(1976). PROBABILITY, LIKELIHOOD AND SUPPORT: A METAMATHEMATICAL APPROACH TO A SYSTEM OF AXIOMS FOR UPPER AND LOWER DEGREES OF BELIEF. Philosophical Papers: Vol. 5, No. 2, pp. 153-161.

Dr Edwards' stimulating and provocative book advances the thesis that the appropriate axiomatic basis for inductive inference is not that of probability, with its addition axiom, but rather likelihood - the concept introduced by Fisher as a measure of relative support amongst different hypotheses. Starting from the simplest considerations and assuming no more than a modest acquaintance with probability theory, the author sets out to reconstruct nothing less than a consistent theory of statistical inference in science.

Likelihoodism is the view that the degree of evidential support should be analysed and measured in terms of likelihoods alone. The paper considers and responds to a popular criticism that a likelihoodist framework is too restrictive to guide belief. First, I show that the most detailed and rigorous version of this criticism, as put forward by Gandenberger (2016), is unsuccessful. Second, I provide a positive argument that a broadly likelihoodist framework can accommodate guidance for comparative belief, even when objectively (...) well-grounded prior probabilities are not available. As I show, the shift from non-relational to comparative probabilities opens up a new space for addressing the belief guidance problem for likelihoodism. (shrink)

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision (...) weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6”) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism. (shrink)

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a "middle way" (...) between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the "Monty Hall" problem. (shrink)

An increasing number of studies indicate that virtues affect brain structure. These studies might shed new light on some neuroethical perspectives suggesting that our brain network activity determines the acquisition and permanence of virtues. According to these perspectives, virtuous behavior could be interpreted as the product of a brain mechanism supervised by genes and environment and not as the result of free choice. In this respect, the neural correlates of virtues would confirm the deterministic theory. In contrast, I maintain that (...) these findings do not undermine the role of willpower and freedom while reinforcing an interactionist view of free will. If virtues affect our neural system, then the predictability of the virtuous behavior follows. The likelihood of our future actions is primarily virtue-dependent; therefore, the acquired naturality of virtuous behavior is a source of predictable behavioral patterns outlining expected actions, which I propose to call Hypotheses of Action. However, the predictability of an action indicates its likeliness and not its certainty or necessity. The neural traces of virtues can be interpreted as major indicators of HAs. It is always possible for the agents to depart from their more likely, virtue-induced actions, but their deviations from the virtuous behavioral pattern are rare, as it is rare for the vicious/non-virtuous person to behave well systematically. This implies a reaffirmation of the notions of veto and consent as they provide a universal practical power affecting the subject’s use of moral virtues. (shrink)

The Greek word eoikos can be translated in various ways. It can be used to describe similarity, plausibility or even suitability. This book explores the philosophical exploitation of its multiple meanings by three philosophers, Xenophanes, Parmenides and Plato. It offers new interpretations of the way that each employs the term to describe the status of their philosophy, tracing the development of this philosophical use of eoikos from the fallibilism of Xenophanes through the deceptive cosmology of Parmenides to Plato's Timaeus. The (...) central premise of the book is that, in reflecting on the eoikos status of their accounts, Xenophanes, Parmenides and Plato are manipulating the contexts and connotations of the term as it has been used by their predecessors. By focusing on this continuity in the development of the philosophical use of eoikos, the book serves to enhance our understanding of the epistemology and methodology of Xenophanes, Parmenides and Plato's Timaeus. (shrink)

The likelihood principle of Bayesian statistics implies that information about the stopping rule used to collect evidence does not enter into the statistical analysis. This consequence confers an apparent advantage on Bayesian statistics over frequentist statistics. In the present paper, I argue that information about the stopping rule is nevertheless of value for an assessment of the reliability of the experiment, which is a pre-experimental measure of how well a contemplated procedure is expected to discriminate between hypotheses. I show that, (...) when reliability assessments enter into inquiries, some stopping rules prescribing optional stopping are unacceptable to both Bayesians and frequentists. (shrink)

