Acquisition of preference in concurrent chains: comparing linear-operator and memory-representational models

Two experiments were conducted to test predictions of 2 models for acquisition of preference in concurrent chains. Pigeons were trained with pairs of fixed-interval and variable-interval terminal-link schedules in a successive-reversal design. Results showed that acquisition rate was faster when fixed-interval schedules preceded and when variable-interval schedules followed the reversal and was approximately constant when the same pair of schedules was used. These results were predicted by both linear-operator and memory-representational models. However, only the linear-operator model predicted effects of schedule duration. Overall, these results demonstrated that a simple linear-operator model can account for the major features of preference acquisition in concurrent chains and suggest that choice in transition and steady state may provide convergent validation of a single delay-discounting function.     

Preference structures and threshold models

Preferences are often represented in terms of a function, in the deterministic case as well as in the probabilistic case. In the present paper we develop a new numerical representation of preference structures for which the strict preference relation (P) is without circuit but not necessarily transitive. Moreover, we investigate the consequences of the representation for the usual preference structures. In particular, we propose new formulations for the numerical representation of the interval order structure.     

Culture and aesthetic preference: comparing the attention to context of East Asians and Americans

Prior research indicates that East Asians are more sensitive to contextual information than Westerners. This article explored aesthetics to examine whether cultural variations were observable in art and photography. Study 1 analyzed traditional artistic styles using archival data in representative museums. Study 2 investigated how contemporary East Asians and Westerners draw landscape pictures and take portrait photographs. Study 3 further investigated aesthetic preferences for portrait photographs. The results suggest that (a) traditional East Asian art has predominantly context-inclusive styles, whereas Western art has predominantly object-focused styles, and (b) contemporary members of East Asian and Western cultures maintain these culturally shaped aesthetic orientations. The findings can be explained by the relation among attention, cultural resources, and aesthetic preference.     

Commentary: comparing the beavers and circumplex models of family functioning

As the cool stream gushed over one hand, she [Annie] spelled into the other the word water, first slowly, then rapidly. I stood still, my whole attention fixed upon the motions of her fingers. Suddenly I felt a misty consciousness as of something forgotten — a thrill of returning thought; and somehow the mystery of language was revealed to me. I knew then that WATER meant the wonderful cool something that was flowing over my hand…. I left the well-house eager to learn. Everything had a name, and each name gave birth to a new thought. As we returned to the house every object which I touched seemed to quiver with life.     

Two models of unawareness: comparing the object-based and the subjective-state-space approaches

This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs to anti-realism, but can meet those challenges and can perhaps convince some realists, at least those who are also naturalists.     

Two models of unawareness: comparing the object-based and the subjective-state-space approaches

Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130:78–94, 2006). In particular, we show that subjective-state-space models (henceforth HMS structures) can be embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse.     

External analyses of preference models

Using Carroll's external analysis, several studies have found that unfolding models account for more, although seldom significantly more, variance in preferences than Tucker's vector model. In studies of sociometric ratings and political preferences, the unfolding model again rarely outpredicted the vector model by a significant amount. Yet on cross-validation, the unfolding model consistently accounted for more variance. Results suggest that sometimes significance tests are less sensitive than cross-validation procedures to the small but consistent superiority of the unfolding model. Future researchers may wish to use significance tests and cross-validation techniques in comparing models.     

Preference or ability: Exploring the relations between risk preference,personality, and cognitive abilities

Key issues in the behavioral sciences are if there exist stable risk preferences that generalize across domains and if these are best measured by revealed risk preference (RRP) in behavioral decision tasks or by surveys eliciting stated risk preference (SRP). We applied network analysis to data from a representative Swedish sample to investigate the relations between RRP, SRP, personality characteristics, and cognitive abilities, using in total over 70 measurements. The results showed that different measures of RRP were poorly intercorrelated and formed a community together with measures of numerical and cognitive abilities. Measures of SRP were weakly correlated with measures of RRP and identified in a distinctly separate community, along with personality characteristics and gender. The ensuing analyses provided support for a model suggesting that RRPs are contaminated by demands on numerical and cognitive abilities. RRPs may thus suffer from poor construct validity, whereas SRPs may better capture people's everyday risk preferences because they are related to more stable traits.     

Iterated revision and minimal change of conditional beliefs

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a virtual manner, using uniterated revision.     

