We report an experiment exploring sequential context effects on strategy choices in one-shot Pris... more We report an experiment exploring sequential context effects on strategy choices in one-shot Prisoner's Dilemma (PD) game. Rapoport and Chammah (1965) have shown that some PDs are cooperative and lead to high cooperation rate, whereas others are uncooperative. Participants played very cooperative and very uncooperative games, against anonymous partners. The order in which these games were played affected their cooperation rate by producing perceptual contrast, which appeared only between the trials, but not between two separate sequences of games. These findings suggest that people may not have stable perceptions of absolute cooperativeness. Instead, they judge the cooperativeness of each fresh game only in relation to the previous game. The observed effects suggest that the principles underlying judgments about highly abstract magnitudes such as cooperativeness may be similar to principles governing the perception of sensory magnitudes.
Children learn their native language by exposure to their linguistic and communicative environmen... more Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes are corrected. Such learning from positive evidence has been viewed as raising logical problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over-general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this logical problem can be dissolved. Here, we review recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favours the simplest encoding of the linguistic input. Results include the ability to learn a linguistic prediction, grammaticality judgements, language production, and form-meaning mappings. The simplicity approach can also be scaled-down to analyse the ability to learn a specific linguistic constructions, and is amenable to emp...
There is some evidence indicating a relationship between variations in affect and risk aversion: ... more There is some evidence indicating a relationship between variations in affect and risk aversion: under certain conditions the behavior observed suggests less risk aversion the more positive the affective state. The research presented in this paper examined how variations in everyday affective states influenced risk taking behavior in the laboratory using simple gambling tasks and then sought to corroborate findings in the laboratory using data on real world financial decision making. We observed a significant and positive relationship between affect and risky behavior in the laboratory that we replicated using structural equation modeling on real world financial data. It is argued that cognitive theories of affect and decision making might have real economic consequences.
This paper investigates the role of transformations and similarity in a perceptual task, the same... more This paper investigates the role of transformations and similarity in a perceptual task, the same-different paradigm. Representational Distortion (RD) theory measures similarity by the complexity required to 'distort' compared object representations. In an experiment, participants compared pairs of geometric shapes that varied across two dimensions (shape and color). We then modelled data using a variety of model of similarity. RD yielded accurate fits and compared favourably with various models of Structural Alignment. Results highlighted the relationship between transformations and low-level stimulus properties.
The transformational approach to similarity views similarity as a function of the complexity of t... more The transformational approach to similarity views similarity as a function of the complexity of the transformations required to 'distort' the representation of one object into another. These transformations may be more complex in one direction than the other, thus giving rise to asymmetric similarity relationships. Using the same-different paradigm we show that response times significantly differ depending on the direction of comparison, in line with the predictions made by the transformational approach. We discuss the implications of this result in reference to featural and spatial models.
A series of experiments is used to investigate the extent to which valuation of a risky prospect ... more A series of experiments is used to investigate the extent to which valuation of a risky prospect is affected by the values from which a participant selects a response. Three variables were considered: a smaller risk-free amount, a larger risky amount, and the probability of winning the larger amount. There were three conditions: in each, two of the three variables were held constant, and participants chose the value for the third variable that made the risky and risk-free options worth the same to them. This was done first by a free-choice valuation, and then, with different participants, by choosing one of four options that were either all below or all above the population free-choice median. The options presented had a strong effect on valuation of the missing variable. This effect remained even when the free-choice and multiple-choice conditions were presented within subjects. This demonstrates that people showing rational and consistent risk evaluation strategies could have thei...
Classical game theory struggles to explain how rational players should decide between a number of... more Classical game theory struggles to explain how rational players should decide between a number of social conventions, even if some yield higher individual payoffs than others. Thus, on a population level a group or society may be stuck in using one convention when there exist alternative and potentially more beneficial ones. Using an agent-based model the current study examines how convention shifts from less to more beneficial conventions can come about. To investigate this, we use the concept of team reasoning, a mode of reasoning in which actors maximise the utility of a group rather than their own. Unlike other social decision-making mechanisms, such as forms of imitation, team reasoning enables the spread of a more profitable convention through a population even if no global knowledge about the population is available to agents.
