 A note on the invariance of the distribution of the maximumMogens Fosgerau, Per Olov Lindberg, Lars-Göran Mattsson and Jörgen Weibull Journal of Mathematical Economics, 2018, vol. 74, issue C, 56-61 Abstract: Many models in economics involve discrete choices where a decision-maker selects the best alternative from a finite set. Viewing the array of values of the alternatives as a random vector, the decision-maker draws a realization and chooses the alternative with the highest value. The analyst is then interested in the choice probabilities and in the value of the best alternative. The random vector has the invariance property if the distribution of the value of a specific alternative, conditional on that alternative being chosen, is the same, regardless of which alternative is considered. This note shows that the invariance property holds if and only if the marginal distributions of the random components are positive powers of each other, even when allowing for quite general statistical dependence among the random components. We illustrate the analytical power of the invariance property by way of examples. Keywords: Discrete choice; Random utility; Extreme value; Leader-maximum; Invariance (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:74:y:2018:i:c:p:56-61 DOI: 10.1016/j.jmateco.2017.10.005 Access Statistics for this article Journal of Mathematical Economics is currently edited by Atsushi (A.) Kajii More articles in Journal of Mathematical Economics from Elsevier |
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