Descriptive and Normative Approaches to Human Behavior

The following sections are included:

• Preface

• Contents

Population axiology concerns how to evaluate populations in regard to their goodness, that is, how to order populations by the relations “is better than” and “is as good as”. This field has been riddled with paradoxes and impossibility results which seem to show that our considered beliefs are inconsistent in cases where the number of people and their welfare varies. All of these results have one thing in common, however. They all involve an adequacy condition that rules out Derek Parfit's Repugnant Conclusion. Moreover, some theorists have argued that we should accept the Repugnant Conclusion and hence that avoidance of this conclusion is not a convincing adequacy condition for a population axiology. As I shall show in this chapter, however, one can replace avoidance of the Repugnant Conclusion with a logically weaker and intuitively more convincing condition. The resulting theorem involves, to the best of my knowledge, logically weaker and intuitively more compelling conditions than the other theorems presented in the literature. As such, it challenges the very existence of a satisfactory population ethics.

This chapter examines the empirical evidence for interference effects in psychological experiments. It also reviews the competing interpretations of these effects with respect to traditional cognitive models and new quantum cognition models.

There is a long tradition of attempts to define the monadic value properties of intrinsic or final goodness and badness in terms of the dyadic betterness relation. Such definitions, if possible, would seem desirable for reasons of theoretical simplicity. It appears that every extant proposal of this kind relies on the concept of negation, presupposing that the value bearers are proposition-like entities, such as states of affairs, facts, or propositions. In this chapter, we shall investigate the possibility of defining the monadic value properties in terms of betterness, without assuming that negation or other logical connectives can be applied to the value bearers. Many value theorists believe that, for example, physical objects can have intrinsic or final value. It is therefore worthwhile to explore whether the monadic value properties can be defined in terms of betterness, within a framework that puts no restrictions on what kinds of entities that can be bearers of value. The conclusion will be that such definitions are possible if, and probably only if, certain admittedly disputable axiological principles are accepted.

“Temporal window of integration” has become a widely accepted concept in multisensory research: crossmodal information falling within this window will typically be integrated, whereas information falling outside will not. Specifically, an infinitely large time window will always allow integration, a zero-width time window would rule out integration entirely. From a decision-making point of view, neither case is likely to be optimal in the long run. In a noisy, complex, and potentially hostile environment exhibiting multiple sources of sensory stimulation, the issue of whether or not two given stimuli of different modality arise from a common source may become critical for a behaving organism. Making explicit assumptions about the arrival time difference between peripheral sensory processing times triggered by a crossmodal stimulus set, we derive a decision rule determining optimal window width as a function of the prior odds in favor of a common multisensory source, the likelihood of arrival time differences, and the payoff for making correct or wrong decisions. The empirical validity of the suggested approach is shown to be supported by data from a recent study measuring head saccades toward visual-auditory stimuli under varying prior probabilities for a common source.

Fechnerian Scaling imposes metrics on two sets of stimuli related to each other by a discrimination function subject to Regular Minimality. The two sets of stimuli usually represent the same set of stimulus values presented to an observer in two distinct observation areas. A discrimination function associates with every pair of stimuli a nonnegative number interpretable as the degree or probability with which, “from the observer's point of view,” the two stimuli differ from each other, overall or in a specified respect. Regular Minimality is a principle according to which the relation “to be the best match for” across the two stimulus areas has certain uniqueness and symmetry properties. Fechnerian distances are computed by means of a dissimilarity cumulation procedure: discrimination values are first converted into an appropriately defined dissimilarity function, the sums of the latter's values are computed for all finite chains of stimuli connecting a given pair of stimuli, and the infimum of such sums (cumulative dissimilarities) is taken to be the distance from one element of this pair to the other. The Fechnerian distance between two stimuli in one observation area is the same as the Fechnerian distance between the corresponding (best matching) stimuli in the other observation area. This chapter deals with the reverse problem of Fechnerian Scaling: under which conditions one can compute the discrimination function values given the Fechnerian distances and the discrimination values between the best matching stimuli.

In this chapter, we review Bayesian adaptive estimation methodology under a formal decision theoretic view, extending on the work reported in Kujala (2010). We present simple concrete examples that illustrate the efficiency of the ubiquitous greedy information maximization algorithm, compare it to the optimal non-adaptive and batch strategies, and consider certain pitfalls of the greedy strategy. In particular, we show that the greedy strategy can be arbitrarily much worse than the optimal strategy for a certain number of trials. Then, we generalize the discussion to the situation where each observable variable is associated with a certain random cost of observation. For example, the cost could be defined as the random time taken by each trial in an experiment, and one might wish to maximize the expected total information gain over as many trials as can be completed in 15 minutes.