Sensitivity to distributional characteristics of sequential linguistic and nonlinguistic stimuli,... more Sensitivity to distributional characteristics of sequential linguistic and nonlinguistic stimuli, have been shown to play a role in learning the underlying structure of these stimuli. A growing body of experimental and computational research with (artificial) grammars suggests that learners are sensitive to various distributional characteristics of their environment (Kuhl, 2004; Onnis, Monaghan, Richmond & Chater, 2005; Rohde & Plaut, 1999). We propose that, at a higher level, statistical characteristics of the full sample of stimuli on which learning is based, also affects learning. We provide a statistical model that accounts for such an effect, and experimental data with the Artificial Grammar Learning (AGL) methodology, showing that learners also are sensitive to distributional characteristics of a full sample of exemplars.
It has been arguedby Shepardthat there is a robust psychological law that relates the distance be... more It has been arguedby Shepardthat there is a robust psychological law that relates the distance between a pair of items in psychological space andthe probability that they will be perceivedas similar. Specifically, this probability is a negative exponential function of the distance between the pair of items. In experimental contexts, distance is typically defined in terms of a multidimensional space—but this assumption seems unlikely to hold for complex stimuli. We show that, nonetheless, the Universal Law of Generalization can be derived in the more complex setting of arbitrary stimuli, using a much more universal measure of distance. This universal distance is defined as the length of the shortest program that transforms the representations of the two items of interest into one another: The algorithmic information distance. It is universal in the sense that it minorizes every computable distance: It is the smallest computable distance. We show that the Universal Law of Generalizati...
A formal model of learning as induction, the simplicity principle (e.g. Chater & Vitányi, 2001) s... more A formal model of learning as induction, the simplicity principle (e.g. Chater & Vitányi, 2001) states that the cognitive system seeks the hypothesis that provides the briefest representation of the available data− here the linguistic input to the child. Data gathered from the CHILDES database were used as an approximation of positive input the child receives from adults. We considered linguistic structures that would yield overgeneralization, according to Baker's paradox (Baker, 1979). A simplicity based simulation was run incorporating two different hypotheses about the grammar: (1) The child assumes that there are no exceptions to the grammar. This hypothesis leads to overgeneralization. (2) The child assumes that some constructions are not allowed. For small corpora of data, the first hypothesis produced a simpler representation. However, for larger corpora, the second hypothesis was preferred as it lead to a shorter input description and eliminated overgeneralization.
In this paper we provide a computational exploration of changes in levels of representation in ch... more In this paper we provide a computational exploration of changes in levels of representation in children's language development. Children demonstrate a progression from awareness of larger units in their language, such as words or syllables, and only later do they develop the ability to manipulate phoneme level representations. We employed a minimum description length approach to encode a corpus of child-directed speech. The analysis indicated that, for early stages of language learning, a word level representation was most efficient, whereas after extended exposure, a phoneme level representation was more efficient. The analysis also accurately predicted which phonemes children would be able to distinguish from syllables at different stages of development.
