The existence of a Richter–Peleg multi-utility representation of a preorder by means of upper semicontinuous or continuous functions is discussed in connection with the existence of a Richter–Peleg utility representation. We give several applications that include the analysis of countable Richter–Peleg multi-utility representations.

The present paper gives a topological solution to representability problems related to multi-utility, in the field of Decision Theory. Necessary and sufficient topologies for the existence of a semicontinuous and finite Richter–Peleg multi-utility for a preorder are studied. It is well known that, given a preorder on a topological space, if there is a lower semicontinuous Richter–Peleg multi-utility, then the topology of the space must be finer than the Upper topology. However, this condition fails (...) to be sufficient. Instead of search for properties that must be satisfied by the preorder, we study finer topologies which are necessary or/and sufficient for the existence of semicontinuous representations. We prove that Scott topology must be contained in the topology of the space in case there exists a finite lower semicontinuous Richter–Peleg multi-utility. However, the existence of this representation cannot be guaranteed. A sufficient condition is given by means of Alexandroff’s topology, for that, we prove that more order implies less Alexandroff’s topology, as well as the converse. Finally, the paper is implemented with a topological study of the maximal elements. (shrink)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, (...) the hallmark of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the (...) dimension of the mixture space is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

This paper discusses random utility representations of the Luce model. Earlier works, such as McFadden, Yellott, and Strauss have discussed random utility representations under the assumption that utilities are additively separable in a deterministic and a random part. Under various conditions, they have established that a separable and independent random utility representation exists if and only if the random terms are type III extreme value distributed. This paper analyzes independent random utility representations without the separability (...) condition and with an infinite universal set of alternatives. Under these assumptions, it turns out that the most general random utility representation of the Luce model is a utility function that is an arbitrary strictly increasing transformation of a separable utility function with extreme value distributed random terms. (shrink)

This article revisits the standard results of demand theory when the preference relation is a continuous preorder that admits an equicontinuous multi-utility representation. We study the consumer problem as the constrained maximization of a continuous vector-valued utility mapping, and show how to rederive those results. In particular, we provide a link between the literature on vector optimization and the analysis of the consumer problem under incomplete preferences.

A detailed theoretical analysis is presented of what five utility representations – subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU – say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive aspects (...) of the representations from data concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models. (shrink)

This article develops an unconventional perspective on the utilitarianism of Bentham and Mill in at least four areas. First, it is shown that both authors conceived of utility as irreducibly multi-dimensional, and that Bentham in particular was very much aware of the ambiguity that multi-dimensionality imposes upon optimal choice under the greatest happiness principle. Secondly, I argue that any attribution of intrinsic worth to any form of human behaviour violates the first principles of Bentham's and Mill's utilitarianism, (...) and that this renders both authors immune to the claim by G. E. Moore that they committed a ‘naturalistic fallacy’. Thirdly, in light of these contentions, I find no flaw in Mill's ‘proof of utility’. Fourthly, I use the notion of intrapersonal utility weights to provide an interpretation of Mill's qualitative hedonism that is entirely consistent with his value monism. (shrink)

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in an expected prospect maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation of a random prospect under constraint that the risk measure is bounded above, he then behaves as a “generalized expected utility maximizer” in the following sense. The DM exhibits ambiguity with respect to a family of (...) utility functions defined on a larger set of decisions than the original one; he adopts pessimism and performs first a minimization of expected utility over this family, then performs a maximization over a new decisions set. This economic behaviour is called “maxmin under risk” and studied by Maccheroni (Econ Theory 19:823–831, 2002). As an application, we make the link between an expected prospect maximization problem, subject to conditional value-at-risk being less than a threshold value, and a non-expected utility economic formulation involving “loss aversion”-type utility functions. (shrink)

In models of multi-level selection, the property of Darwinian fitness is attributed to entities at more than one level of the biological hierarchy, e.g. individuals and groups. However, the relation between individual and group fitness is a controversial matter. Theorists disagree about whether group fitness should always, or ever, be defined as total (or average) individual fitness. This paper tries to shed light on the issue by drawing on work in social choice theory, and pursuing an analogy between fitness (...) and utility. Social choice theorists have long been interested in the relation between individual and social utility, and have identified conditions under which social utility equals total (or average) individual utility. These ideas are used to shed light on the biological problem. (shrink)

