The enormous scale of the available information and products on the Internet has necessitated the development of algorithms that intermediate between options and human users. These algorithms attempt to provide the user with relevant information. In doing so, the algorithms may incur potential negative consequences stemming from the need to select items about which it is uncertain to obtain information about users versus the need to select items about which it is certain to secure high ratings. This tension is an (...) instance of the exploration–exploitation trade‐off in the context of recommender systems. Because humans are in this interaction loop, the long‐term trade‐off behavior depends on human variability. Our goal is to characterize the trade‐off behavior as a function of human variability fundamental to such human–algorithm interaction. To tackle the characterization, we first introduce a unifying model that smoothly transitions between active learning and recommending relevant information. The unifying model gives us access to a continuum of algorithms along the exploration–exploitation trade‐off. We then present two experiments to measure the trade‐off behavior under two very different levels of human variability. The experimental results inform a thorough simulation study in which we modeled and varied human variability systematically over a wide rage. The main result is that exploration–exploitation trade‐off grows in severity as human variability increases, but there exists a regime of low variability where algorithms balanced in exploration and exploitation can largely overcome the trade‐off. (shrink)

Luce and Narens (Journal of Mathematical Psychology, 29:1–72, 1985) showed that rank-dependent utility (RDU) is the most general interval scale utility model for binary lotteries. It can be easily established that this result cannot be generalized to lotteries with more than two outcomes. This article suggests several additional conditions to ensure RDU as the only utility model with the desired property of interval scalability in the general case. The related axiomatizations of some special cases of RDU of independent (...) interest (the quantile utility, expected utility, and Yaari’s dual expected utility) are also given. (shrink)

We develop a model of Disappointment in which disappointment and elation arise from comparing the outcome received, not with an expected value as in previous models, but rather with the other individual outcomes of the lottery. This approach may better reflect the way individuals are liable to experience disappointment. The model obtained accounts for classic behavioral deviations from the normative theory, offers a richer structure than previous disappointment models, and leads to a Rank-Dependent Utility formulation in a transparent (...) way. Thus, our disappointment model may provide a clear psychological rationale for the subjective transformation of probabilities. (shrink)

Empirical evidence from both utility and psychophysical experiments suggests that people respond quite differently—perhaps discontinuously—to stimulus pairs when one consequence or signal is set to `zero.' Such stimuli are called unitary. The author's earlier theories assumed otherwise. In particular, the key property of segregation relating gambles and joint receipts (or presentations) involves unitary stimuli. Also, the representation of unitary stimuli was assumed to be separable (i.e., multiplicative). The theories developed here do not invoke separability. Four general cases based on two (...) distinctions are explored. The first distinction is between commutative joint receipts, which are relevant to utility, and the non-commutative ones, which are relevant to psychophysics. The second distinction concerns how stimuli of the form (x, C; y) and the operation of joint receipt are linked: by segregation, which mixes stimuli and unitary ones, and by distributivity, which does not involve any unitary stimuli. A class of representations more general than rank-dependent utility (RDU) is found in which monotonic functions of increments U(x)-U(y), where U is an order preseving representation of gambles, and joint receipt play a role. This form and its natural generalization to gambles with n > 2 consequences, which is also axiomatized, appear to encompass models of configural weights and decision affect. When joint receipts are not commutative, somewhat similar representations of stimuli arise, and joint receipts are shown to have a conjoint additive representation and in some cases a constant bias independent of signal intensity is predicted. (shrink)

This article uses Lancaster's characteristics approach to rank sets of alternative combinations of commodity characteristics. It is assumed that there exists a reference point or reference level from which the individual evaluates set expansions in appropriate directions. We provide an axiomatic characterization for such a case.

The aim of this paper is to apply a general methodology for constructing statistical methods, which is based on decision theory, to give a statistical description of preferential rankings, with a focus on the rankings’ dependence on categorical variables. In the paper, I use functions of description errors that are based on the Kemeny and Hamming distances between preferential orderings, but the proposed methodology can also be applied to other methods of estimating description errors.

