Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker’s choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains.
The Time To the Most Recent Common Ancestor (TMRCA) based on human mitochondrial DNA (mtDNA) is estimated to be twice that based on the non-recombining part of the Y chromosome (NRY). These TMRCAs have special demographic implications because mtDNA is transmitted only from mother to child, while NRY is passed along from father to son. Therefore, the former locus reflects female history, and the latter, male history. To investigate what caused the two-to-one female-male TMRCA ratio r F/M = T F /T M in humans, we develop a forward-looking agentbased model (ABM) with overlapping generations. Our ABM simulates agents with individual life cycles, including life events such as reaching maturity or menopause. We implemented two main mating systems: polygynandry and polygyny with different degrees in between. In each mating system, the male population can be either homogeneous or heterogeneous. In the latter case, some males are 'alphas' and others are 'betas', which reflects the extent to which they are favored by female mates. A heterogeneous male population implies a competition among males with the purpose of signaling as alpha males. The introduction of a heterogeneous male population is found to reduce by a factor 2 the probability of finding equal female and male TMRCAs and shifts the distribution of r F/M to higher values. In order to account for the empirical observation of the factor 2, a high level of heterogeneity in the male population is needed: less than half the males can be alphas and betas can have at most half the fitness of alphas for the TMRCA ratio to depart significantly from 1. In addition, we find that, in the modes that maximize the probability of having 1.5 < r F/M < 2.5, the present generation has 1.4 times as many female as male ancestors. We also tested the effect of sex-biased migration and sex-specific death rates and found that these are unlikely to explain alone the sex-biased TM-RCA ratio observed in humans. Our results support the view that we are descended from males who were successful in a highly competitive context, while females were facing a much smaller female-female competition.
We introduce a model of dyadic social interactions and establish its correspondence with relational models theory (RMT), a theory of human social relationships. RMT posits four elementary models of relationships governing human interactions, singly or in combination: Communal Sharing, Authority Ranking, Equality Matching, and Market Pricing. To these are added the limiting cases of asocial and null interactions, whereby people do not coordinate with reference to any shared principle. Our model is rooted in the observation that each individual in a dyadic interaction can do either the same thing as the other individual, a different thing or nothing at all. To represent these three possibilities, we consider two individuals that can each act in one out of three ways toward the other: perform a social action X or Y, or alternatively do nothing. We demonstrate that the relationships generated by this model aggregate into six exhaustive and disjoint categories. We propose that four of these categories match the four relational models, while the remaining two correspond to the asocial and null interactions defined in RMT. We generalize our results to the presence of N social actions. We infer that the four relational models form an exhaustive set of all possible dyadic relationships based on social coordination. Hence, we contribute to RMT by offering an answer to the question of why there could exist just four relational models. In addition, we discuss how to use our representation to analyze data sets of dyadic social interactions, and how social actions may be valued and matched by the agents.
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