Random utility model: Difference between revisions

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There are various RUMs, which differ in the assumptions on the probability distributions of the agent's utility, A popular RUM was developed by Luce<ref>{{cite book |last1=Luce |first1=R. Duncan |title=Individual Choice Behavior: A Theoretical Analysis |date=2012 |publisher=Courier Corporation |isbn=978-0-486-15339-1 }}{{pn|date=July 2024}}</ref> and Plackett.<ref>{{cite journal |last1=Plackett |first1=R. L. |title=The Analysis of Permutations |journal=Applied Statistics |date=1975 |volume=24 |issue=2 |pages=193–202 |doi=10.2307/2346567 |jstor=2346567 }}</ref>

The Plackett-Luce model was applied in [[econometrics]],<ref name="McFadden Conditional Logit Analysis">{{cite book |last1=McFadden |first1=Daniel |chapter=Conditional Logit Analysis of Qualitative Choice Behavior |pages=105–142 |editor1-last=Zarembka |editor1-first=Paul |title=Frontiers in Econometrics |date=1974 |publisher=Academic Press |isbn=978-0-12-776150-3 }}</ref> for example, to analyze automobile prices in [[market equilibrium]].<ref>{{Cite journal |last1=Berry |first1=Steven |last2=Levinsohn |first2=James |last3=Pakes |first3=Ariel |date=1995 |title=Automobile Prices in Market Equilibrium |journal=Econometrica |volume=63 |issue=4 |pages=841–890 |doi=10.2307/2171802 |jstor=2171802 }}</ref> It was also applied in [[Machine learning in earth sciences|machine learning]] and [[information retrieval]].<ref>{{cite journal |last1=Liu |first1=Tie-Yan |title=Learning to Rank for Information Retrieval |journal=Foundations and Trends® in Information Retrieval |date=2007 |volume=3 |issue=3 |pages=225–331 |doi=10.1561/1500000016 }}</ref> It was also applied in [[Social choice theory|social choice]], to analyze an opinion poll conducted during the [[1997 Irish presidential election|Irish presidential election]].<ref>{{cite journal |last1=Gormley |first1=Isobel Claire |last2=Murphy |first2=Thomas Brendan |title=A grade of membership model for rank data |journal=Bayesian Analysis |date=June 2009 |volume=4 |issue=2 |doi=10.1214/09-BA410 |hdl=10197/7121 |hdl-access=free }}</ref> Efficient methods for [[expectation-maximization]] and [[Expectation propagation]] exist for the Plackett-Luce model.<ref>{{cite journal |last1=Caron |first1=François |last2=Doucet |first2=Arnaud |title=Efficient Bayesian Inference for Generalized Bradley–Terry Models |journal=Journal of Computational and Graphical Statistics |date=January 2012 |volume=21 |issue=1 |pages=174–196 |doi=10.1080/10618600.2012.638220 |arxiv=1011.1761 }}</ref><ref>{{cite journal |last1=Hunter |first1=David R. |title=MM algorithms for generalized Bradley-Terry models |journal=The Annals of Statistics |date=February 2004 |volume=32 |issue=1 |doi=10.1214/aos/1079120141 }}</ref><ref>{{cite book |doi=10.1145/1553374.1553423 |chapter=Bayesian inference for Plackett-Luce ranking models |title=Proceedings of the 26th Annual International Conference on Machine Learning |date=2009 |last1=Guiver |first1=John |last2=Snelson |first2=Edward |pages=377–384 |isbn=978-1-60558-516-1 }}</ref>

== Application to social choice ==