It is often assumed by friends and foes alike of intelligent design that a likelihood approach to design inferences will require evidenceregarding the specific motives and abilities of any hypothetical designer. Elliott Sober, like Venn before him, indicates that this information is unavailable when the designer is not human (or at least finite) and concludes that there is no good argument for design in biology. I argue that a knowledge of motives and abilities is not always necessary for obtaining a (...) likelihood on design. In many cases, including the case of irreducibly complex objects, frequencies from known agents can supply the likelihood. I argue against the claim that data gathered from humans is inapplicable to non-human agents. Finally, I point out that a broadly Bayesian approach to design inferences, such as that advocated by Sober, is actually advantageous to design advocates in that it frees them from the Popperian requirement that they construct an overarching science which makes high-likelihood predictions. (shrink)

The likelihood justification of cladistic parsimony suggested in Sober (1984) is here shown to be incomplete. Even so, cladistic parsimony remains a counter-example to the principle of the common cause formulated by Reichenbach (1956) and Salmon (1975, 1979, 1984).

Both advocates and opponents of the fine-tuning argument treat multiple universes with a selection effect as a legitimate hypothesis to explain the life-permitting values of the constants in our universe. I argue that, except where there is specific relevant prior information, the occurrence of multiple instances of a low-likelihood causal process should not be treated as an alternative hypothesis to a higher-likelihood causal process. Since an ’ad hoc’ hypothesis can be invented to give high likelihood to any evidence, we must (...) provide some epistemic rationale other than similar likelihood for comparing two hypotheses. (shrink)

A common view among statisticians is that convergence (which statisticians call consistency) is a necessary property of an inference rule or estimator. In this paper, this view is challenged by appeal to an example in which a rule of inference has a likelihood rationale but is not convergent. The example helps clarify the significance of the likelihood concept in statistical inference.

In what follows I will discuss an example of the Duhem-Quine problem in which Pr(H A), Pr(A H), and Pr(OI +H& ?A) (where H is the hypothesis, A the auxiliary assumptions, and O the observational prediction) can be construed objectively; however, only some of those quantities are relevant to the analysis that I provide. The example involves medical diagnosis. The goal is to test the hypothesis that someone has tuberculosis; the auxiliary assumptions describe the er- ror characteristics of the test (...) procedure. Although it can make sense to talk about the objective probability that someone (randomly drawn from a given population) has tuberculosis and it also can make sense to talk about the objective probability that a test procedure has a certain set of error characteristics, neither of these quantities will enter into the analysis. The analysis proceeds entirely via likelihoods, what one needs to consider is just the probability of the observations conditional on four conjunctions of the form (?H & +A).' It is a special feature of the example that all four of these conjunctions are simple statistical hypotheses in the technical sense that each unambigu-ously confers a probability on the observations.'o After describing how the likelihood concept applies to the example concerning medical diagnosis, I will show how similar patterns can arise in the context of a second inferential framework-that of H. Akaike's criterion of model selection;" this time the example will involve phylogenetic inference. (shrink)

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense”. In this paper, we highlight a difficulty in the treatment of this case, and question the great significance that is attached to this (...) measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures, and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush (Tracking Truth: Knowledge, Evidence, and Science, Clarendon Press, Oxford, 2005) claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense” (p. 163). In this paper, we highlight a difficulty in the treatment of (...) this case, and question the great significance that is attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures (such as the Kemeny–Oppenheim measure and the difference measure), and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally. (shrink)

Forster presented some interesting examples having to do with distinguishing the direction of causal influence between two variables, which he argued are counterexamples to the likelihood theory of evidence. In this paper, we refute Forster's arguments by carefully examining one of the alleged counterexamples. We argue that the example is not convincing as it relies on dubious intuitions that likelihoodists have forcefully criticized. More importantly, we show that contrary to Forster's contention, the consilience-based methodology he favored is accountable within the (...) framework of the LTE. (shrink)

The likelihood theory of evidence (LTE) says, roughly, that all the information relevant to the bearing of data on hypotheses (or models) is contained in the likelihoods. There exist counterexamples in which one can tell which of two hypotheses is true from the full data, but not from the likelihoods alone. These examples suggest that some forms of scientific reasoning, such as the consilience of inductions (Whewell, 1858. In Novum organon renovatum (Part II of the 3rd ed.). The (...) philosophy of the inductive sciences. London: Cass, 1967), cannot be represented within Bayesian and Likelihoodist philosophies of science. (shrink)

