ABSTRACT Average utilitarianism and several related axiologies, when paired with the standard expectational theory of decision-making under risk and with reasonable empirical credences, can find their practical prescriptions overwhelmingly determined by the minuscule probability that the agent assigns to solipsism—that is, to the hypothesis that there is only one welfare subject in the world, namely, herself. This either (i) constitutes a reductio of these axiologies, (ii) suggests that they require bespoke decision theories, or (iii) furnishes an unexpected argument for ethical (...) egoism. (shrink)

This paper compares two well-known arguments in the units of selection literature, one due to , the other due to . Both arguments concern the legitimacy of averaging fitness values across contexts and making inferences about the level of selection on that basis. The first three sections of the paper shows that the two arguments are incompatible if taken at face value, their apparent similarity notwithstanding. If we accept Sober and Lewontin's criterion for when averaging genic fitnesses across diploid genotypes (...) is illegitmate, we cannot accept Sober and Wilson's criterion for when averaging individual fitnesses across groups is illegitimate, and vice versa. The final section suggests a possible way of reconciling the two arguments, by invoking an ambiguity in the concept of genic selection. (shrink)

Chang's MV algebras are the algebras of the infinite-valued sentential calculus of ukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of average degree of truth of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC*-algebras stand to commutative AFC*-algebras, states are naturally related to noncommutativeC*-algebraic measures.

Average-NPs, such as the one in the title of this paper, have been claimed to be ‘linguistically identical’ to any other definite-NPs but at the same time to be ‘semantically inconsistent’ with these other definite-NPs. To some this is an ironclad proof of the irrelevance of semantics to linguistics. We argue that both of the initial claims are wrong: average-NPs are not ‘linguistically identical’ to other definite-NPs but instead show a number of interesting divergences, and we provide a plausible semantic (...) account for them that is not ‘semantically inconsistent’ with the account afforded other definite-NPs but in fact blends quite nicely with one standard account of the semantics for NPs. (shrink)

We consider the extent to which one can compute bounds on the rate of convergence of a sequence of ergodic averages. It is not difficult to construct an example of a computable Lebesgue measure preserving transformation of [0, 1] and a characteristic function f = χA such that the ergodic averages Anf do not converge to a computable element of L2([0, 1]). In particular, there is no computable bound on the rate of convergence for that sequence. On the other hand, (...) we show that, for any nonexpansive linear operator T on a separable Hilbert space and any element f , it is possible to compute a bound on the rate of convergence of Anf from T , f , and the norm f ∗ of the limit. In particular, if T is the Koopman operator arising from a computable ergodic measure preserving transformation of a probability space X and f is any computable element of L2 (X ), then there is a computable bound on the rate of convergence of the sequence Anf. (shrink)

When faced with uncertainty, consequentialists often advocate choosing the option with the largest expected utility, as calculated using the arithmetic average. I provide some arguments to suggest that instead, one should consider choosing the option with the largest geometric average of utility. I explore the difference between these two approaches in a variety of ethical dilemmas and argue that geometric averaging has some appealing properties as a normative decision-making tool.

Jeffrey conditioning tells an agent how to update her priors so as to grant a given probability to a particular event. Weighted averaging tells an agent how to update her priors on the basis of testimonial evidence, by changing to a weighted arithmetic mean of her priors and another agent’s priors. We show that, in their respective settings, these two seemingly so different updating rules are axiomatized by essentially the same invariance condition. As a by-product, this sheds new light on (...) the question how weighted averaging should be extended to deal with cases when the other agent reveals only parts of her probability distribution. The combination of weighted averaging and Jeffrey conditioning is a comprehensive updating rule to deal with such cases, which is again axiomatized by invariance under embedding. We conclude that, even though one may dislike Jeffrey conditioning or weighted averaging, the two make a natural pair when a policy for partial testimonial evidence is needed. (shrink)