Standard probability theory is based on event spaces that are Boolean algebras of sets. Its main alternative in science—quantum probability theory—is based on non-Boolean event spaces consisting of closed subspaces of a Hilbert space. Quantum probability theory differs from standard probability theory in the following two ways: (i) Its probability functions are not additive over all pairs of disjoint elements of its event algebra; and (ii) it need not satisfy an equivalent of the distributivity property of Boolean algebras of sets, that is, it need not satisfy an equivalent of A∩(B∪C) = (A∩B)∪(A∩C). This chapter focuses on situations where, like in standard probability theory, probability functions are additive over all pairs of disjoint elements belonging to their event algebras. It is shown that this and technical considerations involving elements having probability 0 result in the algebras being greatly constrained, because they must (1) satisfy a property called “modularity,” which is a generalization of the distributivity property, and (2) unless they are Boolean algebras, they cannot be uniquely complemented. An example of a nonBoolean probability theory with an algebra satisfying a generalization of unique complementation is used to formulate a new decision theory where the decision maker can change “modes”, e.g., be in various emotional states while making a decision. The example's algebra is shown to be distributive. Its generalization of complementation—called “pseudocomplementation”—has the properties of the negation operation of a well-studied alternative to classical logic known in the literature as “intuitionistic logic.” The example uses pseudo-complementation to allow for multiple interpretations of an event as the decision maker transitions through modes. A particular model of decision making is presented that (i) allows for modes, (ii) has an equation for utility that is very similar to the SEU decision model used throughout science, and (iii) is arguably normative for human decision makers, given that humans are emotional creatures.

Presumption of Equality enjoins that individuals be treated equally in the absence of discriminating information. My objective in this chapter is to make this principle more precise, viewing it as a norm of fairness, in order to determine why and under what conditions it should be obeyed.

Presumption norms are procedural constraints, but their justification might come from the expected outcomes of the procedures they regulate. This outcome-oriented approach to fairness is pursued in the chapter. The suggestion is that in the absence of information that would discriminate between the individuals, equal treatment minimizes the expected unfairness in the outcome. Another suggestion is that, under these circumstances, equal treatment also minimizes maximal possible unfairness, i.e., it is minimally unfair if ‘worst comes to worst’. Whether these suggestions are correct depends on the properties of the underlying unfairness measure.

Loomes and Sugden (1995) discussed how to incorporate a probabilistic element into decision theories. We follow up on their discussion of random preference specifications for transitivity of preference, including a well-known necessary condition for these models, the triangle inequality. This condition applies traditionally to binary forced choice, whereas we consider ternary paired comparisons, in which respondents are permitted to express indifference between two offered choice alternatives. We review a general method for fully specifying necessary and sufficient conditions for certain random preference models. We provide such specifications for the random preference models whose core theories are semiorders or interval orders, in the case of four choice alternatives.

In this chapter knowledge space theory is developed from a different point of view. It takes the skills as primitives of the theory and shows how the usual theory can be derived from this setup. The skills are known to be closely related to the basis of the space, they are assumed to be partially ordered. The test items are introduced via a set representation of this partial order. The knowledge space is seen to be determined both by the skill order and the set representation. The interaction between both components is described and viewed from a lattice theoretic perspective. When the lattice structure is regarded, it must be kept in mind that non-isomorphic spaces can have isomorphic lattices.

In general cognitive systems are comprised of more than a single subprocess. The arrangement and linkages of these subprocesses are known as “mental architecture”. The simplest non-trivial systems or manner of carrying out multi-tasking on discrete items is found in two diametrically opposite models that have been classically used to describe the architecture of this processing. Serial systems allow only one subsystem at a time to operate. The antithesis of serial processing assumes that all subsystems operate simultaneously, or in parallel. Mathematical characterizations of these and other architectures have been developed. Models of serial vs. parallel systems, seemingly so distinct, are shockingly hard to tell apart with experimental methodology. Here we review the history of psychological work on the subject, both theoretical and experimental. We also describe three additional properties of systems that must be considered simultaneously (and have often been conflated with architecture): stopping rule, dependency, and capacity. We present formal mathematical descriptions that can allow us to examine in which cases the two will be indistinguishable, and summarize successful paradigms for differentiating the models in the context of various psychological tasks.

Normalized maximal likelihood (NML) is a probability distribution over the sample space associated with a parametric model class. At each sample point, the value of an NML distribution is obtained by taking the value of the maximum likelihood estimator (ML value) corresponding to that sample point (data), and then normalizing across the sample space to give rise to a probability measure. In this chapter the minimax problem that leads to the above (non-informative) NML as its solution is revisited by introducing an arbitrary weighting function over sample space. The solution then becomes “informative NML”, which involves both a prior distribution over the sample space (“data prior”) and a prior distribution over a model class (“model prior”), with the obvious Bayesian interpretations of the ML values. This approach avoids the so-called “infinity problem” of the non-informative NML, namely the unboundedness of the logarithm of the normalization factor (which serves as an index for model complexity), while at the same time providing a notion of consistency between modeler's prior beliefs about models and about data.

The following sections are included:

• Subject Index