Probabilistic methods are providing new explanatory approaches to fundamental cognitive science q... more Probabilistic methods are providing new explanatory approaches to fundamental cognitive science questions of how humans structure, process and acquire language. This review examines probabilistic models defined over traditional symbolic structures. Language comprehension and production involve probabilistic inference in such models; and acquisition involves choosing the best model, given innate constraints and linguistic and other input. Probabilistic models can account for the learning and processing of language, while maintaining the sophistication of symbolic models. A recent burgeoning of theoretical developments and online corpus creation has enabled large models to be tested, revealing probabilistic constraints in processing, undermining acquisition arguments based on a perceived poverty
In this article we consider whether perceptual magnitudes are represents on unified underlying sc... more In this article we consider whether perceptual magnitudes are represents on unified underlying scales. We exploit the ubiquitous sequential effects seen in judgments concerning the attributes of simple perceptual stimuli. Participants made judgments about the intensity of sinusoidal tones and white noise hisses. On each trial in Experiment 1, participants heard a tone and a hiss and judged which was the louder. The loudness of a stimulus was assimilated much more towards a stimulus of the same type on the previous trial, compared to a stimulus of the other type. In Experiment 2, the effect of the stimulus on the previous trial in an absolute identification of loudness task was larger when previous and current stimuli were of the same type. The attenuation of sequential effects by a switch of stimulus types suggests that the loudness of tones is not represented in the same way as the loudness of hisses. We argue that these sequential effects are indicative of the relativity of percep...
Why does looking at a painting take so long? [1] Looking at Breughel the Elder’s Landscape with t... more Why does looking at a painting take so long? [1] Looking at Breughel the Elder’s Landscape with the Fall of Icarus (Royal Museums of Fine Arts of Belgium, Brussels), for example, we feel that we are somehow taking in the entire painting within a single visual “gulp.” We see the steep hillside, the ploughman blithely tilling his field, the great galleons and placid sea below; the rich red of the ploughman’s shirt, the pale green of the sea, the whitish-yellow of the evening sky. All of this, and much more, seems somehow to fuse into a complex, fascinating and harmonious whole, all loaded, in its entirety, into our conscious experience. So why do we continue to look, to examine, to scrutinise, and to ponder? Have we not mentally “hoovered up” Breughel’s painting within little more than a glance?
Category learning without labels—A simplicity approach Emmanuel Minos Pothos (e.pothos@ed.ac.uk) ... more Category learning without labels—A simplicity approach Emmanuel Minos Pothos (e.pothos@ed.ac.uk) Department of Psychology, University of Edinburgh; 7 George Square Edinburgh, EH8 9JZ UK Nick Chater ( nick.chater@warwick.ac.uk ) Department of Psychology, University of Warwick; Coventry, CV4 7AL UK Abstract In an extensive research tradition in categorization, re- searchers have looked at how participants will classify new objects into existing categories; or the factors af- fecting learning to associate category labels with a set of objects. In this work, we examine a complementary as- pect of categorization, that of the spontaneous classifi- cation of items into categories. In such cases, there is no “correct” category structure that the participants must in- fer. We argue that the this second type of categorization, unsupervised categorization, can be seen as some form of perceptual organization. Thus, we take advantage of theoretical work in perceptual organization to use sim- pli...
Existing models of interactive game-theoretic decision making typically assume that only the attr... more Existing models of interactive game-theoretic decision making typically assume that only the attributes of the game need be considered when reaching a decision, i.e., these theories assume that the utility of a strategy is determined by the utility of the outcomes of the game, and transforms of the probabilities of each outcome. The strategic decisions are assumed to be based on these utilities. The two experiments presented here provide strong evidence against these assumptions. We investigated choice and predictions about the choices of other players in Prisoners Dilemma game. The cooperativeness of the games in each condition was varied and the results demonstrate that the average cooperation rate and the predicted cooperation of the other player in each game strongly depended on the cooperativeness of the preceding games, which suggests that games are not considered independently. It is proposed that people have poor notions of absolute cooperativeness, risk, and utility, and in...
The transformational approach to similarity views similarity as a function of the complexity of t... more The transformational approach to similarity views similarity as a function of the complexity of the transformations required to ‘distort’ the representation of one object into another. These transformations may be more complex in one direction than the other, thus giving rise to asymmetric similarity relationships. Using the same-different paradigm we show that response times significantly differ depending on the direction of comparison, in line with the predictions made by the transformational approach. We discuss the implications of this result in reference to featural and spatial models.