Due to the non-invasiveness and high precision of electroencephalography, the combination of EEG and artificial intelligence is often used for emotion recognition. However, the internal differences in EEG data have become an obstacle to classification accuracy. To solve this problem, considering labeled data from similar nature but different domains, domain adaptation usually provides an attractive option. Most of the existing researches aggregate the EEG data from different subjects and sessions as a source domain, which ignores the assumption that the source (...) has a certain marginal distribution. Moreover, existing methods often only align the representation distributions extracted from a single structure, and may only contain partial information. Therefore, we propose the multi-source and multi-representation adaptation for cross-domain EEG emotion recognition, which divides the EEG data from different subjects and sessions into multiple domains and aligns the distribution of multiple representations extracted from a hybrid structure. Two datasets, i.e., SEED and SEED IV, are used to validate the proposed method in cross-session and cross-subject transfer scenarios, experimental results demonstrate the superior performance of our model to state-of-the-art models in most settings. (shrink)

We propose a descriptive version of the classical multi-attribute utility model; to that end, we add a new parameter, momentary salience, to the customary formulation. The addition of this parameter allows the theory to accommodate changes in the decision maker’s mood and circumstances, as the saliencies of anticipated consequences are driven by concerns of the moment. By allowing for the number of consequences given attention at the moment of decision to vary, the new model mutes the criticism that (...) SEU models call for an omniscient decision maker. Use of the model is illustrated with a large-scale longitudinal study showing that adolescent smokers have higher utility for smoking than nonsmokers. We also propose to use the model hierarchically to describe everyday decisions that people deal with repeatedly. Big decisions, which set policy, guide a host of nested little decisions, which in turn lead to action. For a little decision, one of the options will be consistent with the policy, and will inherit its high utility. Accordingly, most little decisions will be made quickly and will follow the policy. However, people do sometimes decide to violate their own policies, and we describe how these lapses can lead to collapse of the policy. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. (...) As a result, we should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

Consider a subjective expected utility preference relation. It is usually held that the representations which this relation admits differ only in one respect, namely, the possible scales for the measurement of utility. In this paper, I discuss the fact that there are, metaphorically speaking, two additional dimensions along which infinitely many more admissible representations can be found. The first additional dimension is that of state-dependence. The second—and, in this context, much lesser-known—additional dimension is that of act-dependence. The simplest (...) implication of their usually neglected existence is that the standard axiomatizations of subjective expected utility fail to provide the measurement of subjective probability with satisfactory behavioral foundations. (shrink)

The standard representation theorem for expected utility theory tells us that if a subject’s preferences conform to certain axioms, then she can be represented as maximising her expected utility given a particular set of credences and utilities—and, moreover, that having those credences and utilities is the only way that she could be maximising her expected utility. However, the kinds of agents these theorems seem apt to tell us anything about are highly idealised, being always probabilistically coherent (...) with infinitely precise degrees of belief and full knowledge of all a priori truths. Ordinary subjects do not look very rational when compared to the kinds of agents usually talked about in decision theory. In this paper, I will develop an expected utility representation theorem aimed at the representation of those who are neither probabilistically coherent, logically omniscient, nor expected utility maximisers across the board—that is, agents who are frequently irrational. The agents in question may be deductively fallible, have incoherent credences, limited representational capacities, and fail to maximise expected utility for all but a limited class of gambles. (shrink)

We present here a direct elementary construction of continuous utility functions on perfectly separable totally preordered sets that does not make use of the well-known Debreu’s open gap lemma. This new construction leans on the concept of a separating countable decreasing scale. Starting from a perfectly separable totally ordered structure, we give an explicit construction of a separating countable decreasing scale, from which we show how to get a continuous utility map.

In this paper weak utilities are obtained for acyclic binary relations satisfying a condition weaker than semicontinuity on second countable topological spaces. In fact, in any subset of such a space we obtain a weak utility that characterizes the maximal elements as maxima of the function. The addition of separability of the relation yields the existence of semicontinuous representations. This property of the utility provides a result of existence of maximal elements for a class of spaces that include (...) compact spaces. However, we offer a negative result that continuity may not be reached under such hypotheses. (shrink)

Expressivism in logic is the view that logical vocabulary plays a primarily expressive role: that is, that logical vocabulary makes perspicuous in the object language structural features of inference and incompatibility (Brandom, 1994, 2008). I present a precise, technical criterion of expressivity for a logic (§2). I next present a logic that meets that criterion (§3). I further explore some interesting features of that logic: first, a representation theorem for capturing other logics (§3.1), and next some novel logical vocabulary (...) for expressing structural features of inference (§4). (shrink)

