Conditions on Load-Sharing Models which Avoid Paradoxes of Stochastic Precedence and Voting Theory

Tassi Niccolo, Universidad de Granada

Multivariate Stochastic Precedence is a natural way to compare random variables that has been widely studied in the literature and it is of interest in many contexts. Different types of paradoxes, that may emerge in the related analysis, have been pointed out in recent papers (see references below). Related to these aspects, [1] has introduced the properties of "pair-determined" and "ordered by pairs". These properties convey conditions under which multivariate probabilistic models are not prone to manifest the aforementioned paradoxes. This talk will be devoted to study these properties for a specific class of multivariate probability models known as time-homogeneous load-sharing models. Although being very special, these models offer a good tool to study multivariate stochastic precedence and to connect it to basic questions in voting theory (see [2], [3]). On these bases, and as one of the main purposes of this talk, I aim to demonstrate the connections between these properties for Load Sharing Models and the properties of (corresponding) voting situations. I will also focus on the analysis of models’ parameters, giving an insight into their meaning in the context of voting theory. Joint work with Emilio De Santis and Fabio Spizzichino. References [1] De Santis, E., Malinovsky, Y., Spizzichino, F.; Stochastic Precedence and Minima Among Dependent Variables. Methodol Comput Appl Probab 23, (2021), 187–205. [2] De Santis, E., Spizzichino F.; Construction of aggregation paradoxes through load-sharing mod- els. Adv. Appl. Prob., 55, (2023), 223–244. [3] De Santis, E., Spizzichino, F;. Construction of voting situations concordant with ranking pat- terns. Decis. Econ. Finance, 46, (2023), 129–156. [4] De Santis, E., Tassi N., Spizzichino, F.; Conditions on Load-Sharing Models which Avoid Para- doxes of Stochastic Precedence and Voting Theory. In preparation. [5] Montes, I., Rademaker, M., Pèrez-Fernandez, R., De Baets, B. A.; A correspondence between voting procedures and stochastic orderings. J. Oper. Res. 285, (2020), 977-987

Area: CS53 - Connections between stochastic models and game and voting theory (Emilio De Santis)

Keywords: Parameters of load sharing models, multivariate stochastic prefedence, nontransitive paradoxes

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