On the strategic equivalence of multiple-choice test scoring rules

A disadvantage of multiple-choice tests is that students have incentives to guess. To discourage guessing, it is common to use scoring rules that either penalize wrong answers or reward omissions. These scoring rules are considered equivalent in psychometrics, although experimental evidence has not always been consistent with this claim. We model students' decisions and show, first, that equivalence holds only under risk neutrality and, second, that the two rules can be modified so that they become equivalent even under risk aversion. This paper presents the results of a field experiment in which we analyze the decisions of subjects taking multiple-choice exams. The evidence suggests that differences between scoring rules are due to risk aversion as theory predicts. We also find that the number of omitted items depends on the scoring rule, knowledge, gender and other covariates.

Learning to perceive in the sensor motor approach: Piaget's theory of equilibration interpreted dynamically

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the "laws" of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget's theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget's theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level.

Hartle's model within the general theory of perturbatiye matchings: the change in mass

Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit assumptions, there are some implicit, like the "continuity" of the functions in the perturbed metric across the surface of the body. In this work we sketch the basics for the analysis of the second order problem using the modern theory of perturbed matchings. In particular, the result we present is that when the energy density of the fluid in the static configuration does not vanish at the boundary, one of the functions of the second order perturbation in the setting of the original work by Hartle is not continuous. This discrepancy affects the calculation of the change in mass of the rotating star with respect to the static configuration needed to keep the central energy density unchanged.