The so-called Final Ranking of the Philebus offers Socrates’ final evaluation of the relative merits of pleasure and reason in the best life. I begin by examining two common lines of interpretation as they address the criterion according to which the final ranking is organized. I then discuss the role ‘similarity’ has in organizing the investigation throughout the dialogue, from the initial comparison of the two lives (of reason and pleasure singly) down through the final ranking. I then consider the (...) thematic discussions of pleasure and reason separately, arguing that their treatments display an intriguing structural similarity. Next, I propose my own reading of the final ranking, whereby the ‘dependence’ relation at work in those two specific discussions may be see as the through-line of all (now five) tiers of the final ranking. I conclude by suggesting that this interpretation is able to preserve what is worthwhile in the two traditional lines of interpretation, while avoiding the pitfalls that tend to accompany them. (shrink)

We introduce a family of local ranks $D_Q$ depending on a finite set Q of pairs of the form $(\varphi (x,y),q(y)),$ where $\varphi (x,y)$ is a formula and $q(y)$ is a global type. We prove that in any NSOP $_1$ theory these ranks satisfy some desirable properties; in particular, $D_Q(x=x)<\omega $ for any finite tuple of variables x and any Q, if $q\supseteq p$ is a Kim-forking extension of types, then $D_Q(q) (...) Kim-non-forking extension, then $D_Q(q)=D_Q(p)$ for every Q that involves only invariant types whose Morley powers are -stationary. We give natural examples of families of invariant types satisfying this property in some NSOP $_1$ theories. We also answer a question of Granger about equivalence of dividing and dividing finitely in the theory $T_\infty $ of vector spaces with a generic bilinear form. We conclude that forking equals dividing in $T_\infty $, strengthening an earlier observation that $T_\infty $ satisfies the existence axiom for forking independence. Finally, we slightly modify our definitions and go beyond NSOP $_1$ to find out that our local ranks are bounded by the well-known ranks: the inp-rank (burden), and hence, in particular, by the dp-rank. Therefore, our local ranks are finite provided that the dp-rank is finite, for example, if T is dp-minimal. Hence, our notion of rank identifies a non-trivial class of theories containing all NSOP $_1$ and NTP $_2$ theories. (shrink)

In traditional consequentialism the good is position-neutral. A single evaluative ranking of states of affairs is correct for everyone, everywhere regardless of their positions. Recently, position-relative forms of consequentialism have been developed. These allow for the correct rankings of states to depend on connections that hold between the state being evaluated and the position of the evaluator. For example, perhaps being an agent who acts in a certain state requires me to rank that state differently from someone else who (...) lacks this connection. In this chapter several different kinds of position-relative rankings related to agents, times, physical locations, and possible worlds are explored. Arguments for and against adopting a position-relative axiology are examined, and it is suggested that position-relative consequentialism is a promising moral theory that has been underestimated. (shrink)

The study of classes of models of a finite diagram was initiated by S. Shelah in 1969. A diagram D is a set of types over the empty set, and the class of models of the diagram D consists of the models of T which omit all the types not in D. In this work, we introduce a natural dependence relation on the subsets of the models for the 0-stable case which share many of the formal properties of forking. This (...) is achieved by considering a rank for this framework which is bounded when the diagram D is 0-stable. We can also obtain pregeometries with respect to this dependence relation. The dependence relation is the natural one induced by the rank, and the pregeometries exist on the set of realizations of types of minimal rank. Finally, these concepts are used to generalize many of the classical results for models of a totally transcendental first-order theory. In fact, strong analogies arise: models are determined by their pregeometries or their relationship with their pregeometries; however the proofs are different, as we do not have compactness. This is illustrated with positive results as well as negative results . We also give a proof of a Two Cardinal Theorem for this context. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence (...) relation for superstable homogeneous models. (shrink)

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence (...) relation for superstable homogeneous models. (shrink)