Recent work by Eliot Sober regarding the logical structure of the design argument challenges widely held views on how the history of this argument should be understood. This novel “likelihood interpretation” denies that the design argument is an analogical argument. Instead, Sober suggests that all references to artifacts serve an exclusively heuristic function, and do not play an evidential role in the design argument. In contrast, I contend that philosophical considerations as well as historical analysis of the works of David (...) Hume and William Paley establish that the design argument should be understood as a sophisticated analogical argument, albeit one susceptible to Philo’s most refined skeptical arguments. (shrink)

Deception has been practiced by sellers since the beginning of the marketplace. Research in marketing ethics has established benchmarks and parameters forethical behavior that include honesty, full disclosure, equity, and fairness. Deception in marketing, however, has not received the same level of attention. This paper proposes to treat deception in marketing within the context of criminology. By examining deception in marketing within the context of criminology, additional insight can be gained into identifying its antecendents and the likelihood of its occurrence. (...) To this end, deception in marketing is interpreted under the empathy/harm matrix, Cressey’s fraud triangle, and the transparency/time-lag matrix. These frameworks are then combined into a diagram detailing antecedents affecting the likelihood of marketing agents participating in deceptive marketing actions. A number of propositions are presented. (shrink)

An adequate account of laws should satisfy at least five desiderata: it should provide a unified account of laws and chances, it should yield plausible relations between laws and chances, it should vindicate numerical chance assignments, it should accommodate dynamical and non-dynamical chances, and it should accommodate a plausible range of nomic possibilities. No extant account of laws satisfies these desiderata. This paper presents a non-Humean account of laws, the Nomic Likelihood Account, that does.

Standardly, epistemic peers regarding a given matter are said to be people of equal competence who share all relevant evidence. Alternatively, one can define epistemic peers regarding a given matter as people who are equally likely to be right about that matter. I argue that a definition in terms of likelihood captures the essence of epistemic peerhood better than the standard definition or any variant of it. What is more, a likelihood definition implies the truth of the central thesis in (...) the debate on peer disagreement, the so-called Equal Weight View, according to which we should give the opinions of our peers the same weight we give our own. Adopting a likelihood definition, however, does not end the debate on peer disagreement, because the alleged theoretical alternatives to the Equal Weight View, reinterpreted in the light of a likelihood definition, can in fact be shown to be compatible with this view—though the reinterpreted versions may appear less plausible than the original ones. (shrink)

In the recent literature on confirmation there are two leading approaches to the provision of a probabilistic measure of the degree to which a hypothesis is confirmed by evidence. The first is to construe the degree to which evidence E confirms hypothesis H as a function that is directly proportional to p and inversely proportional to p . I shall refer to this as the probability approach. The second approach construes the notion as a function that is directly proportional to (...) the true-positive rate – the probability of the evidence if the hypothesis is true, p – and inversely proportional to the false-positive rate – the probability of the evidence if the hypothesis is false, p . These reverse conditional probabilities – of the evidence on the truth or falsehood of the hypothesis – are sometimes known as likelihoods. I shall refer to the approach to confirmation that uses them as the likelihood approach.For each of these approaches, there are two obvious options as to how to define the confirmation function. The first is to define it as the difference between the magnitude that is treated as increasing confirmation or p ) and the magnitude that is treated as decreasing confirmation or p ). The second is to define confirmation as the quotient of these two magnitudes.This yields four different measures of confirmation, represented in the following table: Differences RatiosProbabilities PD = p – p1 PR = Graphic2Likelihoods LD = p – p3 LR = Graphic4All these measures agree on whether or not E provides some support for H. Intuitively, we want to say that E provides some support for H just in case learning that E is true would make us assign a higher probability to H, i.e. when p(H …. (shrink)

High-quality arguments have strong and lasting persuasive effects, suggesting that people can distinguish high- from low-quality arguments. However, we know little of what norms people employ to make that distinction. Some studies have shown that, in evaluating arguments from consequences, people are more sensitive to differences with respect to the desirability of these consequences than to differences in the likelihood that these consequences will occur. This raises the question of whether people lack the criteria to distinguish high-quality from low-quality arguments (...) in support of such claims. In an experiment, 196 participants without any training in argument theory rated their acceptance of 30 claims about the likelihood that a certain outcome would result from a certain action. These claims were supported by an argument from authority, or from cause to effect, or from example. Arguments were systematically manipulated to violate nine specific criteria. For seven out of the nine criteria violation decreased acceptance of the claim supported. These findings show that people can use argument type specific criteria to distinguish high- from low-quality arguments. (shrink)

Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References Overview Setting the Stage Consistency Redundancy Goodbye ? Conclusion & References..

Most philosophers accept some version of the requirement of total evidence (RTE), which tells us to always update on our complete evidence, which often includes ‘background information’ about how that evidence was collected. But different philosophers disagree about how to implement that requirement. In this article, I argue against one natural picture of how to implement the RTE in likelihood arguments, and I argue in favor of a different picture. I also apply my picture to the controversy over the so-called (...) ‘Objection from Anthropic Bias’ to the fine-tuning argument, and argue that the Objection from Anthropic Bias fails. (shrink)

Many studies of bribery acknowledge the important role of bribe-givers, but their true motives remain unclear. We propose that the likelihood of bribery depends on the willingness of an organization to affiliate with local parties or to be successful in a host country, or to have power over local parties. We further argue that different opportunities, either pervasive or arbitrary, facilitate different types of motives that affect the likelihood of bribery. In addition, we investigate the effect of perceived fairness on (...) the likelihood of bribery. We employ a 3 (motives: affiliation vs. achievement vs. power) × 2 (opportunities: pervasiveness vs. arbitrariness) × 2 (perceived fairness: high vs. low) factorial design in experimental settings among Executive MBA students in southern Taiwan. Our findings indicate that, when companies perceive a higher level of distributive fairness, high-achieving organizations are more likely to offer a bribe when the condition is pervasive. When they have a powerful motive, arbitrariness engenders a higher likelihood of bribery. When they perceive less distributive fairness, there are no significant differences between motive and opportunity. (shrink)

I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.

Maximum-likelihood updating is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility decision-maker to prefer a bet on an ambiguous over a risky urn and be more willing to bet on the ambiguous urn compared to an subjective expected utility decision-maker. This is challenging, since prior to observing draws from the urns, the MEU decision-maker actually preferred the risky over the ambiguous bet (...) and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process. (shrink)

The likelihood principle is typically understood as a constraint on any measure of evidence arising from a statistical experiment. It is not sufficiently often noted, however, that the LP assumes that the probability model giving rise to a particular concrete data set must be statistically adequate—it must “fit” the data sufficiently. In practice, though, scientists must make modeling assumptions whose adequacy can nevertheless then be verified using statistical tests. My present concern is to consider whether the LP applies to these (...) techniques of model verification. If one does view model verification as part of the inferential procedures that the LP intends to constrain, then there are certain crucial tests of model verification that no known method satisfying the LP can perform. But if one does not, the degree to which these assumptions have been verified is bracketed from the evidential evaluation under the LP. Although I conclude from this that the LP cannot be a universal constraint on any measure of evidence, proponents of the LP may hold out for a restricted version thereof, either as a kind of “ideal” or as defining one among many different forms of evidence. (shrink)

The nationwide economic reform in 1986 transformed Vietnam from a centrally planned economy to a socialist-oriented market economy. Entrepreneurs and entrepreneurial spirits within the populace are suggested to fuel the structural changes. Despite the importance of entrepreneurship in Vietnam’s economy, studies in Vietnam mainly pay attention to the practical aspects of entrepreneurial activities and neglect the cognitive and theoretical aspects of entrepreneurship. Thus, the current study employs the information-processing perspective of the Mindsponge Theory to explore how entrepreneurs’ knowledge accumulation can (...) affect their perceived likelihood of business success. Bayesian analysis indicates that business-related experience positively affects entrepreneurs’ business success likelihood. Greater willingness/readiness to transform thinking, acting, and beliefs can improve the business success of entrepreneurs who study others’ failures carefully. However, for entrepreneurs who perceive learning from others’ failures as unnecessary, higher willingness/readiness to transform diminishes their chance of success. Based on these findings, we recommend Vietnamese entrepreneurs accumulate knowledge through experience, learning, and an open mind for better decision-making and innovation creation capabilities. However, the learning process should be selective. (shrink)

