Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but only preference aggregation rules which achieve it (and are minimally Paretian continuous) linear-geometric rules, combine individual values linearly beliefs geometrica...

We propose three new robust aggregation rules for distributed synchronous Stochastic Gradient Descent (SGD) under a general Byzantine failure model. The attackers can arbitrarily manipulate the data transferred between the servers and the workers in the parameter server (PS) architecture. We prove the Byzantine resilience properties of these aggregation rules. Empirical analysis shows that the ...

The Analytic Hierarchy Process (AHP) has been considerably criticized for its possible rank reversal phenomenon. Many variants of the original AHP have been proposed to preserve rank orders. The validity of the original AHP and its variants have been a subject of long-lasting debate. In this paper we propose four criteria to evaluate the validity of AHP aggregation rules and examine three typic...

Subjective Bayesian prior distributions elicited from experts can be aggregated together to form group priors. This paper compares priors formed by Equal Weight Aggregation, the Classical Method, and Sheffield Elicitation Framework each other individual expert priors, using an elicitation carried out for a clinical trial. Aggregation methods are compared proper scoring rules compare informative...

The rise of the social media sites, such as blogs, wikis, Digg and Flickr among others, underscores the transformation of the Web to a participatory medium in which users are collaboratively creating, evaluating and distributing information. The innovations introduced by social media has lead to a new paradigm for interacting with information, what we call ’social information processing’. In th...

Abstract It is shown how infinite sequences of densities with defined properties can be used to evaluate the expected performance of mathematical aggregation rules for elicited densities. The performance of these rules is measured through the expected variance, calibration, and expected Brier score of the aggregate. A general result for the calibration of the arithmetic average of densities fro...

The acyclicity of individual improvements in a generalized congestion game (where the sums of local utilities are replaced with arbitrary aggregation rules) can be established with a Rosenthalstyle construction if aggregation rules of all players are “quasi-separable.” Every universal separable ordering on a finite set can be represented as a combination of addition and lexicography. MSC2010 Cl...

This paper deals with aggregation of fuzzy individual opinions into a single group opinion, based upon hierarchical intensity aggregation rules. Characterization theorems are given, and it is also shown that Montero's rationality and standard ethical conditions propagate under hierarchical aggregations.

The present paper examines how the aggregation and feature randomization principles underlying the algorithm Random Forest (Breiman (2001)) can be adapted to bipartite ranking. The approach taken here is based on nonparametric scoring and ROC curve optimization in the sense of the AUC criterion. In this problem, aggregation is used to increase the performance of scoring rules produced by rankin...

Data warehouses are based on multidimensional modeling. Using On-Line Analytical Processing (OLAP) tools, decision makers navigate through and analyze multidimensional data. Typically, users need to analyze data at different aggregation levels (using roll-up and drill-down functions). Therefore, aggregation knowledge should be adequately represented in conceptual multidimensional models, and ma...