We report an experiment exploring sequential context effects on strategy choices in one-shot Pris... more We report an experiment exploring sequential context effects on strategy choices in one-shot Prisoner's Dilemma (PD) game. Rapoport and Chammah (1965) have shown that some PDs are cooperative and lead to high cooperation rate, whereas others are uncooperative. Participants played very cooperative and very uncooperative games, against anonymous partners. The order in which these games were played affected their cooperation rate by producing perceptual contrast, which appeared only between the trials, but not between two separate sequences of games. These findings suggest that people may not have stable perceptions of absolute cooperativeness. Instead, they judge the cooperativeness of each fresh game only in relation to the previous game. The observed effects suggest that the principles underlying judgments about highly abstract magnitudes such as cooperativeness may be similar to principles governing the perception of sensory magnitudes.
Children learn their native language by exposure to their linguistic and communicative environmen... more Children learn their native language by exposure to their linguistic and communicative environment, but apparently without requiring that their mistakes are corrected. Such learning from positive evidence has been viewed as raising logical problems for language acquisition. In particular, without correction, how is the child to recover from conjecturing an over-general grammar, which will be consistent with any sentence that the child hears? There have been many proposals concerning how this logical problem can be dissolved. Here, we review recent formal results showing that the learner has sufficient data to learn successfully from positive evidence, if it favours the simplest encoding of the linguistic input. Results include the ability to learn a linguistic prediction, grammaticality judgements, language production, and form-meaning mappings. The simplicity approach can also be scaled-down to analyse the ability to learn a specific linguistic constructions, and is amenable to emp...
There is some evidence indicating a relationship between variations in affect and risk aversion: ... more There is some evidence indicating a relationship between variations in affect and risk aversion: under certain conditions the behavior observed suggests less risk aversion the more positive the affective state. The research presented in this paper examined how variations in everyday affective states influenced risk taking behavior in the laboratory using simple gambling tasks and then sought to corroborate findings in the laboratory using data on real world financial decision making. We observed a significant and positive relationship between affect and risky behavior in the laboratory that we replicated using structural equation modeling on real world financial data. It is argued that cognitive theories of affect and decision making might have real economic consequences.
This paper investigates the role of transformations and similarity in a perceptual task, the same... more This paper investigates the role of transformations and similarity in a perceptual task, the same-different paradigm. Representational Distortion (RD) theory measures similarity by the complexity required to 'distort' compared object representations. In an experiment, participants compared pairs of geometric shapes that varied across two dimensions (shape and color). We then modelled data using a variety of model of similarity. RD yielded accurate fits and compared favourably with various models of Structural Alignment. Results highlighted the relationship between transformations and low-level stimulus properties.
The transformational approach to similarity views similarity as a function of the complexity of t... more The transformational approach to similarity views similarity as a function of the complexity of the transformations required to 'distort' the representation of one object into another. These transformations may be more complex in one direction than the other, thus giving rise to asymmetric similarity relationships. Using the same-different paradigm we show that response times significantly differ depending on the direction of comparison, in line with the predictions made by the transformational approach. We discuss the implications of this result in reference to featural and spatial models.
A series of experiments is used to investigate the extent to which valuation of a risky prospect ... more A series of experiments is used to investigate the extent to which valuation of a risky prospect is affected by the values from which a participant selects a response. Three variables were considered: a smaller risk-free amount, a larger risky amount, and the probability of winning the larger amount. There were three conditions: in each, two of the three variables were held constant, and participants chose the value for the third variable that made the risky and risk-free options worth the same to them. This was done first by a free-choice valuation, and then, with different participants, by choosing one of four options that were either all below or all above the population free-choice median. The options presented had a strong effect on valuation of the missing variable. This effect remained even when the free-choice and multiple-choice conditions were presented within subjects. This demonstrates that people showing rational and consistent risk evaluation strategies could have thei...