This (brief) note is about the (evidential) “favoring” relation. Pre-theoretically, favoring is a three-place (epistemic) relation, between an evidential proposition E and two hypotheses H1 and H2. Favoring relations are expressed via locutions of the form: E favors H1 over H2. Strictly speaking, favoring should really be thought of as a four-place relation, between E, H1, H2, and a corpus of background evidence K. But, for present purposes (which won't address issues involving K), I will suppress the background corpus, so (...) as to simplify our discussion. Moreover, the favoring relation is meant to be a propositional epistemic relation, as opposed to a doxastic epistemic relation. That is, the favoring relation is not meant to be restricted to bodies of evidence that are possessed (as evidence) by some actual agent(s), or to hypotheses that are (in fact) entertained by some actual agent(s). In this sense, favoring is analogous to the relation of propositional justification — as opposed to doxastic justification (Conee 1980). In order to facilitate a comparison of Likelihoodist vs Bayesian explications of favoring, I will presuppose the following bridge principle, linking favoring and evidential support: • E favors H1 over H2 iff E supports H1 more strongly than E supports H2.1 Finally, I will only be discussing instances of the favoring relation involving contingent, empirical claims. So, it is to be understood that “favoring” will not apply if any of E, H1, or H2 are non-contingent (and/or non-empirical). With this background in place, we're ready to begin. (shrink)

This paper investigates the possibility of extending the likelihood treatment of support to situations in which the evidence and the hypotheses supported by the evidence are all outcomes of a chance process. An example is when we ask how much support the observed sequence of heads and tails gives to the hypothesis that the next toss will be a head. I begin by discussing Sober’s approach to a problem of this type: that of estimating how much support the observation that (...) I have a mind gives to the hypothesis that you do. I criticize his approach, and offer a general solution to the problem. (shrink)

Es wird begründet, daß die Konstruktion des Kartenparadoxons von Kerridge auf einer fehlerhaften Betrachtungsweise beruht. Eine genauere Analyse zeigt, daß das Kerridge-Argument mit dem Hackingschen Likelihood-Stützungsargument im Einklang steht.

We propose an alternative resolution of Simpson's paradox in multiple classification experiments, using a different maximum likelihood estimator. In the center of our analysis is a formal representation of free choice and randomization that is based on the notion of incompatible measurements.We first introduce a representation of incompatible measurements as a collection of sets of outcomes. This leads to a natural generalization of Kolmogoroff's axioms of probability. We then discuss the existence and uniqueness of the maximum likelihood estimator for a (...) probability weight on such a generalized sample space, given absolute frequency data.As a first example, we discuss an estimation problem with censured data that classically admits only biased ad hoc estimators.Next, we derive an explicit solution of the maximum likelihood estimation problem for a large class of experiments that arise from various kids of compositions of sample spaces. We identify the (categorical) direct sum of sample spaces as a representation of “free choice,” and the (categorical) direct product as a representation of “randomization.”Finally, we apply the foregoing discussion to the case of multiple classification experiments in order to show that there is no Simpson's paradox if the difference between free choice and randomization is recognized in the structure of the experiment.A comparison between our new estimator and the “usual” calculation can be summarized as follows: Pooling the data over one classification factor in the “usual” way in fact destroys or ignores the information contained in it, whereas our proposed maximum likelihood estimator is a proper marginal over this factor that “averages out” the information contained in it. The estimators agree with each other in the case of proportional sample sizes. (shrink)

We propose a new hybrid data mining method for predicting protein-protein interactions combining Likelihood-Ratio with rule induction algorithms. In essence, the new method consists of using a rule induction algorithm to discover rules representing partitions of the data, and then the discovered rules are interpreted as “bins” which are used to compute likelihood ratios. This new method is applied to the prediction of protein-protein interactions in the Saccharomyces Cerevisiae genome, using predictive genomic features in an integrated scheme. The results show (...) that the new hybrid method outperforms a pure likelihood ratio based approach. (shrink)