Conventionally, multilevel analysis of covariance (ML-ANCOVA) has been the recommended approach for analyzing treatment effects in quasi-experimental multilevel designs with treatment application at the cluster-level. In this paper, we introduce the generalized ML-ANCOVA with linear effect functions that identifies average and conditional treatment effects in the presence of treatment-covariate interactions. We show how the generalized ML-ANCOVA model can be estimated with multigroup multilevel structural equation models that offer considerable advantages compared to traditional ML-ANCOVA. The proposed model takes into account measurement (...) error in the covariates, sampling error in contextual covariates, treatment-covariate interactions, and stochastic predictors. We illustrate the implementation of ML-ANCOVA with an example from educational effectiveness research where we estimate average and conditional effects of early transition to secondary schooling on reading comprehension. (shrink)

For many philosophers working in the area of Population Ethics, it seems that either they have to confront the Repugnant Conclusion , or they have to confront the Non-Identity Problem . To them it seems there is no escape, they either have to face one problem or the other. However, there is a way around this, allowing us to escape the Repugnant Conclusion, by using what I will call Negative Average Preference Utilitarianism – which though similar to anti-frustrationism, has some (...) important differences in practice. Current “positive” forms of utilitarianism have struggled to deal with the Repugnant Conclusion, as their theory actually entails this conclusion; however, it seems that a form of Negative Average Preference Utilitarianism easily escapes this dilemma. (shrink)

This article investigates the semantics of sentences that express numerical averages, focusing initially on cases such as 'The average American has 2.3 children'. Such sentences have been used both by linguists and philosophers to argue for a disjuncture between semantics and ontology. For example, Noam Chomsky and Norbert Hornstein have used them to provide evidence against the hypothesis that natural language semantics includes a reference relation holding between words and objects in the world, whereas metaphysicians such as Joseph Melia and (...) Stephen Yablo have used them to provide evidence that apparent singular reference need not be taken as ontologically committing. We develop a fully general and independently justified compositional semantics in which such constructions are assigned truth conditions that are not ontologically problematic, and show that our analysis is superior to all extant rivals. Our analysis provides evidence that a good semantics yields a sensible ontology. It also reveals that natural language contains genuine singular terms that refer to numbers. (shrink)

We propose an "explanation scheme" for why the Gibbs phase average technique in classical equilibrium statistical mechanics works. Our account emphasizes the importance of the Khinchin-Lanford dispersion theorems. We suggest that ergodicity does play a role, but not the one usually assigned to it.

There has been increasing interest in recent years in the development of approaches to estimate causal effects when the number of potential confounders is prohibitively large. This growth in interest has led to a number of potential estimators one could use in this setting. Each of these estimators has different operating characteristics, and it is unlikely that one estimator will outperform all others across all possible scenarios. Coupling this with the fact that an analyst can never know which approach is (...) best for their particular data, we propose a synthetic estimator that averages over a set of candidate estimators. Averaging is widely used in statistics for problems such as prediction, where there are many possible models, and averaging can improve performance and increase robustness to using incorrect models. We show that these ideas carry over into the estimation of causal effects in high-dimensional scenarios. We show theoretically that averaging provides robustness against choosing a bad model, and show empirically via simulation that the averaging estimator performs quite well, and in most cases nearly as well as the best among all possible candidate estimators. Finally, we illustrate these ideas in an environmental wide association study and see that averaging provides the largest benefit in the more difficult scenarios that have large numbers of confounders. (shrink)

In this paper, we propose the model averaging estimation method for multiplicative error model and construct the corresponding weight choosing criterion based on the Kullback–Leibler divergence with a hyperparameter to avoid the problem of overfitting. The resulting model average estimator is proved to be asymptotically optimal. It is shown that the Kullback–Leibler model averaging estimator asymptotically minimizes the in-sample Kullback–Leibler divergence and improves the forecast accuracy of out-of-sample even under different loss functions. In simulations, we show that the KLMA estimator (...) compares favorably with smooth-AIC estimator, smooth-BIC estimator, and Mallows model averaging estimator, especially when some nonlinear noise is added to the data generation process. The empirical applications in the daily range of S&P500 and price duration of IBM show that the out-of-sample forecasting capacity of the KLMA estimator is better than that of other methods. (shrink)

