Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity condition...

In this paper we characterize the set of rules satisfying additivity on the estate along with additivity on the estate and the claims in bankruptcy problems and other related problems. Moreover, new characterizations of the well known rules based on the principles of “equal award”, “equal loss”, and “proportionality” are provided using these additivity properties.

It is known that the additivity conjecture of Holevo capacity, output minimum entoropy, and the entanglement of formation (EoF), are equivalent with each other. Among them, the output minimum entropy is simplest, and hence many researchers are focusing on this quantity. Here, we suggest yet another entanglement measure, whose strong superadditivity and additivity are equivalent to the additivit...

Several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity, are given. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for cer...

In quantum information theory, there are several important open problems which center around whether certain quantities are additive or not. Especially, additivity conjecture about Holevo capacity and additivity/strong superadditivity conjecture about entanglement of formation have been attracting many researchers. It recently turned out that these are equivalent to the additivity of the minimu...

While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti’s central argument against countable additivity and provide a new Dutch book proof of the principle, to argue that if we accept the Dutch book foundations of subjective probability, countable additivity is a...

Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity condition...

Recent research suggests that outcome additivity pretraining modulates blocking in human causal learning. However, the existing evidence confounds outcome additivity and outcome maximality. Here the authors present evidence for the influence of presenting information about outcome maximality (Experiment 1) and outcome additivity (Experiment 2) on subsequent forward blocking. The results of Expe...