Abstract.
This paper introduces a different approach to the study of the existence of numerical representations of totally ordered sets (chains). We pay attention to the properties of non-representable chains showing that, under certain conditions, those chains must have a sort of lexicographic behaviour similar to that of the lexicographic plane. We prove that a countably bounded connected chain \((Z, \prec )\) admits a lexicographic decomposition as a subset of the lexicographic product \(\Bbb R \times Z\). Then we apply our approach to state both a sufficient and a necessary condition for the lack of utility functions. The concept of planar chain is also introduced.
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Received: 10.10.1996
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Candeal, J., Induráin, E. Lexicographic behaviour of chains. Arch. Math. 72, 145–152 (1999). https://doi.org/10.1007/s000130050315
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DOI: https://doi.org/10.1007/s000130050315