Intuitions about sample size: the empirical law of large numbers

According to Jacob Bernoulli, even the ‘stupidest man’ knows that the larger one's sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Two-and-a-half centuries later, psychologists empirically tested people's intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the ‘empirical law of large numbers’ and distinguish between two kinds of tasks–one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results. © 1997 John Wiley & Sons, Ltd.     

The influence of prior choices on current choice

Three pigeons chose between random-interval (RI) and tandem, continuous-reinforcement, fixed-interval (crf-FI) reinforcement schedules by pecking either of two keys. As long as a pigeon pecked on the RI key, both keys remained available. If a pigeon pecked on the crf-FI key, then the RI key became unavailable and the crf-FI timer began to time out. With this procedure, once the RI key was initially pecked, the prospective value of both alternatives remained constant regardless of time spent pecking on the RI key without reinforcement (RI waiting time). Despite this constancy, the rate at which pigeons switched from the RI to the crf-FI decreased sharply as RI waiting time increased. That is, prior choices influenced current choice-an exercise effect. It is argued that such influence (independent of reinforcement contingencies) may serve as a sunk-cost commitment device in self-control situations. In a second experiment, extinction was programmed if RI waiting time exceeded a certain value. Rate of switching to the crf-FI first decreased and then increased as the extinction point approached, showing sensitivity to both prior choices and reinforcement contingencies. In a third experiment, crf-FI availability was limited to a brief window during the RI waiting time. When constrained in this way, switching occurred at a high rate regardless of when, during the RI waiting time, the crf-FI became available.     

Hick's Law in a Stochastic Race Model with Speed-Accuracy Tradeoff

We present an analytic solution for a race model of n stochastic accumulators for multiple choice reaction time. We show that to maintain a constant level of accuracy, the response criterion needs to be increased approximately logarithmically with n, to compensate for the increase with n in the likelihood that an incorrect alternative will be most active after any fixed amount of time accumulating information. Assuming that participants monitor and maintain a constant level of performance can then explain the logarithmic dependency of the response latency on n as specified by Hick's law. Moreover, we show that for short time intervals, the Shannon information that observers extract from a stimulus, is predicted to increase linearly with processing time.     

Forgetting curves: implications for connectionist models

Forgetting in long-term memory, as measured in a recall or a recognition test, is faster for items encoded more recently than for items encoded earlier. Data on forgetting curves fit a power function well. In contrast, many connectionist models predict either exponential decay or completely flat forgetting curves. This paper suggests a connectionist model to account for power-function forgetting curves by using bounded weights and by generating the learning rates from a monotonically decreasing function. The bounded weights introduce exponential forgetting in each weight and a power-function forgetting results when weights with different learning rates are averaged. It is argued that these assumptions are biologically reasonable. Therefore power-function forgetting curves are a property that may be expected from biological networks. The model has an analytic solution, which is a good approximation of a power function displaced one lag in time. This function fits better than any of the 105 suggested two-parameter forgetting-curve functions when tested on the most precise recognition memory data set collected by. Unlike the power-function normally used, the suggested function is defined at lag zero. Several functions for generating learning rates with a finite integral yield power-function forgetting curves; however, the type of function influences the rate of forgetting. It is shown that power-function forgetting curves cannot be accounted for by variability in performance between subjects because it requires a distribution of performance that is not found in empirical data. An extension of the model accounts for intersecting forgetting curves found in massed and spaced repetitions. The model can also be extended to account for a faster forgetting rate in item recognition (IR) compared to associative recognition in short but not long retention intervals.     