This is a follow-up article toPhilip Brey's ``The ethics of representation andaction in Virtual Reality'' (published in thisjournal in January 1999). Brey's call for moreanalysis of ethical issues of virtual reality(VR) is continued by further analyzing issuesin a specialized domain of VR – namelymulti-user environments. Several elements ofBrey's article are critiqued in order to givemore context and a framework for discussion.Issues surrounding representations ofcharacters in multi-user virtual realities aresurveyed in order to focus attention on theimportance of additional discussion (...) andanalysis of specialized aspects of VR. (shrink)

Higher-order theories of consciousness posit that a mental state is conscious by virtue of being represented by another mental state, which is therefore a higher-order representation (HOR). Whether HORs are construed as thoughts or experiences, higher-order theorists have generally contested whether such metarepresentations have any significant cognitive function. In this paper, I argue that they do, focusing on the value of conscious thinking, as distinguished from conscious perceiving, conscious feeling, and other forms of conscious mentality. A thinking process is (...) constituted by propositional-attitude states, and during conscious thinking some or all of these states would be targeted by HORs. Since cases of nonconscious thinking are widely accepted, the question arises as to the use of representing one's thoughts during thinking. Contra the views of Armstrong and Rolls, I argue that HORs do not facilitate first-order thinking. Rather, I propose that such representations enable reasoning about one's act of thinking, and I give various examples of this sort of metacognition in support of the theory. I further argue that the general correlation between complex thinking and its being conscious is merely due to the fact that assessing one's mental act is particularly useful during such thinking, not because consciousness somehow facilitates first-order inference-making, as folk psychology implies. My view is thus consistent with recent empirical evidence that complex thinking sometimes yields better results when nonconscious. (shrink)

Humans communicate with different modalities. We offer an account of multi-modal meaning coordination, taking speech-gesture meaning coordination as a prototypical case. We argue that temporal synchrony (plus prosody) does not determine how to coordinate speech meaning and gesture meaning. Challenging cases are asynchrony and broadcasting cases, which are illustrated with empirical data. We propose that a process algebra account satisfies the desiderata. It models gesture and speech as independent but concurrent processes that can communicate flexibly with each other and (...) exchange the same information more than once. The account utilizes the ψ-calculus, allowing for agents, input-output-channels, concurrent processes, and data transport of typed λ-terms. A multi-modal meaning is produced integrating speech meaning and gesture meaning into one semantic package. Two cases of meaning coordination are handled in some detail: the asynchrony between gesture and speech, and the broadcasting of gesture meaning across several dialogue contributions. This account can be generalized to other cases of multi-modal meaning. (shrink)

We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, (...) each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language. (shrink)

In this paper we argue that awareness comes in degrees, and we propose a novel multi-factor account that spans both subjective experiences and perceptual representations. At the subjective level, we argue that conscious experiences can be degraded by being fragmented, less salient, too generic, or flash-like. At the representational level, we identify corresponding features of perceptual representations—their availability for working memory, intensity, precision, and stability—and argue that the mechanisms that affect these features are what ultimately modulate the degree of (...) awareness. We conclude the paper by demonstrating why the original interpretations of certain empirical findings that apparently pose problems for our account are, in fact, flawed. (shrink)

This chapter of the Handbook of Utility Theory aims at covering the connections between utility theory and social ethics. The chapter first discusses the philosophical interpretations of utility functions, then explains how social choice theory uses them to represent interpersonal comparisons of welfare in either utilitarian or non-utilitarian representations of social preferences. The chapter also contains an extensive account of John Harsanyi's formal reconstruction of utilitarianism and its developments in the later literature, especially when society faces uncertainty (...) rather than probabilistic risk. (shrink)

I contend that Alva Noë’s Enactive Approach to Perception fails to give an adequate account of the periphery of attention. Noë claims that our peripheral experience is not produced by the brain’s representation of peripheral items, but rather by our mastery of sensorimotor skills and contingencies. I offer a two-pronged assault on this account of the periphery of attention. The first challenge comes from Mack and Rock’s work on inattentional blindness, and provides robust empirical evidence for the semantic processing (...) (and hence representation) of some wholly unattended stimuli. The second challenge draws on LaBerge’s theory of attention to provide a substantial advantage to peripheral representations, saving time whenever we shift the focus of our attention to something which had been in the periphery, allowing us to respond to that thing more quickly than would be possible if Noë’s account of perception were correct. (shrink)

