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A simple derivation of the Williams-Daly-Zachery theorem
KTH, School of Architecture and the Built Environment (ABE), Transport Science, Transport and Location Analysis.
2012 (English)Report (Other academic)
Abstract [en]

In this note we give a simple elementary proof of the Williams-Daly-Zachery theorem for additive random utility (ARU) models. This theorem says that the choice probabilities in an ARU model are the partial derivatives of the expected achieved utility. This is proved under the condition that the choice probabilities are continuous. We further prove that the choice probabilities are continuous exactly when the probability of ties is zero. Finally we prove that the probability of ties is zero if the cdf of the random term (of the ARU model) is differentiable with locally bounded gradient.

Place, publisher, year, edition, pages
2012.
National Category
Transport Systems and Logistics
Identifiers
URN: urn:nbn:se:kth:diva-95398OAI: oai:DiVA.org:kth-95398DiVA: diva2:528087
Note
QC 20120524Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2012-05-24Bibliographically approved
In thesis
1. Contributions to Probabilistic Discrete Choice
Open this publication in new window or tab >>Contributions to Probabilistic Discrete Choice
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. x, 20 p.
Series
TRITA-TSC-PHD, 12:001
National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-95402 (URN)978-91-85539-86-4 (ISBN)
Public defence
2012-06-01, D2, Lindstedtsvägen 5, KTH, Stockholm, 09:15 (English)
Opponent
Supervisors
Funder
TrenOp, Transport Research Environment with Novel Perspectives
Note

QC 20120524

Available from: 2012-05-24 Created: 2012-05-24 Last updated: 2016-01-20Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf