Regularization of languages by adults and children: A mathematical framework

The fascinating ability of humans to modify the linguistic input and “create” a language has been widely discussed. In the work of Newport and colleagues, it has been demonstrated that both children and adults have some ability to process inconsistent linguistic input and “improve” it by making it more consistent. In Hudson Kam and Newport (2009), artificial miniature language acquisition from an inconsistent source was studied. It was shown that (i) children are better at language regularization than adults and that (ii) adults can also regularize, depending on the structure of the input. In this paper we create a learning algorithm of the reinforcement-learning type, which exhibits patterns reported in Hudson Kam and Newport (2009) and suggests a way to explain them. It turns out that in order to capture the differences between children’s and adults’ learning patterns, we need to introduce a certain asymmetry in the learning algorithm. Namely, we have to assume that the reaction of the learners differs depending on whether or not the source’s input coincides with the learner’s internal hypothesis. We interpret this result in the context of a different reaction of children and adults to implicit, expectation-based evidence, positive or negative. We propose that a possible mechanism that contributes to the children’s ability to regularize an inconsistent input is related to their heightened sensitivity to positive evidence rather than the (implicit) negative evidence. In our model, regularization comes naturally as a consequence of a stronger reaction of the children to evidence supporting their preferred hypothesis. In adults, their ability to adequately process implicit negative evidence prevents them from regularizing the inconsistent input, resulting in a weaker degree of regularization.     

Application of the generalized matching law to point-after-touchdown conversions and kicker selection in college football

Coaches make a variety of complex decisions in American-rules college football, especially related to point-after-touchdown (PAT) conversions and, historically, kicker selection. However, little research has characterized the pattern of these choices and whether they are sensitive to environmental manipulations, such as increased effort to score. In the present study, the generalized matching law (GML)—a model that predicts a linear relation between log-transformed choices for two alternatives and the amount of reinforcement garnered from them—was applied to PAT-conversion (1 point vs. 2 point) and kicker (soccer-style vs. conventional-style) selection using archived data from the National Collegiate Athletic Association. Overall, PAT-conversion and kicker selection exhibited matching. Further, narrowing the goal-post width was associated with decreased preference for one-point (relative to two-point) PAT attempts and enhanced sensitivity to increases in points scored from one-point (relative to two-point) PAT attempts. This investigation provides support for the ecological validity of the GML and demonstrates that complex decisions in football conform to an orderly pattern that can be described using the GML.