Online debates typically possess a large number of argumentative comments. Most readers who would like to see which comments are winning arguments often only read a part of the debate. Many platforms that host such debates allow for the comments to be sorted, say from the earliest to latest. How can argumentation theory be used to evaluate the effectiveness of such policies of sorting comments, in terms of the actually winning arguments displayed to a reader who may not have read (...) the whole debate? We devise a pipeline that captures an online debate tree as a bipolar argumentation framework, which is sorted depending on the policy, giving a sequence of induced sub-BAFs representing how and how much of the debate has been read. Each sub-BAF has its own set of winning arguments, which can be quantitatively compared to the set of winning arguments of the whole BAF. We apply this pipeline to evaluate policies on Kialo debates, where it is shown that reading comments from most to least liked, on average, displays more winners than reading comments earliest first. Therefore, in Kialo, reading comments from most to least liked is on average more effective than reading from the earliest to the most recent. (shrink)

PurposeThe aim of the study was to establish the differences in affective states of swimmers depending on the subjective rank of the competition and the relationship between affective states and performance in sports competitions of low, medium and high subjectively perceived rank.MethodsThe respondents aged from 15 to 23 years were studied using the psychological questionnaires Perceived Stress Scale, Profile of Mood State, and Positive and Negative Affect Schedule during sports events. 362 measurements using POMS and 232 measurements using (...) PANAS before the starts were collected. The significance of intergroup differences was determined using the Kruskal-Wallis test. A stepwise regression analysis was used to determine the emotional predictors of sports results.ResultsSubjective rank of sports competition differentiated significantly anger, confusion, depression, fatigue, vigour, positive emotions, and negative emotions. Regression analysis showed the influence of mood states and positive emotions on the sports result.ConclusionThe swimmers’ affective state changed depending on the subjective rank of the competition. Depression and positive emotional state made it possible to predict the result in medium- and high-rank competition. (shrink)

The paper investigates the prospects of Spohn’s ranking theory with respect to Goodman’s New Riddle of Induction. Based on a novel analysis of the riddle (Freitag [manuscript]), we show it to be an inductive extension of Hansson’s puzzle (Hansson 1992, 1999). As a consequence, a solution needs to take into account the dependence relations between evidential beliefs: “grue” is unprojectible because it depends on evidence whose projection is defeated. It will be suggested that this solution can be implemented into Spohn’s (...) ranking theory, but that ranking theory is unable to provide a proper explanation of the required conditional ranks. (shrink)

Supererogatory acts are, in some sense, morally better their non-supererogatory alternatives. In this sense, what is it for one option A to be better than an alternative B? I argue for three main conclusions. First, relative rankings are a type of all-in action guidance. If A is better than B, then morality recommends that you A rather than B. Such all-in guidance is useful when acts have the same deontic status. Second, I argue that Right > Wrong: permissible acts are (...) always better than their impermissible alternatives. If Right > Wrong were false, then morality’s deontic verdicts would sometimes conflict with its relative rankings. Such conflict would undermine the thought that morality is a coherent, authoritative guide to action. Third, the All or Nothing Problem is not a counterexample to Right > Wrong as is commonly thought. Instead, it involves an interesting ranking reversal: whether A > B can depend on whether a certain alternative is added as a third option. (shrink)

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility (...) theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness. (shrink)

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several possible (...) choices. Each choice can lead to a different "unique" probability and utility. By focusing attention on statedependent utilities, we determine conditions under which a truly unique probability and utility can be determined from an agent's expressed preferences among acts. Suppose that an agent's preference can be represented in terms of a probability P and a utility U.That is, the agent prefers one act to another iff the expected utility of that act is higher than that of the other. There are many other equivalent representations in terms of probabilities Q, which are mutually absolutely continuous with P, and state-dependent utilities V, which differ from U by possibly different positive affine transformations in each state of nature. We describe an example in which there are two different but equivalent state-independent utility representations for the same preference structure. They differ in which acts count as constants. The acts involve receiving different amounts of one or the other of two currencies, and the states are different exchange rates between the currencies. It is easy to see how it would not be possible for constant amounts of both currencies to have simultaneously constant values across the differentstates. Savage (1954, sec. 5.5) discovered a situation in which two seemingly equivalent preference structures are represented by different pairs of probability and utility. He attributed the phenomenon to the construction of a "small world." We show that the small world problem is just another example of two different, but equivalent, representations treating different actsas constants. Finally, we prove a theorem (similar to one of Karni 1985) that shows how to elicit a unique state-dependent utility and does not assume that there are prizes with constant value. To do this, we define a new hypothetical kind of act in which both the prize to be awarded and the state of nature are determined by an auxiliary experiment. (shrink)