Human group choice: discrete-trial and free-operant tests of the ideal free distribution

Ideal free distribution theory predicts that foragers will form groups proportional in number to the resources available in alternative resource sites or patches, a phenomenon termed habitat matching. Three experiments tested this prediction with college students in discrete-trial simulations and a free-operant simulation. Sensitivity to differences in programmed reinforcement rates was quantified by using the sensitivity parameter of the generalized matching law (s). The first experiment, replicating prior published experiments, produced a greater degree of undermatching for the initial choice (s = 0.59) compared to final choices (s = 0.86). The second experiment, which extended prior findings by allowing only one choice per trial, produced comparable undermatching (s = 0.82). The third experiment used free-operant procedures more typical of laboratory studies of habitat matching with other species and produced the most undermatching (s = 0.71). The results of these experiments replicated previous results with human groups, supported predictions of the ideal free distribution, and suggested that undermatching represents a systematic deviation from the ideal free distribution. These results are consistent with a melioration account of individual behavior as the basis for group choice.     

台湾实践基因科技应用于临床试验的政策发展可能视野

台湾目前的基因科技发展存在着瓶颈和危机。在日前台湾举办的《基因治疗与临床试验－务实取向的共识凝聚研讨会》上,与会者提出了制约台湾目前基因研究的十大瓶颈,以及面对困境的十项解决方案。     

Opinion on directive 98/44/EC on the legal protection of biotechnical inventions,and its implementation in Sweden

The following statement is the formal opinion by the Swedish National Council on Medical Ethics concerning the implementation of Directive 98/44/EC of the European Parliament concerning legal protection of biotechnical inventions, and the implications and implementation of this Directive in Sweden.     

Group choice: the ideal free distribution of human social behavior

Group choice refers to the distribution of group members between two choice alternatives over time. The ideal free distribution (IFD), an optimal foraging model from behavioral ecology, predicts that the ratio of foragers at two resource sites should equal the ratio of obtained resources, a prediction that is formally analogous to the matching law of individual choice, except that group choice is a social phenomenon. Two experiments investigated the usefulness of IFD analyses of human group choice and individual-based explanations that might account for the group-level events. Instead of nonhuman animals foraging at two sites for resources, a group of humans chose blue and red cards to receive points that could earn cash prizes. The groups chose blue and red cards in ratios in positive relation to the ratios of points associated with the cards. When group choice ratios and point ratios were plotted on logarithmic coordinates and fitted with regression lines, the slopes (i.e., sensitivity measures) approached 1.0 but tended to fall short of it (i.e., undermatching), with little bias and little unaccounted for variance. These experiments demonstrate that an IFD analysis of group choice is possible and useful, and suggest that group choice may be explained by the individual members' tendency to optimize reinforcement.     

The general matching law describes choice on concurrent variable-interval schedules of wheel-running reinforcement.

Six male Wistar rats were exposed to concurrent variable-interval schedules of wheel-running reinforcement. The reinforcer associated with each alternative was the opportunity to run for 15 s, and the duration of the changeover delay was 1 s. Results suggested that time allocation was more sensitive to relative reinforcement rate than was response allocation. For time allocation, the mean slopes and intercepts were 0.82 and 0.008, respectively. In contrast, for response allocation, mean slopes and intercepts were 0.60 and 0.03, respectively. Correction for low response rates and high rates of changing over, however, increased slopes for response allocation to about equal those for time allocation. The results of the present study suggest that the two-operant form of the matching law can be extended to wheel-running reinforcement. 'I'he effects of a low overall response rate, a short Changeover delay, and long postreinforcement pausing on the assessment of matching in the present study are discussed.     

Theological Ethics, Moral Philosophy, and Natural Law

The article deals with the relationship between theological ethics and moral philosophy. The former is seen as a theoretical reflection on Christian ethics, the latter as one on secular ethics. The main questions asked are: (1) Is there one and only one pre-theoretical knowledge about acting rightly? (2) Does philosophy provide us with the theoretical framework for understanding both Christian and secular ethics? Both questions are answered in the negative. In the course of argument, four positions are presented: theological ‘unificationism’, philosophical ‘unificationism’, theological ‘separationism’ and Lutheran ‘dualism’. It is argued that the latter position is most convincing. It is dual in the sense of being both a theory of Christian ethics and of including a recognition of natural law. Hence, it unites a particularistic and a universalistic point of view. In the last section a reformulation of the Lutheran position is attempted in making use of the ethical theory of Knud E. Løgstrup's The Ethical Demand.