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Joint desirability foundations of social choice and opinion pooling

Casanova, Arianna ; Miranda, Enrique ; Zaffalon, Marco

In: Annals of Mathematics and Artificial Intelligence, 2021, no. 89, p. 965–1011

We develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an...

Robust inference of trees

Zaffalon, Marco ; Hutter, Marcus

In: Annals of Mathematics and Artificial Intelligence, 2005, vol. 45, no. 1-2, p. 215-239

Limits of learning about a categorical latent variable under prior near-ignorance

Piatti, Alberto ; Zaffalon, Marco ; Trojani, Fabio ; Hutter, Marcus

In: International journal of approximate reasoning, 2009, vol. 50, no. 4, p. 597-611

In this paper, we consider the coherent theory of (epistemic) uncertainty of Walley, in which beliefs are represented through sets of probability distributions, and we focus on the problem of modeling prior ignorance about a categorical random variable. In this setting, it is a known result that a state of prior ignorance is not compatible with learning. To overcome this problem, another...