Rationality as weighted averaging

Weighted averaging is a method for aggregating the totality of information, both regimented and unregimented, possessed by an individual or group of individuals. The application of such a method may be warranted by a theorem of the calculus of probability, simple conditionalization, or Jeffrey's formula for probability kinematics, all of which average in terms of the prior probability of evidence statements. Weighted averaging may, however, be applied as a method of rational aggregation of the probabilities of diverse perspectives or persons in cases in which the weights cannot be articulated as the prior probabilities of statements of evidence. The method is justified by Wagner's Theorem exhibiting that any method satisfying the conditions of the Irrelevance of Alternatives and Zero Unanimity must, when applied to three or more alternatives, be weighted averaging.     

An Excel macro for transformed and weighted averaging

An Excel macro is presented for averaging spreadsheet data. The macro has several special features: (1) The data are weighted by the inverse variance of each datum to decrease the contribution-of noisy outliers. (2) There is a provision for a power or a log transform of the data before averaging. The rationale for transforming the data before averaging is discussed (3) The output includes the average value, its standard error, and the reduced chi-square that measures the goodness of fit (4) The standard error is corrected by a heterogeneity factor based on the reduced chi-square The averaging of data is rarely done properly, and the intent of this article is to clarify the issues and provide a tool that allows researchers to improve their averaging techniques.     

Rational consensual procedure: Argumentation or weighted averaging?

The following is a defense of Jurgen Habermas' argumentational consensual procedure against Keith Lehrer and Carl Wagner's weighted averaging consensual procedure (and, I tentatively claim, against any weighted averaging consensual procedure). The argument is twofold: if Lehrer and Wagner intend, implicity, to replace what is for Habermas the metatheoretical stage of a discussion with the aggregation of judgments of respect, then their procedure fails to make use of all available information and the participants are not committed to the weighted average position on these grounds; if, on the other hand, they do not intend to replace metatheoretical discussion by aggregation, then the conditions under which the discussion could conceivably have come to a halt are such as to provide no support for the claim that it is rational to aggregate, rather than to consider the discussion unresolved until more information is available.An earlier and abbreviated draft of this paper was read at the 10th Annual International Wittgenstein Symposium, August 1985, in Kirchberg, Austria.     

Deference,respect and intensionality

This paper is about the standard Reflection Principle (van Fraassen in J Philos 81(5):235–256, 1984) and the Group Reflection Principle (Elga in Nous 41(3):478–502, 2007; Bovens and Rabinowicz in Episteme 8(3):281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124(494):449–491, 2015). I argue that these principles are incomplete as they stand. The key point is that deference is an intensional relation, and so whether you are rationally required to defer to a person at a time can depend on how that person and that time are designated. In this paper I suggest a way of completing the Reflection Principle and Group Reflection Principle, and I argue that so completed these principles are plausible. In particular, they do not fall foul of the Sleeping Beauty case (Elga in Analysis 60(2):143–147, 2000), the Cable Guy Paradox (Hajek in Analysis 65(286):112–119, 2005), Arntzenius’ prisoner cases (Arntzenius in J Philos, 100(7):356–370, 2003), or the Puzzle of the Hats (Bovens and Rabinowicz in Episteme 8(3):281–300, 2011).     

Individualism, Communitarianism and Consensus

There is a contemporary conflict between individualistic andcommunitarian conceptions of rationality. Robert Goodin describes it asa conflict between an enlightenment individualistic conception of a``sovereign artificer'' and ``a socially unencumbered self'' ascontrasted with the communitarian conception of a ``socially embeddedself'' whose identity is formed by his or her community. Should wejustify and explain rationality individualistically or socially? This isa false dilemma when consensus is reached by a model articulated byKeith Lehrer and Carl Wagner. According to this model, the consensusresults from the positive weights individuals give to others and use tocontinually average and, thus, aggregate their allocations. Aggregationconverges toward a consensus in which the social preference and theindividual preferences become identical. The truth of communitarianismis to be found in the aggregate and the truth of individualism in theaggregation. The original conflict dissolves in rational consensus.     

Hysteresis,cooperativity, and depth averaging in dynamic random-dot stereograms

Experiments were performed to assess the response of the human visual system to dynamic random-dot patterns composed of disparity mixtures. In Experiment 1, the perceived depth and relative stability of two patterns were compared; one pattern depicted two transparent layers of dots, and the other depicted a volume of dots. Two effects were found: (1) the volume pattern exhibited a large degree of disparity averaging; and (2) asymmetries were observed in the relative stability of these two patterns. Experiment 2 was designed to determine whether these findings could be attributed to spatially localized processes occurring-at the location of disparity discontinuities. This was accomplished by introducing unpaired noise points localized either along the disparity discontinuities or in the center of the layered and volume patterns. The amount of depth averaging and the direction of the asymmetry did not appear to depend on processes localized along the disparity discontinuities. Results of these experiments, taken in conjunction with those of previous studies, suggest that hysteresis is independent of cooperative persistence mechanisms.     