On the relation between preference and resistance to change

Nevin (1979) noted that preference in concurrent chains and resistance to change in multiple schedules were correlated, in that both measures were affected similarly by variations in parameters of reinforcement such as rate, immediacy, and magnitude. To investigate the relationship between preference and resistance to change directly, we used a within-session procedure that arranged concurrent chains in one half of the session and a multiple schedule in the other half. The same variable-interval schedules served as terminal links in concurrent chains and as the components of the multiple schedule, and were signaled by the same stimuli. After performances had stabilized, responding in the multiple schedule was disrupted by delivering response-independent reinforcement during the blackout periods between components. Both preference in concurrent chains and relative resistance to change of multiple-schedule responding were well described as power functions of relative reinforcement rate, as predicted by current quantitative models (Grace, 1994; Nevin, 1992b). In addition, unsystematic variation in preference and resistance to change was positively correlated, which suggests that preference and resistance to change are independent measures of a single construct. That construct could be described as the learning that occurs regarding the prevailing conditions of reinforcement in a distinctive stimulus situation.     

Preference,resistance to change,and the cumulative decision model

According to behavioral momentum theory (Nevin & Grace, 2000a), preference in concurrent chains and resistance to change in multiple schedules are independent measures of a common construct representing reinforcement history. Here I review the original studies on preference and resistance to change in which reinforcement variables were manipulated parametrically, conducted by Nevin, Grace and colleagues between 1997 and 2002, as well as more recent research. The cumulative decision model proposed by Grace and colleagues for concurrent chains is shown to provide a good account of both preference and resistance to change, and is able to predict the increased sensitivity to reinforcer rate and magnitude observed with constant‐duration components. Residuals from fits of the cumulative decision model to preference and resistance to change data were positively correlated, supporting the prediction of behavioral momentum theory. Although some questions remain, the learning process assumed by the cumulative decision model, in which outcomes are compared against a criterion that represents the average outcome value in the current context, may provide a plausible model for the acquisition of differential resistance to change.     

Preference and resistance to change in concurrent variable-interval schedules

Pigeons were trained on a multiple schedule in which separate concurrent schedules were presented in the two components of the schedule. During one component, concurrent variable-interval 40-sec variable-interval 80-sec schedules operated. In the second component, concurrent variable-interval 40-sec variable-interval 20-sec schedules operated. After stable baseline performance was obtained in both components, extinction probe choice tests were presented to assess preference between the variable-interval 40-sec schedules from the two components. The variable-interval 40-sec schedule paired with the variable-interval 80-sec schedule was preferred over the variable-interval 40-sec schedule paired with the variable-interval 20-sec schedule. The subjects were also exposed to several resistance-to-change manipulations: (1) prefeeding prior to the experimental session, (2) a free-food schedule added to timeout periods separating components, and (3) extinction. The results indicated that preference and resistance to change do not necessarily covary.     

Preference and resistance to change with constant-duration schedule components

Previous research on preference between variable-interval terminal links in concurrent chains has most often used variable-duration terminal links ending with a single reinforcer. By contrast, most research on resistance to change in multiple schedules has used constant-duration components that include variable numbers of reinforcers in each presentation. Grace and Nevin (1997) examined both preference and resistance in variable-duration components; here, preference and resistance were examined in constant-duration components. Reinforcer rates were varied across eight conditions, and a generalized-matching-law analysis showed that initial-link preference strongly over-matched terminal-link reinforcer ratios. In multiple schedules, baseline response rates were unaffected by reinforcer rates, but resistance to intercomponent food, to extinction, and to intercomponent food plus extinction was greater in the richer component. The between-component difference in resistance to change exhibited additive effects for the three resistance tests, and was systematically related to reinforcer ratios. However, resistance was less sensitive to reinforcer ratios than was preference. Resistance to intercomponent food and to intercomponent food plus extinction was more sensitive to reinforcer ratios in the present study than in Grace and Nevin (1997). Thus, relative to variable-duration components, constant-duration components increased the sensitivity of both preference and relative resistance, supporting the proposition that these are independent and convergent measures of the effects of a history of reinforcement.     

Bayesian estimation and testing of structural equation models

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, for example, output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters underidentified models, as we illustrate on a simple errors-in-variables model.We thank David Spiegelhalter for suggesting applying the Gibbs sampler to structural equation models to the first author at a 1994 workshop in Wiesbaden. We thank Ulf Böckenholt, Chris Meek, Marijtje van Duijn, Clark Glymour, Ivo Molenaar, Steve Klepper, Thomas Richardson, Teddy Seidenfeld, and Tom Snijders for helpful discussions, mathematical advice, and critiques of earlier drafts of this paper.     

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.