Classical game theory struggles to explain how rational players should decide between a number of... more Classical game theory struggles to explain how rational players should decide between a number of social conventions, even if some yield higher individual payoffs than others. Thus, on a population level a group or society may be stuck in using one convention when there exist alternative and potentially more beneficial ones. Using an agent-based model the current study examines how convention shifts from less to more beneficial conventions can come about. To investigate this, we use the concept of team reasoning, a mode of reasoning in which actors maximise the utility of a group rather than their own. Unlike other social decision-making mechanisms, such as forms of imitation, team reasoning enables the spread of a more profitable convention through a population even if no global knowledge about the population is available to agents.
Sensitivity to distributional characteristics of sequential linguistic and nonlinguistic stimuli,... more Sensitivity to distributional characteristics of sequential linguistic and nonlinguistic stimuli, have been shown to play a role in learning the underlying structure of these stimuli. A growing body of experimental and computational research with (artificial) grammars suggests that learners are sensitive to various distributional characteristics of their environment (Kuhl, 2004; Onnis, Monaghan, Richmond & Chater, 2005; Rohde & Plaut, 1999). We propose that, at a higher level, statistical characteristics of the full sample of stimuli on which learning is based, also affects learning. We provide a statistical model that accounts for such an effect, and experimental data with the Artificial Grammar Learning (AGL) methodology, showing that learners also are sensitive to distributional characteristics of a full sample of exemplars.
It has been arguedby Shepardthat there is a robust psychological law that relates the distance be... more It has been arguedby Shepardthat there is a robust psychological law that relates the distance between a pair of items in psychological space andthe probability that they will be perceivedas similar. Specifically, this probability is a negative exponential function of the distance between the pair of items. In experimental contexts, distance is typically defined in terms of a multidimensional space—but this assumption seems unlikely to hold for complex stimuli. We show that, nonetheless, the Universal Law of Generalization can be derived in the more complex setting of arbitrary stimuli, using a much more universal measure of distance. This universal distance is defined as the length of the shortest program that transforms the representations of the two items of interest into one another: The algorithmic information distance. It is universal in the sense that it minorizes every computable distance: It is the smallest computable distance. We show that the Universal Law of Generalizati...
A formal model of learning as induction, the simplicity principle (e.g. Chater & Vitányi, 2001) s... more A formal model of learning as induction, the simplicity principle (e.g. Chater & Vitányi, 2001) states that the cognitive system seeks the hypothesis that provides the briefest representation of the available data− here the linguistic input to the child. Data gathered from the CHILDES database were used as an approximation of positive input the child receives from adults. We considered linguistic structures that would yield overgeneralization, according to Baker's paradox (Baker, 1979). A simplicity based simulation was run incorporating two different hypotheses about the grammar: (1) The child assumes that there are no exceptions to the grammar. This hypothesis leads to overgeneralization. (2) The child assumes that some constructions are not allowed. For small corpora of data, the first hypothesis produced a simpler representation. However, for larger corpora, the second hypothesis was preferred as it lead to a shorter input description and eliminated overgeneralization.
In this paper we provide a computational exploration of changes in levels of representation in ch... more In this paper we provide a computational exploration of changes in levels of representation in children's language development. Children demonstrate a progression from awareness of larger units in their language, such as words or syllables, and only later do they develop the ability to manipulate phoneme level representations. We employed a minimum description length approach to encode a corpus of child-directed speech. The analysis indicated that, for early stages of language learning, a word level representation was most efficient, whereas after extended exposure, a phoneme level representation was more efficient. The analysis also accurately predicted which phonemes children would be able to distinguish from syllables at different stages of development.