The origin of the genetic code has been attributed in part to an accidental assignment of codons to amino acids. Although several lines of evidence indicate the subsequent expansion and improvement of the genetic code, the hypothesis of Francis Crick concerning a frozen accident occurring at the early stage of genetic code evolution is still widely accepted. Considering Crick’s hypothesis, mathematical descriptions of hypothetical scenarios involving a huge number of possible coexisting random genetic codes could be very important to explain (...) the origin and evolution of a selected genetic code. This work aims to contribute in this regard, that is, it provides a theoretical framework in which statistical parameters of error functions are calculated. Given a genetic code and an amino acid property, the functional code robustness is estimated by means of a known error function. In this work, using analytical calculations, general expressions for the average and standard deviation of the error function distributions of completely random codes with standard stop codons were obtained. As a possible biological application of these results, any set of amino acids and any pure or mixed amino acid properties can be used in the calculations, such that, in case of having to select a set of amino acids to create a genetic code, possible advantages of natural selection of the genetic codes could be discussed. (shrink)

The problem of missingness in observational data is ubiquitous. When the confounders are missing at random, multiple imputation is commonly used; however, the method requires congeniality conditions for valid inferences, which may not be satisfied when estimating average causal treatment effects. Alternatively, fractional imputation, proposed by Kim 2011, has been implemented to handling missing values in regression context. In this article, we develop fractional imputation methods for estimating the average treatment effects with confounders missing at random. We show that the (...) fractional imputation estimator of the average treatment effect is asymptotically normal, which permits a consistent variance estimate. Via simulation study, we compare fractional imputation’s accuracy and precision with that of multiple imputation. (shrink)

With the advent of the era of artificial intelligence, deep reinforcement learning has achieved unprecedented success in high-dimensional and large-scale artificial intelligence tasks. However, the insecurity and instability of the DRL algorithm have an important impact on its performance. The Soft Actor-Critic algorithm uses advanced functions to update the policy and value network to alleviate some of these problems. However, SAC still has some problems. In order to reduce the error caused by the overestimation of SAC, we propose a new (...) SAC algorithm called Averaged-SAC. By averaging the previously learned action-state estimates, it reduces the overestimation problem of soft Q-learning, thereby contributing to a more stable training process and improving performance. We evaluate the performance of Averaged-SAC through some games in the MuJoCo environment. The experimental results show that the Averaged-SAC algorithm effectively improves the performance of the SAC algorithm and the stability of the training process. (shrink)

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); (...) Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper. (shrink)

Good scientific explanations sometimes appear to make use of averages. Using concrete examples from current economic theory, I argue that some confusions about how averages might work in explanations lead to both philosophical and economic problems about the interpretation of the theory. I formulate general conditions on potentially proper uses of averages to refine a notion of average explanation. I then try to show how this notion provides a means for resolving longstanding philosophical problems in economics and other quantitative social (...) sciences. (shrink)

Contemporary population ethics is dominated by views that aggregate by summing, whether of well-being or of some construct based on well-being. In contrast, average well-being is generally considered axiologically irrelevant. To many of us, however, the number of future people does not seem important, as long as it is sufficient to enable rich and varied life experiences, and as long as the population continues throughout time. It therefore seems relatively plausible to aggregate future well-being by averaging. In particular, it seems (...) plausible to value high average well-being at any particular time, and to do so for all future times. I present a time-sensitive version of the Average View that underpins such axiological intuitions. I also address a series of issues and objections that confront such a view. (shrink)

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. (shrink)

It has sometimes been claimed (usually without evidence) that the harm caused by an individual's participation in a greenhouse-gas-intensive economy is negligible. Using data from several contemporary sources, this paper attempts to estimate the harm done by an average American. This estimate is crude, and further refinements are surely needed. But the upshot is that the average American is responsible, through his/her greenhouse gas emissions, for the suffering and/or deaths of one or two future people.