Meets what? Ranking theory is, as far as I know, the only existing theory suited for underpinning Keith Lehrer’s account of knowledge and justification. If this is true, it’s high time to bring both together. This is what I shall do in this paper. However, the result of defining Lehrer’s primitive notions in terms of ranking theory will be disappointing: justified acceptance will, depending on the interpretation, either have an unintelligible structure or reduce to mere acceptance, and in the latter (...) interpretation knowledge will reduce to true belief. Of course, this result will require a discussion of who should be disappointed. So, the plan of the paper is simple: In section 1 I shall briefly state what is required for underpinning Lehrer’s account and why most of the familiar theories fail to do so. In section 2 I shall briefly motivate and introduce ranking theory. Basing Lehrer’s account on it will be entirely straightforward. Section 3 proves the above-mentioned results. Section 4, finally, discusses the possible conclusions. (shrink)

Isolated habitats can be compared and ranked by comparing their interior-to-edge ratio (I/E). We would like to show here that results based on ranking by I/E ratio sometimes contradict Diamond's rule, which ranks the most rounded habitat (i.e. most compact) as the best one. The reason for this contradiction is the frequently overlooked size dependence of the I/E. Being the interior-to-edge ratio size dependent, from a given set of habitats of different sizes, compact shaped (rounded) habitats might have worse (...) I/E ratios than elongated or irregular ones. (shrink)

We develop a basic theory of rosy groups and we study groups of small Uþ-rank satisfying NIP and having finitely satisfiable generics: Uþ-rank 1 implies that the group is abelian-by-finite, Uþ-rank 2 implies that the group is solvable-by-finite, Uþ-rank 2, and not being nilpotent-by-finite implies the existence of an interpretable algebraically closed field.

MacIntyre’s latest volume ranks among his best works to date. Together with his last three books, Dependent Rational Animals forms a body of work unrivalled in contemporary social and ethical philosophy. In this short space I will consider both how the new book relates to MacIntyre’s earlier work and some new lines of argument.

The aim of the paper is to propose a preferences representation model under risk where risk perception can be past experience dependent. A first step consists in considering a one period decision problem where individual preferences are no more defined only on decisions but on pairs (decision, past experience). The obtained criterion is used in the construction of a dynamic choice model under risk. The paper ends with an illustrative example concerning insurance demand. It appears that our model allows (...) to explain modifications in the insurance demand behavior over time observed on the insurance markets for catastrophic risk and difficult to justify with standard models. (shrink)

Many applications of intuitionistic fuzzy sets depend on ranking or comparing intuitionistic fuzzy numbers. This paper presents a novel ranking method for intuitionistic fuzzy numbers based on the preference attitudinal accuracy and score functions. The proposed ranking method considers not only the preference attitude of decision maker, but also all the possible values in feasible domain. Some desirable properties of preference attitudinal accuracy and score functions are verified in detail. A total order on the set of intuitionistic fuzzy numbers is (...) established by using the proposed two functions. The proposed ranking method is also applied to select renewable energy. The advantage and validity of the proposed method are shown by comparing with some representative ranking methods. (shrink)