Probabilistic methods are providing new explanatory approaches to fundamental cognitive science q... more Probabilistic methods are providing new explanatory approaches to fundamental cognitive science questions of how humans structure, process and acquire language. This review examines probabilistic models defined over traditional symbolic structures. Language comprehension and production involve probabilistic inference in such models; and acquisition involves choosing the best model, given innate constraints and linguistic and other input. Probabilistic models can account for the learning and processing of language, while maintaining the sophistication of symbolic models. A recent burgeoning of theoretical developments and online corpus creation has enabled large models to be tested, revealing probabilistic constraints in processing, undermining acquisition arguments based on a perceived poverty
In this article we consider whether perceptual magnitudes are represents on unified underlying sc... more In this article we consider whether perceptual magnitudes are represents on unified underlying scales. We exploit the ubiquitous sequential effects seen in judgments concerning the attributes of simple perceptual stimuli. Participants made judgments about the intensity of sinusoidal tones and white noise hisses. On each trial in Experiment 1, participants heard a tone and a hiss and judged which was the louder. The loudness of a stimulus was assimilated much more towards a stimulus of the same type on the previous trial, compared to a stimulus of the other type. In Experiment 2, the effect of the stimulus on the previous trial in an absolute identification of loudness task was larger when previous and current stimuli were of the same type. The attenuation of sequential effects by a switch of stimulus types suggests that the loudness of tones is not represented in the same way as the loudness of hisses. We argue that these sequential effects are indicative of the relativity of percep...
Why does looking at a painting take so long? [1] Looking at Breughel the Elder’s Landscape with t... more Why does looking at a painting take so long? [1] Looking at Breughel the Elder’s Landscape with the Fall of Icarus (Royal Museums of Fine Arts of Belgium, Brussels), for example, we feel that we are somehow taking in the entire painting within a single visual “gulp.” We see the steep hillside, the ploughman blithely tilling his field, the great galleons and placid sea below; the rich red of the ploughman’s shirt, the pale green of the sea, the whitish-yellow of the evening sky. All of this, and much more, seems somehow to fuse into a complex, fascinating and harmonious whole, all loaded, in its entirety, into our conscious experience. So why do we continue to look, to examine, to scrutinise, and to ponder? Have we not mentally “hoovered up” Breughel’s painting within little more than a glance?
Category learning without labels—A simplicity approach Emmanuel Minos Pothos (e.pothos@ed.ac.uk) ... more Category learning without labels—A simplicity approach Emmanuel Minos Pothos (e.pothos@ed.ac.uk) Department of Psychology, University of Edinburgh; 7 George Square Edinburgh, EH8 9JZ UK Nick Chater ( nick.chater@warwick.ac.uk ) Department of Psychology, University of Warwick; Coventry, CV4 7AL UK Abstract In an extensive research tradition in categorization, re- searchers have looked at how participants will classify new objects into existing categories; or the factors af- fecting learning to associate category labels with a set of objects. In this work, we examine a complementary as- pect of categorization, that of the spontaneous classifi- cation of items into categories. In such cases, there is no “correct” category structure that the participants must in- fer. We argue that the this second type of categorization, unsupervised categorization, can be seen as some form of perceptual organization. Thus, we take advantage of theoretical work in perceptual organization to use sim- pli...
Existing models of interactive game-theoretic decision making typically assume that only the attr... more Existing models of interactive game-theoretic decision making typically assume that only the attributes of the game need be considered when reaching a decision, i.e., these theories assume that the utility of a strategy is determined by the utility of the outcomes of the game, and transforms of the probabilities of each outcome. The strategic decisions are assumed to be based on these utilities. The two experiments presented here provide strong evidence against these assumptions. We investigated choice and predictions about the choices of other players in Prisoners Dilemma game. The cooperativeness of the games in each condition was varied and the results demonstrate that the average cooperation rate and the predicted cooperation of the other player in each game strongly depended on the cooperativeness of the preceding games, which suggests that games are not considered independently. It is proposed that people have poor notions of absolute cooperativeness, risk, and utility, and in...
The transformational approach to similarity views similarity as a function of the complexity of t... more The transformational approach to similarity views similarity as a function of the complexity of the transformations required to ‘distort’ the representation of one object into another. These transformations may be more complex in one direction than the other, thus giving rise to asymmetric similarity relationships. Using the same-different paradigm we show that response times significantly differ depending on the direction of comparison, in line with the predictions made by the transformational approach. We discuss the implications of this result in reference to featural and spatial models.
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