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    Gain control of saccadic eye movements is probabilistic

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    Saccades are rapid eye movements that orient the visual axis toward objects of interest to allow their processing by the central, highacuity retina. Our ability to collect visual information efficiently relies on saccadic accuracy, which is limited by a combination of uncertainty in the location of the target and motor noise. It has been observed that saccades have a systematic tendency to fall short of their intended targets, and it has been suggested that this bias originates from a cost function that overly penalizes hypermetric errors. Here we tested this hypothesis by systematically manipulating the positional uncertainty of saccadic targets. We found that increasing uncertainty produced not only a larger spread of the saccadic endpoints but also more hypometric errors and a systematic bias toward the average of target locations in a given block, revealing that prior knowledge was integrated into saccadic planning. Moreover, by examining how variability and bias co-varied across conditions, we estimated the asymmetry of the cost function and found that it was related to individual differences in the additional time needed to program secondary saccades for correcting hypermetric errors, relative to hypometric ones. Taken together, these findings reveal that the saccadic system uses a probabilistic-Bayesian control strategy to compensate for uncertainty in a statistically principled way and to minimize the expected cost of saccadic errors

    Paradoxes in Fair Computer-Aided Decision Making

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    Computer-aided decision making--where a human decision-maker is aided by a computational classifier in making a decision--is becoming increasingly prevalent. For instance, judges in at least nine states make use of algorithmic tools meant to determine "recidivism risk scores" for criminal defendants in sentencing, parole, or bail decisions. A subject of much recent debate is whether such algorithmic tools are "fair" in the sense that they do not discriminate against certain groups (e.g., races) of people. Our main result shows that for "non-trivial" computer-aided decision making, either the classifier must be discriminatory, or a rational decision-maker using the output of the classifier is forced to be discriminatory. We further provide a complete characterization of situations where fair computer-aided decision making is possible
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