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Continuously representable Paretian quasi-orders. (English) Zbl 1105.91012

This article investigates relations between topologies defined employing Pareto order relations, establishing conditions for continuity of Pareto representations. Taking in the domain the Pareto order topology, conditions are determined for continuity as the image is endowed with the Pareto Topology and, alternatively, for coordinate-continuity. The conditions for the existence of continuous representations are, in the first case, that all indifference sets are open in the Pareto order topology and, in the second case, that this holds for the incomparability sets.

MSC:

91B08 Individual preferences
91B12 Voting theory
58C07 Continuity properties of mappings on manifolds
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References:

[1] Aizerman, M. and Aleskerov, F. (1995), Theory of Choice, North-Holland, Amsterdam. · Zbl 0947.91028
[7] Knoblauch, V. (2005), Continuous lexicographic preferences, Journal of Mathematical Economics, forthcoming. · Zbl 1121.91031
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