. 33.(3)% of random agreement), lower when lower inter-cue corr. (2)Model with continuous cues outperform their binary counterparts (except DR). –DRb > DRc. Choosing at random: DRb = in 51%, DRc = in 81%. (3)Larger inter-cue correlation reduces performance of all models (except SV). Some results

Regression of model performance

20 Illustration: 4 empirical datasets 1) Golf all-around ranking, N=60 1. Birdie average (*-1) 2. Scoring average 3. Putting average 2) Golf earnings, N=60 1. Top 10 finishes 2. All-around ranking (*-1) 3. Consecutive cuts 3) PhD economics programs: ratings-1993, N=107http:// 1. # of PhDs for the academic year to Total # of program citations 88-92/ number program faculty 3. % Faculty with research support 4) Consumer reports:test score for digital cameras, 1. Image quality 2. Picture download time 3. Focusing

21 Illustration: empirical datasets

22 Golf ranking Golf earnings Economics PhD programs Consumer reports

23 (1)Our contributions –Analytical analysis –Regions of rationality: a multidimensional terrain (2)Further research & implications –Non-random sampling of alternatives –Hybrids with categorical & continuous variables –Different loss functions –Predicting consumer preferences –Bounded rationality and expertise: how do people build maps of their decision making terrain? Discussion