Affine representations in psychophysics and the near-miss to Weber’s law

A theoretical account for the near-miss to Weber’s law in the form of a power function, with a special emphasis on the interpretation of the exponent, was proposed by Falmagne [Falmagne, J.-C. (1985). Elements of psychophysical theory. New York: Oxford University Press] within the framework of a subtractive representation, P(x,y)=F(u(x)−g(y)). In this paper, we examine a more general affine representation, P(x,y)=F(u(x)h(y)+g(y)). We first obtain a uniqueness theorem for the affine representation. We then study the conditions that force an affine representation to degenerate to a subtractive one. Part of that study involves the case for which two different affine representations co-exist for the same data. We also show that the balance condition P(x,y)+P(y,x)=1 constrains an affine representation to be a special kind of subtractive representation, a Fechnerian one. We further show that Falmagne’s power law takes on a special form for a so-called weakly balanced system of probabilities, in which case the affine representation is Fechnerian. Finally, following Iverson [Iverson, G.J. (2006a). Analytical methods in the theory of psychophysical discrimination I: Inequalities, convexity and integration of just noticeable differences. Journal of Mathematical Psychology, 50, 271-282], we generalize the Fechner method to construct the sensory scales in a weakly balanced affine representation by integrating (derivatives of) just noticeable differences.     

Psychophysics of remembering: to bias or not to bias

Delayed matching to sample is typically a two-alternative forced-choice procedure with two sample stimuli. In this task the effects of varying the probability of reinforcers for correct choices and the resulting receiver operating characteristic are symmetrical. A version of the task where a sample is present on some trials and absent on others is analogous to a yes/no recognition task. We describe data from two experiments where an asymmetry in performance in the yes/no task could be attributed to a change in response bias with increasing retention-interval duration from a matching-law perspective, but not from a signal-detection perspective. Both approaches make explicit assumptions about response bias. The apparent inconsistency between the two approaches to the treatment of response bias is resolved in terms of a model proposed by K. G. White and J. T. Wixted (1999) which predicts asymmetrical matching-law functions and receiver operating characteristics without making any assumptions about response bias.     

Matching in an undisturbed natural human environment

Data from the Oregon Youth Study, consisting of the verbal behavior of 210 adolescent boys determined to be at risk for delinquency (targets) and 210 of their friends (peers), were analyzed for their conformance to the complete family of matching theory equations in light of recent findings from the basic science, and using recently developed analytic techniques. Equations of the classic and modern theories of matching were fitted as ensembles to rates and time allocations of the boys' rule-break and normative talk obtained from conversations between pairs of boys. The verbal behavior of each boy in a conversation was presumed to be reinforced by positive social responses from the other boy. Consistent with recent findings from the basic science, the boys' verbal behavior was accurately described by the modern but not the classic theory of matching. These findings also add support to the assertion that basic principles and processes that are known to govern behavior in laboratory experiments also govern human social behavior in undisturbed natural environments.     

Identities and Their Uses: Response to ��Rate, Probability And Matching�� by Rachlin And Locey

Some of the differences between Rachlin & Locey (2010) and Thorne (2010) are due to what assumptions are taken as givens versus questionable. Most of the other apparent differences are largely linguistic and can be resolved by agreeing on terminology. The identity combining both rate and probability of reinforcement is general, has already revealed order not previously noted, even in its currently simple form, and provides a way of incorporating additional variables known to influence and characterize behavior.     

Dynamics of choice: a tutorial

Choice may be defined as the allocation of behavior among activities. Since all activities take up time, choice is conveniently thought of as the allocation of time among activities, even if activities like pecking are most easily measured by counting. Since dynamics refers to change through time, the dynamics of choice refers to change of allocation through time. In the dynamics of choice, as in other dynamical systems that include feedback, change is away from perturbation and toward a steady state. Steady state or equilibrium is assessed on a longer time scale than change because change is only visible on a smaller time scale. When we compare laws of equilibrium, such as the matching law with laws of dynamics, two possibilities emerge. Self-similarity occurs when the same law can be seen across smaller time scales, with the result that the law at longer time scales may be understood as the expression of its application at smaller time scales. Reduction occurs when the dynamics at a small time scale are incommensurate with the dynamics at longer time scales. Then the process at the longer time scale is reduced to a qualitatively different process at the smaller time scale, as when choice is reduced to switching patterns. When reduction occurs, the dynamics at the longer time scale may be derived from the process at the smaller time scale, but not the other way around. Research at different time scales is facilitated by the molar view of behavior.     

Covenant,blood, and violence: America at war with itself and others

Religious nationalism is dangerous, because it tends toward violence. In the case of America, religious nationalism is preceded by, and dependent upon, a covenant with God that renders judgment against the nation when it fails to embody divine justice. The second use of the law in Lutheran theology, combined with René Girard's scapegoat theory, provides the prophetic public theologian with a searchlight to make visible the nation's justification of violence. The haunting question becomes this: should the prophetic public theologian expose the lie on which American religious nationalism is built and risk sundering human community?     

Is there a world Lutheranism? Accountability and representation in ecumenical dialogue

The following thoughts were occasioned by my experiences representing the Lutheran World Federation (LWF) and the Evangelical Lutheran Church in America (ELCA) in a variety of international ecumenical dialogues over the past thirteen years. I reflect on some of the fundamental challenges faced by many Lutherans as we seek to represent, as conscientiously as possible, the global communion of which we are members. The question we face is a very simple one: Whom do we represent?     

医患关系的本质属性及其立法取向

考察医患关系的本质属性,结合国家医疗事业的公益性、医疗立法的宗旨和发展趋势,得出如下结论：医患关系本质平等,医事法属平权法。医事法律关系本质平等,是一种民事法律关系,现行医患关系立法体系下医患关系的某些特征,不能反映医事法律关系的本质属性。     

图形用户界面环境中的鼠标操作活动分析

本研究探讨GUI环境中目标的方向、大小和距离对鼠标指点定位和拖动操作的影响。实验结果表明 ,鼠标指点定位和拖动操作的MT随着目标距离的增加而增加 ,随着目标的增大而减小 ,但下降率呈递减趋势。对于指点定位任务 ,目标方向对鼠标操作的MT有影响 ,而对于拖动操作任务 ,这一影响不明显。总体上 ,以上 3个因素交互地影响鼠标操作的MT。根据本实验数据 ,我们为上述两种常规鼠标操作任务建立了 8个方向的费茨模型。这些结果有助于GUI的工效学设计。     

Virtue Jurisprudence A Virtue–Centred Theory of Judging

"Virtue jurisprudence" is a normative and explanatory theory of law that utilises the resources of virtue ethics to answer the central questions of legal theory. The main focus of this essay is the development of a virtue–centred theory of judging. The exposition of the theory begins with exploration of defects in judicial character, such as corruption and incompetence. Next, an account of judicial virtue is introduced. This includes judicial wisdom, a form of phronesis , or sound practical judgement. A virtue–centred account of justice is defended against the argument that theories of fairness are prior to theories of justice. The centrality of virtue as a character trait can be drawn out by analysing the virtue of justice into constituent elements. These include judicial impartiality (even–handed sympathy for those affected by adjudication) and judicial integrity (respect for the law and concern for its coherence). The essay argues that a virtue–centred theory accounts for the role that virtuous practical judgement plays in the application of rules to particular fact situations. Moreover, it contends that a virtue–centred theory of judging can best account for the phenomenon of lawful judicial disagreement. Finally, a virtue–centred approach best accounts for the practice of equity, departure from the rules based on the judge's appreciation of the particular characteristics of individual fact situations.