Formal and social epistemologists have devoted significant attention to the question of how to aggregate the credences of a group of agents who disagree about the probabilities of events. Moss and Pettigrew argue that group credences can be a linear mean of the credences of each individual in the group. By contrast, I argue that if the epistemic value of a credence function is determined solely by its accuracy, then we should, where possible, aggregate the underlying statistical models that individuals (...) use to generate their credence functions, using “stacking” techniques from statistics and machine learning first developed by Wolpert. (shrink)

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action–angle variables, we separate the different time scales of the motion. The method of averaging then allows us to reduce the system to two degrees of freedom, and to classify the most important periodic orbits.

Within contemporary science, it is common practice to compare data points to the average, i.e., to the statistical mean. Because this practice is so familiar, it might at first appear not to be the sort of thing that requires explanation. But recent research in cognitive science and in the history of science gives us reason to adopt the opposite perspective. Cognitive science research on the ways people ordinarily make sense of the world suggests that, instead of using a purely statistical (...) notion of the average, people tend to use a value-laden notion of the normal. Similarly, historical research on the scientific practices used in other time periods indicates that, prior to the nineteenth century, scientists tended to make use of a notion of the normal that was overtly value-laden. These findings give us reason to rethink certain familiar facts about scientific practice. In particular, they suggest that the fact that scientists so often make use of the statistical average should be seen as a highly surprising fact, the sort of thing that calls out for explanation. (shrink)

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real (...) numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method. (shrink)

Prior research suggests that most people perceive themselves to be more altruistic than the average population, an observation known as the better-than-average (BTA) effect. Understanding the BTA effect carries significant public health implications, as self-perceived altruism is closely related to altruistic behaviors, which plays a significant role in individual and societal well-being. However, little is known about whether subpopulations with specific sociodemographic profiles are more likely to hold BTA altruistic self-perceptions, making it difficult to design targeted programs based on multiple (...) sociodemographic characteristics to promote altruistic behaviors. This study addresses this gap by identifying the sociodemographic profiles of populations who are more likely to exhibit BTA effects on trait altruism. Data were derived from a representative sample of Hong Kong citizens (n= 1,185) in the 2017 Hong Kong Altruism Survey. A latent class analysis was performed using four domains of sociodemographic characteristics: sex, age, religion, and socioeconomic status. Multivariate multinomial logistic regressions were conducted to examine associations between class membership, BTA effect, and altruistic behaviors. The results yielded four classes of sociodemographic profiles. Middle-aged, Christian/Catholic, highly educated, and high-income individuals (Class 4, 17.8%) were most likely to exhibit BTA effects and behave altruistically; Class 3 (14.0%) were older, male, no/other religious belief, low education, and least likely to exhibit BTA effects and behave altruistically. Findings improve the understanding of the sociodemographic profiles of people showing BTA effects and facilitate targeted policy development to effectively promote altruism. (shrink)

The popular science of phrenology is known for its preoccupation with geniuses and criminals, but this article shows that phrenologists also introduced ideas about the ‘average’ person. Popular phrenologists in the US and the UK examined the heads of their clients to give an indication of their character. Based on the publications of phrenologists and on a large collection of standardized charts with clients’ scores, this article analyses their definition of what they considered to be the ‘average’. It can be (...) concluded that phrenologists were some of the first to teach individuals to see their identity in relation to an imagined statistical community. (shrink)

Seemingly every theory of population ethics is confronted with unpalatable implications. While various approaches to the subject have been taken, including non-consequentialist approaches, this area has been dominated by utilitarian thought. The two main approaches to population ethics have been total utilitarianism () and average utilitarianism (). According to TU, we should seek to bring about the state of affairs that maximizes the total amount of happiness. According to AU, we should seek to bring about the state of affairs that (...) maximizes average per capita happiness. Both theories have been afflicted by seemingly strong objections, and as a result, numerous variations and hybrids have been introduced. Despite the widespread disagreement in the field, though, a near consensus has developed in rejecting AU as an absurd view. In this article, however, I will go against the grain and argue that AU is the theory of population ethics that we should endorse. (shrink)