Consensus, clinical decision making, and unsettled cases

The model of clinical ethics consultation (CEC) defended in the ASBH Core Competencies report has gained significant traction among scholars and healthcare providers. On this model, the aim of CEC is to facilitate deliberative reflection and thereby resolve conflicts and clarify value uncertainty by invoking and pursuing a process of consensus building. It is central to the model that the facilitated consensus falls within a range of allowable options, defined by societal values: prevailing legal requirements, widely endorsed organizational policies, and professional standards of practice and codes of conduct. Moreover, the model stipulates that ethics consultants must refrain from giving substantive recommendations regarding how parties to a moral disagreement in the clinic should evaluate their options. We argue that this model of CEC is incomplete, because it wrongly assumes that what counts as the proper set of allowable options among which the parties are to deliberate will itself always be clearly discernible. We illustrate this problem with a recent case on which one of us consulted-a neonate born with trisomy 18 (T18). We try to show that law, policy, and standards of practice reveal no clear answer to the question posed by the case: namely, whether forgoing gastrostomy tube feedings for a baby with T18 is allowable. We suggest there may be other kinds of cases in which it may simply be unsettled whether a given choice falls within the set of allowable options within which consensus is to be facilitated. What should an ethicist do when confronting such unsettled cases? We agree with the facilitation model that an ethicist should remain neutral among the allowable options, when it is clear what the allowable options are. But, in unsettled cases, the role of a consultant should be expanded to include a process of moral inquiry into what the allowable options should be. We end by raising the issue of whether this means an ethicist should share his or her own conclusions or views about the allowability of a given clinical option.     

Spatial memory averaging, the landmark attraction effect, and representational gravity

The effect of a large stationary landmark on memory for the location of a stationary target was examined. Memory for a stationary target was displaced toward the landmark, and targets that were larger, further from, or above the landmark exhibited greater magnitudes of displacement. Displacement was generally larger when the landmark vanished prior to judgment than when the landmark was visible during judgment. Memory for stationary targets offset from the major vertical or horizontal cardinal axis of the landmark was also displaced toward that cardinal axis. The data support the hypotheses that spatial memory averaging of the locations of a target and landmark occurs, and that this averaging may be combined with representational gravity in determining the remembered position of a stationary target. Received: 17 May 1999 / Accepted: 8 February 2000     

Hysteresis, cooperativity, and depth averaging in dynamic random-dot stereograms.

Experiments were performed to assess the response of the human visual system to dynamic random-dot patterns composed of disparity mixtures. In Experiment 1, the perceived depth and relative stability of two patterns were compared; one pattern depicted two transparent layers of dots, and the other depicted a volume of dots. Two effects were found: (1) the volume pattern exhibited a large degree of disparity averaging; and (2) asymmetries were observed in the relative stability of these two patterns. Experiment 2 was designed to determine whether these findings could be attributed to spatially localized processes occurring at the location of disparity discontinuities. This was accomplished by introducing unpaired noise points localized either along the disparity discontinuities or in the center of the layered and volume patterns. The amount of depth averaging and the direction of the asymmetry did not appear to depend on processes localized along the disparity discontinuities. Results of these experiments, taken in conjunction with those of previous studies, suggest that hysteresis is independent of cooperative persistence mechanisms.     

交流 诠释 求同尊异——关于生命伦理学的跨文化研究

生命伦理学的跨文化研究,重在诠释不同文化传统伦理观念的历史轨迹,尊重道德的多元性,同时寻求共同点,以促进人类之间的合作和交流。不同伦理思想的交流中形成的某种共识和趋同,是社会共荣和医学发展的需要。否定伦理观念的多元和把伦理观念多元绝对化,都无益于人类健康事业的繁荣。     

Political efficacy,respect for agency,and adaptive preferences

Serene Khader and Rosa Terlazzo have each recently proposed theories of adaptive preferences (APs) which purport to both respect persons’ agency and provide an effective political tool. While Khader and Terlazzo thus share a similar goal, they take fundamentally different paths in its pursuit: Khader offers a perfectionist account of APs and Terlazzo an autonomy-based theory. In this paper, I argue first that if it is to adequately respect persons’ agency, a theory of APs should in some way include autonomy considerations. If it is to provide an effective political tool, however, our theory should not be entirely autonomy-based, but include a condition addressing a preference’s compatibility with basic flourishing. The suggestion is thus that it is worth considering the possibility of a ‘mixed,’ rather than exclusively perfectionist or exclusively autonomy-based, theory of APs. I outline two such theories. The first, I argue, does quite well with respect to the political efficacy aim of AP theorizing, but has difficulty satisfying the respect for agency aim. The reverse is true of the second. I conclude by suggesting that respect for agency should in this context take priority over political efficacy and that we therefore should accept the latter of the two theories outlined.     

Attention shifts and memory averaging

When observers are asked to localize the final position of a moving stimulus, judgements may be influenced by additional elements that are presented in the visual scene. Typically, judgements are biased toward a salient non-target element. It has been assumed that the non-target element acts as a landmark and attracts the remembered final target position. The present study investigated the effects of briefly flashed non-target elements on localization performance. Similar to landmark attraction, localization was biased toward these elements. However, an influence was only noted if the distractor was presented at the time of target disappearance or briefly thereafter. It is suggested that memory traces of distracting elements are only averaged with the final target position if they are highly activated at the time the target vanishes.     

Trash talking,respect for opponents and good competition

Trash talking, which is the North American term for verbal barbs directed at opponents during a sporting event in order to gain a competitive edge, is widely accepted by athletes and the athletic community as a legitimate part of sport. It is, however, morally indefensible. A simple Kantian injunction against treating opponents merely as objects to be overcome is sufficient to condemn this verbal abuse. Attempts to justify trash talking as a strategic ploy that implies no disrespect are disingenuous in view of the fact that its effectiveness depends on opponents' being offended by it. Nor can we defend trash talking as enhancing the goal of athletic competition, since the ability to verbally abuse opponents and remain impervious to their abuse are extraneous to the athletic excellence that contests are designed to measure. Attempts to deflect criticisms by partially immunizing sport from moral scrutiny are implausible. With few exceptions, we judge actions in sport by the same moral standards that we use in any other context. Moreover, the view that neither trash talking nor other actions in sport are fit subjects for strict moral scrutiny is inconsistent with the often-heard claim that sport promotes moral development.