In the present paper we study the framework of additive utility theory, obtaining new results derived from a concurrence of algebraic and topological techniques. Such techniques lean on the concept of a connected topological totally ordered semigroup. We achieve a general result concerning the existence of continuous and additive utility functions on completely preordered sets endowed with a binary operation ``+'', not necessarily being commutative or associative. In the final part of the paper we get some applications to (...) expected utility theory, and a representation theorem for a class of complete preorders on a quite general family of real mixture spaces. (shrink)

An increasingly prevalent approach to studying human cognition is to construe the mind as optimally allocating limited cognitive resources among cognitive processes. Under this bounded rationality approach (Icard in Philos Sci 85(1):79–101, 2018; Simon in Utility and probability, Palgrave Macmillan, 1980), it is common to assume that resource-bounded cognitive agents approximate normative solutions to statistical inference problems, and that much of the bias and variability in human performance can be explained in terms of the approximation strategies we employ. In (...) this paper, we argue that this approach restricts itself to an unnecessarily narrow scope of cognitive models, which limits its ability to explain how humans flexibly adapt their representations to novel environments. We argue that more attention should be paid to how we form our cognitive representations in the first place, and advocate for pluralistic framework which jointly optimizes over both representations and algorithms for manipulating them. We identify several fundamental trade-offs that manifest in this joint optimization, and draw on recent work to motivate a unified formal framework for this analysis. We illustrate a simplified version of this analysis with a case study in social cognition, and outline several new directions for research that this approach suggests. (shrink)

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

The present paper describes a joint action paradigm in which individuals or pairs utilized two computer keys to keep a dot stimulus moving inside a larger rectangle. Members of a pair could neither see nor hear each other. This paradigm allowed us to combine the discrete-trial type dependent variables commonly utilized by representational theorists, with the continuous, temporal dependence variables utilized by dynamical theorists. Analysis revealed that individuals kept the dot in the rectangle longer than dyads and did so by (...) moving it back and forth within the rectangle. Dyads, however, pressed their individual buttons as quickly as possible in order to keep the dot near the middle of the rectangle. These findings indicate that joint action constitutes a multi-scale phenomena that is best investigated via multiple, complementary methodologies versus single-measure, competing theories. (shrink)

This is an excerpt from a report that highlights and explores five questions which arose from the workshop on perceptual learning and perceptual recognition at the University of Toronto, Mississauga on May 10th and 11th, 2012. This excerpt explores the question: Does our representation of time provide and amodal framework for multi-sensory integration?

Projections of future climate change cannot rely on a single model. It has become common to rely on multiple simulations generated by Multi-Model Ensembles (MMEs), especially to quantify the uncertainty about what would constitute an adequate model structure. But, as Parker points out (2018), one of the remaining philosophically interesting questions is: “How can ensemble studies be designed so that they probe uncertainty in desired ways?” This paper offers two interpretations of what General Circulation Models (GCMs) are and how (...) MMEs made of GCMs should be designed. In the first interpretation, models are combinations of modules and parameterisations; an MME is obtained by “plugging and playing” with interchangeable modules and parameterisations. In the second interpretation, models are aggregations of expert judgements that result from a history of epistemic decisions made by scientists about the choice of representations; an MME is a sampling of expert judgements from modelling teams. We argue that, while the two interpretations involve distinct domains from philosophy of science and social epistemology, they both could be used in a complementary manner in order to explore ways of designing better MMEs. (shrink)

Using Reidenbach and Robin‘s ( Journal of Business Ethics 7, 871–879, 1988) multi-criteria ethics instrument, we carried out the first empirical test of Robertson and Crittenden‘s (Strategic Management Journal 24, 385–392, 2003) cross-cultural map of moral philosophies to examine what ethical criteria guide business people in Russia and the U.S. in their intention to behave. Competing divergence and convergence hypotheses were advanced. Our results support a convergence hypothesis, and reveal a common emphasis on relativism. Americans are also influenced by (...) the justice criterion while Russians tend to emphasize utilitarianism. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be (...) defended on the basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

Representation has been one of the main themes in the recent discussion of models. Several authors have argued for a pragmatic approach to representation that takes users and their interpretations into account. It appears to me, however, that this emphasis on representation places excessive limitations on our view of models and their epistemic value. Models should rather be thought of as epistemic artifacts through which we gain knowledge in diverse ways. Approaching models this way stresses their materiality (...) and media-specificity. Focusing on models as multi-functional artifacts loosens them from any pre-established and fixed representational relationships and leads me to argue for a two-fold approach to representation. (shrink)