We present a method to characterize the preferences of a decision maker in decisions with multiple attributes. The approach modifies the outcomes of a multivariate lottery with a multivariate transformation and observes the change in the decision maker’s certain equivalent. If the certain equivalent follows this multivariate transformation, we refer to this situation as multiattribute transformation invariance, and we derive the functional form of the utility function. We then show that any additive or multiplicative utility function that is formed of (...) continuous and strictly monotonic utility functions of the individual attributes must satisfy transformation invariance with a multivariate transformation. This result provides a new interpretation for multiattribute utility functions with mutual utility independence as well as a necessary and sufficient condition that must be satisfied when assuming these widely used functional forms. We work through several examples to illustrate the approach. (shrink)

Some of the significant features of our era include the design of large-scale systems; advances in medicine, manufacturing, and artificial intelligence; the role of social media in influencing behavior and toppling governments, and the surge of online transactions that are replacing human face-to-face interactions. Most of these features have resulted from advances in technology. While spanning a variety of disciplines, these features also have two important aspects in common: the need for sound decision making about the technology that is evolving, (...) and the need to understand the ethical implications of these decisions to all stakeholders. Technology is amoral: it does not know how it will be used. In fact, technological advancements have made it even easier to deceive, partly because of the new capabilities that are enabled by the technology (such as creating fake videos from selfies, known as "Deep Fakesʺ) and partly because of the level of complexity that is added to new advancements making the internal structure of a product less obvious to users and policy makers. (shrink)

In the probability literature, a martingale is often referred to as a “fair game.” A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor’s current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker would not be (...) indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a “risk-adjusted martingale”; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function. (shrink)