A note on the invariance of the distribution of the maximum

Publisher's full text
Mogens Fosgerau
Per Olov Lindberg
Lars-Göran Mattsson
Jörgen Weibull

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.

MEET US


25-27
Aug

ICTTP 2020

ICTTP, International Conference on Traffic and Transport Psychology, is held in Gothenburg, Sweden.

LATEST NEWS


2018-11-19

Report regarding government commission on the costs of traffic to society has been submitted

Since 2013, the Swedish National Road and Transport Research Institute (VTI) has had several government commissions to produce documentation on the costs to society caused by traffic. On 1 November 2018, the agency reported its latest commission, Samkost 3....


2018-10-29

International standardisation efforts have many advantages

VTI participates in several international standardisation committees. The work is important because it helps to ensure that standards can be adapted to Swedish conditions and it also provides access to valuable contacts and networks.


2018-10-24

China wants to work with the best

Through the CTS cooperation, VTI is gaining valuable research contacts with China. The country is facing major challenges in the field of road safety but also has enormous potential.


2018-10-23

VTI participated in conference on electric roads

Systems with electrified roads are a relatively new concept and many projects have been launched in recent years. To stimulate the transfer of knowledge and collaboration, the Research and Innovation Platform for Electric Roads arranged its second...


2018-10-18

ADAS&ME is tackling the interaction between people and technology

ADAS&ME is a major EU project focused on automation, the human condition and the human environment. The budget is EUR 9.6 million and VTI is the coordinator.


2018-10-05

Users contribute to the development of train simulators

Apart from advanced driving simulators, VTI has developed several variations of train simulators which are used for training, education and research. In recent years, interest has increased drastically among major actors in the railway sector, and VTI has...