Consistency of Monomial and Difference Representations of Functions Arising from Empirical Phenomena

AbstractChoice probabilities in the behavioral sciences are often analyzed from the standpoint of a differencerepresentation such as P(x,x,y)=F[u(x,x)−g(y)]. Here, x and y are real, positive vector variables, x is a positive real variable, P(x,x,y) is the probability of choosing alternative (x,x) over alternative y, and u, g and F are real valued, continuous functions, strictly increasing in all arguments. In some situations (e.g. in psychophysics), the researchers are more interested in the functions u and g than in the function F. In such cases, they investigate the choice phenomenon by estimating empirically the value x such that P(x,x,y)=ρ, for some values of ρ, and for many values of the variables involved in x and y. In other words, they study the function ξ satisfying ξ(x,y;ρ)=x⇔P(x,x,y)=ρ. A reasonable model to consider for the function ξ is offered by the monomialrepresentationξx,y;ρ=∏n−1i=1x−ηi(ρ)i∏mj=1yζj(ρ)jCρ,in which the ηi's, the ζj's and C are functions of ρ. In this paper we investigate the consistency of these difference and monomial representations. The main result is that, under some background conditions, if both the difference and the monomial representations are assumed, then: (i) all functions ηi (1≤i≤n−1) must be constant; (ii) if one of the functions ζj is nonconstant, then all of them must be of the form ζj(ρ)=θjexp[δF−1(ρ)], for some constants θj>0 (1≤j≤m) and δ≠0, where F−1 is the inverse of the function F of the difference representation. Surprisingly, F can be chosen rather arbitrarily

Real-time Flexibility Feedback for Closed-loop Aggregator and System Operator Coordination

Aggregators have emerged as crucial tools for the coordination of distributed, controllable loads. However, to be used effectively, aggregators must be able to communicate the available flexibility of the loads they control to the system operator in a manner that is both (i) concise enough to be scalable to aggregators governing hundreds or even thousands of loads and (ii) informative enough to allow the system operator to send control signals to the aggregator that lead to optimization of system-level objectives, such as cost minimization, and do not violate private constraints of the loads, such as satisfying specific load demands. In this paper, we present the design of a real-time flexibility feedback signal based on maximization of entropy. The design provides a concise and informative signal that can be used by the system operator to perform online cost minimization and real-time capacity estimation, while provably satisfying the private constraints of the loads. In addition to deriving analytic properties of the design, we illustrate the effectiveness of the design using a dataset from an adaptive electric vehicle charging network.Comment: The Eleventh ACM International Conference on Future Energy Systems (e-Energy'20

Foundations of the Social Futuring Index

This paper presents a new, multidisciplinary concept called “Social Futuring” and introduces an index based on this concept, entitled the “Social Futuring Index”. Settled into the intersection of philosophy, psychology, sociology, political theory and geopolitics among many other fields of social sciences social futuring and its application as an index addresses both academia and policymakers. In the present article the concept is explained and then placed in the broader context of social sciences. We highlight that the most unique characteristic of social futuring is its fixed normative, analytical and discursive framework, the center of which is “a good life in a unity of order”. Finally, we present the key elements of the index that are currently under construction