According to decision making theory, if we know the user's utility Ui=U(si) of all possible alternatives si, then we can uniquely predict the user's preferences. In practice, we often only know approximate values Vi~Ui of the user's utilities. Based on these approximate values, we can only make...

In 1951, K. J. Arrow proved that, under certain assumptions, it is impossible to have group decision making rules which satisfy reasonable conditions like symmetry. This Impossibility Theorem is often cited as a proof that reasonable group decision making is impossible.We start our paper by...

An important part of statistical data analysis is hypothesis testing. For example, we know the probability distribution of the characteristics corresponding to a certain disease, we have the values of the characteristics describing a patient, and we must make a conclusion whether this patient...

In many practical situations, there exist regulatory thresholds: e.g., a concentration of certain chemicals in the car exhaust cannot exceed a certain level, etc. If we know the exact value of the corresponding quantity, then we can immediately tell whether, e.g., a car design resulting in this...

Traditional decision theory describes human behavior and human preferences in terms of utility functions. In the last decades, it was shown that in many economic situations, a reasonable description of the actual decisions can be found if we use a different approach -- of spectral risk measures....

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy:first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional...

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy:first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional...

In traditional econometrics, the quality of an individual investment -- and of the investment portfolio -- is characterized by its expected return and its risk (variance). For an individual investment or portfolio, we can estimate the future expected return and a future risk by tracing the...