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# Multivariate winning probabilities

(2019) 362. p.129-143
Author
Organization
Abstract
Stochastic dominance and statistical preference are two important tools for the pairwise comparison of random variables. However, pairwise methods are not always appropriate in the case of more than two alternatives. In this work, we generalize the notion of winning probability to the notion of multivariate winning probability. The latter allows to establish a ranking (with ties) on any set of random variables and naturally leads to the notion of probabilistic preference. We investigate the relationship between the latter notion and the classical notions of stochastic dominance and statistical preference.
Keywords
Winning probabilities, Stochastic dominance, Probabilistic relation, Statistical preference, Decision making

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## Citation

Chicago
Montes, Ignacio, Susana Montes, and Bernard De Baets. 2019. “Multivariate Winning Probabilities.” Fuzzy Sets and Systems 362: 129–143.
APA
Montes, I., Montes, S., & De Baets, B. (2019). Multivariate winning probabilities. Fuzzy Sets and Systems, 362, 129–143.
Vancouver
1.
Montes I, Montes S, De Baets B. Multivariate winning probabilities. Fuzzy Sets and Systems. Elsevier BV; 2019;362:129–43.
MLA
Montes, Ignacio, Susana Montes, and Bernard De Baets. “Multivariate Winning Probabilities.” Fuzzy Sets and Systems 362 (2019): 129–143. Print.
```@article{8607572,
abstract     = {Stochastic dominance and statistical preference are two important tools for the pairwise comparison of random variables. However, pairwise methods are not always appropriate in the case of more than two alternatives. In this work, we generalize the notion of winning probability to the notion of multivariate winning probability. The latter allows to establish a ranking (with ties) on any set of random variables and naturally leads to the notion of probabilistic preference. We investigate the relationship between the latter notion and the classical notions of stochastic dominance and statistical preference.},
author       = {Montes, Ignacio and Montes, Susana and De Baets, Bernard},
issn         = {0165-0114},
journal      = {Fuzzy Sets and Systems},
pages        = {129--143},
publisher    = {Elsevier BV},
title        = {Multivariate winning probabilities},
url          = {http://dx.doi.org/10.1016/j.fss.2018.09.012},
volume       = {362},
year         = {2019},
}

```
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