Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Pierpaolo Angelini and Angela De Sanctis
Pages: [83] - [104]
Received Date: June 9, 2018
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121973
We show a choice model based on application the principles of the economic theory of preferences of consumers to the two-dimensional convex set of all coherent previsions of two or more than two random gains. Such a model is well-founded because we establish an essential analogy between the properties of consumer preferences about consumption bundles and the ones of coherent previsions of random quantities. We deal with a unified approach to an integrated and simplified formulation of decision-making theory in its two components, probability and utility. The path followed in order to study coherence properties of prevision is guided by the economic criteria of the decision-making theory which is however presented in a simplified form. Indeed, the fundamental hypothesis of additivity of prevision tells us that the decision-maker is not risk-averse but he is risk-neutral, so the certain gain equivalent to a random quantity viewed as a random gain coincides with a particular and coherent prevision of this random gain. We are the first in the world to do this kind of work and for this reason we believe that it is not inappropriate that our references limit themselves to those pioneering works which will always be very meaningful from heuristic point of view too. We prove that it is occasionally necessary to look further back than one could usually think in order to imagine works developing interesting and original ideas.
preference, utility function, subjective probability, coherence, closed convex hull, hyperplane, risk neutrality.
