Humans have great difficulty comparing quotients including fractions, proportions, and probabilities and often erroneously isolate the whole numbers of the numerators and denominators to compare them. Some have argued that the whole number bias is a compensatory strategy to deal with difficult comparisons. We examined adult humans' preferences for gambles that differed only in numerosity, and not in factors that influence their expected value (probabilities and stakes). Subjects consistently preferred gambles with more winning balls to ones with fewer, even though the probabilities were mathematically identical, replicating prior results. In a second experiment, we found that subjects accurately represented the relative probabilities of the choice options during rapid nonverbal probability judgments but nonetheless showed biases based on whole numbers. We mathematically formalized and quantitatively evaluated cognitive rules based on existing hypotheses that attempt to explain subjects' whole number biases during quotient comparisons. The results show that the whole number bias is intrinsic to the way humans solve quotient comparisons rather than a compensatory strategy. (PsycINFO Database Record
A dominant mechanism in the Judgment and Decision Making literature states that information is accumulated about each choice option until a decision threshold is met. Only after that threshold does a subject start to execute a motor response to indicate their choice. However, recent research has revealed spatial gradients in motor responses as a function of comparison difficulty as well as changes-of-mind in the middle of an action, both suggesting continued accumulation and processing of decision-related signals after the decision boundary. Here we present a formal model and supporting data from a number comparison task that a continuous motor planner, combined with a simple statistical inference scheme, can model detailed behavioral effects without assuming a threshold. This threshold-free model reproduces subjects’ sensitivity to numerical distance in reaching, accuracy, reaction time, and changes of mind. We argue that the motor system positions the effectors using an optimal biomechanical feedback controller, and continuous statistical inference on outputs from cognitive processes.
Gaze, pointing, and reaching movements are thought to provide a window to internal cognitive states. In the case of numerical cognition, it has been found that the left-right deviation of a reaching movement is modulated by the relative magnitude of values in a number comparison task. Some have argued that these patterns directly reflect the representation of a logarithmically compressed mental number line (direct mapping view). However, other studies suggest that the modulation of motor outputs by numerical value could be a more general decision-making phenomenon (response competition view). Here we test the generality of interactions between the motor system and numerical processing by comparing subjects' reach trajectories during two different nonverbal tasks: numerosity comparison and facial expression comparison. We found that reaching patterns were practically identical in both tasks -reach trajectories were equally sensitive to stimulus similarity in the numerical and face comparisons. The data provide strong support for the response competition view that motor outputs are modulated by domain-general decision processes, and reflect generic decision confidence or accumulation of evidence related to mental comparison. When asked to point to the larger of two numbers, one presented to the left and another to the right, subjects trajectories take a medial route when the numerical distance is close, and a more direct one when it is far (Santens, Goossens, & Verguts, 2011;Song & Nakayama, 2008). Such results imply that motor computations are penetrated by cognitive processing -the task of comparing numbers interacts with the path of the motor response. Modulations of motor responses by cognitive processes are not exclusive to number but are observed across a variety of domains, including intertemporal discounting, random dot motion, and phonology (Chapman et al., 2010a;Dshemuchadse, Scherbaum, & Goschke, 2013;Freeman & Ambady, 2011;Freeman, Ambady, Rule, & Johnson, 2008;Friedman, Brown, & Finkbeiner, 2013;Gallivan et al., 2011;Koop & Johnson, 2013;McKinstry, Dale, & Spivey, 2008;Spivey, Grosjean, & Knoblich, 2005;van der Wel, Sebanz, & Knoblich, 2014). jnc.psychopen.eu | 2363-8761 Although prior research suggests that reach trajectories are affected by cognitive processes across a variety of domains, a strong test of the domain-generality of these effects would be to compare performance with stimuli from different domains within a common task. Such a test is important for determining whether number-based modulations of motor responses are domain-specific (Chapman et al., 2014;Dotan & Dehaene, 2013;Song & Nakayama, 2008) or domain-general (Alonso-Diaz, Cantlon, & Piantadosi, 2015Santens et al., 2011). Surprisingly, to date, no studies have pitted domains against each other in equivalent reaching tasks to assess the effect of domain on dynamic motor behavior. In the literature on number processing, interactions between stimulus values and motor responses have only been tested with numerical stimuli alo...
Negative numbers are central in math. However, they are abstract, hard to learn, and manipulated slower than positive numbers regardless of math ability. It suggests that confidence, namely the post-decision estimate of being correct, should be lower than positives. We asked participants to pick the larger single-digit numeral in a pair and collected their implicit confidence with button pressure (button pressure was validated with three empirical signatures of confidence). We also modeled their choices with a drift-diffusion decision model to compute the post-decision estimate of being correct. We found that participants had relatively low confidence with negative numerals. Given that participants compared with high accuracy the basic base-10 symbols (0–9), reduced confidence may be a general feature of manipulating abstract negative numerals as they produce more uncertainty than positive numerals per unit of time.
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