How much context-sensitivity is there in English? Cappelen and Lepore’s answer: Not very much. On their view, context-sensitivity is confined to a ‘Basic List’, ‘plus or minus a bit’, that includes pronouns, demonstratives, temporal and spatial adverbs like ‘here’, ‘now’, and ‘yesterday’, and a short list of context dependent nouns and adjectives. Shockingly, the authors claim that ‘Lepore is ready’, ‘Cappelen has had enough’, and ‘Cappelen is quite tall,’ have a context-invariant meaning. Nor is that meaning incomplete, in the (...) sense of being something that can only be given a truth value relative to an enrichment. No, simultaneous utterances of ‘Lepore is ready’ always express the same proposition—that Lepore is ready—one that is true or false. When is it true? Cagily, the authors inform us that it is true if and only if Lepore is ready. One might wish to inquire further as to when Lepore is ready. For example: ‘If Lepore is ready for breakfast but not ready to learn to play golf, is Lepore ready?’ and ‘Given that I am always ready for a fulfilling relationship, am I ever not ready?’ Whenever they are faced with questions such as these, the authors defer to the arena of metaphysics, where they admit to being ‘rank amateurs’. (shrink)

The paper characterizes axiomatically a class of temptation-driven preferences. The key (but not the only) novelty of the paper is the idea that the alternative which tempts when an item x is consumed may not be the same as the alternative which tempts when another item y is consumed. For any single item to be ultimately consumed, the other items can be ranked by how much they tempt. An individual contemplates, as an alternative consumption, only the item that tempts most. (...) The utility of a menu is then equal to the utility of the item that is consumed less a (psychological) cost of resisting temptation; this cost depends on both: the item to be consumed and the item that tempts. Unlike most of the existing literature, the axioms are imposed on deterministic menus, not on menus of lotteries. (shrink)

Rational consequence relations and Popper functions provide logics for reasoning under uncertainty, the former purely qualitative, the latter probabilistic. But few researchers seem to be aware of the close connection between these two logics. I’ll show that Popper functions are probabilistic versions of rational consequence relations. I’ll not assume that the reader is familiar with either logic. I present them, and explicate the relationship between them, from the ground up. I’ll also present alternative axiomatizations for each logic, showing them to (...) depend on weaker axioms than usually recognized. (shrink)

In traditional and popular accounts, Zen Buddhism is depicted as a practice that rejects literary study and intellectualization in favor of a direct experience of enlightenment that is beyond words. Indeed, the Zen school has traditionally defined itself as a "separate transmission outside the teachings, not dependent on words and letters". Even when regarding the tradition's literary output, Zen literature is famous for its antinomian dialogues replete with outrageous antics, frequent non sequiturs, and crude, illiterate utterances that appear to (...) validate the perspective that Zen simply rejects logical thinking, rational discourse, literary cultivation, and any systematic means of study. While it is... (shrink)

We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

Drawing upon a developmental perspective, we investigated the differences in power acquisition between only and non-only children as well as the mediating role of cooperative and competitive orientations and the moderating role of dependency on parents. To test our hypotheses, we conducted two field studies in 155 part-time Master of Business Administration students and 375 senior students. Results showed that: non-only children were more likely to achieve higher rank at work than only children; only children were less likely than (...) non-only children to acquire power in organizations because they scored lower in cooperative orientation; however, the mediating effect of competitive orientation was not significant; the difference in cooperative orientation between only and non-only children was smaller when dependency on parents was high, whereas it became larger when dependency on parents was low. Our research contributes to the understanding of how family structure influences individual power acquisition. (shrink)

Explores the relationship of a person's inner world to the outer world of reality, and suggests ways to manipulate the outer world through positive externalization of the will.

For the English speaking reader of today, Ranke is surprisingly inaccessible; indeed, he has become something of a patron saint, more praised than read. Now all his major works have been translated, while almost none of his letters, notes, or essays, so important in getting an informal appraisal of his craft of history, is in English. Many of his of books, whether in German or in English, are no longer in print, and the modern reader is less likely to bear (...) up with the four or six volume works which are. Thus the purpose of this anthology is to bring attention to some of the riches which a reader might find in a more extended study of Ranke's histories. Its emphasis is on Ranke as an historian, with translations of essays and addresses which lay down his program for research, politics, and the relationship between and historian's values and his work. It also attempts to give some sense of Ranke's literary skill, by including examples of his historical portraiture from his History of the Popes, History of France, and History of the Reformation. Finally, a selection of letters and brief reflections culled from his works and notes tries to recapture the man, whose own inner development joined with the tendencies of his age to make him a world-historical figure in Ranke's own sense of the word. (shrink)