## Abstract

Preferences differ in the population, and this heterogeneity may not be adequately described by observed characteristics and additive error terms. As a first contribution, this study shows that preference heterogeneity can be represented graphically by means of violations of the Weak Axiom of Revealed Preference (WARP), and that computing the minimum number of partitions necessary to break all WARP violations in the sample is equivalent to computing the chromatic number of this graph. Second, the study builds the bridge between revealed preference theory and cluster analysis to assign individuals to these partitions (i.e. preference types). The practical methods are applied to Dutch labour supply data, to recover reservation wages of individuals who belong to particular preference types.

## Keywords

Preference heterogeneity Chromatic number Revealed preference Labour supply Constrained clustering## JEL Classifications

C14 C38 C44 D12 D13## Notes

### Acknowledgements

I thank Laurens Cherchye, Thomas Demuynck and Ian Crawford, and also Bart Cap éau, John Dagsvik, André Decoster, Bram De Rock, Yuichi Kitamura, Arthur Lewbel, Lars Nesheim, Johannes Spinnewijn and Frederic Vermeulen for valuable suggestions. Furthermore, I am grateful to seminar participants in Kortrijk and Leuven (University of Leuven), Cergy–Pontoise (ADRES conference), Namur (University of Namur) and Esch–sur–Alzette (LISER). The LISS panel data were collected by CentERdata (Tilburg University, The Netherlands) through its MESS project funded by the Netherlands Organization for Scientific Research.

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