Alternation bias and reduction in St. Petersburg gambles:an experimental investigation

Reduction of compound lotteries is implicit both in the statement of the St. Petersburg Paradox and in its resolution by Expected Utility (EU).We report three real-money choice experiments between truncated compound-form St. Petersburg gambles and their reduced-form equivalents. The first tests for differences in elicited Certainty Equivalents. The second develops the distinction between ‘weak-form’ and ‘strong-form’ rejection of Reduction, as well as a novel experimental task that verifiably implements Vernon Smith’s dominance precept. The third experiment checks for robustness against range and increment manipulation. In all three experiments the null hypothesis of Reduction is rejected, with systematic deprecation of the compound form in favor of the reduced form. This is consistent with the predictions of alternation bias. Together these experiments offer evidence that the Reduction assumption may have limited descriptive validity in modelling St. Petersburg gambles, whether by EU or non-EU theories

Fragments of first-order logic over infinite words

We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic FO[<] for omega-languages: Sigma_2, FO^2, the intersection of FO^2 and Sigma_2, and Delta_2 (and by duality Pi_2 and the intersection of FO^2 and Pi_2). These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke and Bojanczyk and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties.Comment: Conference version presented at 26th International Symposium on Theoretical Aspects of Computer Science, STACS 200

Trial-by-Trial Changes in a Priori Informational Value of External Cues and Subjective Expectancies in Human Auditory Attention

Background: Preparatory activity based on a priori probabilities generated in previous trials and subjective expectancies would produce an attentional bias. However, preparation can be correct (valid) or incorrect (invalid) depending on the actual target stimulus. The alternation effect refers to the subjective expectancy that a target will not be repeated in the same position, causing RTs to increase if the target location is repeated. The present experiment, using the Posner’s central cue paradigm, tries to demonstrate that not only the credibility of the cue, but also the expectancy about the next position of the target are changedin a trial by trial basis. Sequences of trials were analyzed. Results: The results indicated an increase in RT benefits when sequences of two and three valid trials occurred. The analysis of errors indicated an increase in anticipatory behavior which grows as the number of valid trials is increased. On the other hand, there was also an RT benefit when a trial was preceded by trials in which the position of the target changed with respect to the current trial (alternation effect). Sequences of two alternations or two repetitions were faster than sequences of trials in which a pattern of repetition or alternation is broken. Conclusions: Taken together, these results suggest that in Posner’s central cue paradigm, and with regard to the anticipatory activity, the credibility of the external cue and of the endogenously anticipated patterns of target location are constantly updated. The results suggest that Bayesian rules are operating in the generation of anticipatory activity as

Fragments of first-order logic over infinite words

We give topological and algebraic characterizations as well as language theoretic descriptions of the following subclasses of first-order logic for omega-languages: Sigma2, FO2, the intersection of FO2 and Sigma2, and Delta2 (and by duality Pi2 and the intersection of FO2 and Pi2). These descriptions extend the respective results for finite words. In particular, we relate the above fragments to language classes of certain (unambiguous) polynomials. An immediate consequence is the decidability of the membership problem of these classes, but this was shown before by Wilke and Bojanczyk and is therefore not our main focus. The paper is about the interplay of algebraic, topological, and language theoretic properties

An Investigation of the Perruchet Effect

The single versus dual processing systems debate is one that has taken centre stage in the human learning literature. The existence of a propositional reasoning system is not disputed in this thesis, but whether a secondary processing system is required is. This is specifically tackled by investigating the mechanisms which underlie the Perruchet effect, an effect which is used widely to support a dual processing systems stance. During the Perruchet paradigm a single conditioned stimulus (CS) is partially reinforced by an unconditioned stimulus (US). Conditioned responding is found to dissociate from conscious expectation of the US across runs of reinforced (CS-US) and non-reinforced (CS-noUS) trials. US expectancy ratings typically fluctuate in accordance with the gambler’s fallacy. Conversely associative mechanisms are postulated to govern the variable strength of the conditioned response (CR). The associative nature of the CR is the subject of this thesis as it is queried whether a non-associative mechanism might explain this result. Three different methodological strands of the Perruchet effect are studied in this thesis: autonomic conditioning (Chapters 2 and 3), eyeblink conditioning (Chapter 3) and reaction time (RT) studies (Chapters 4 and 5). Additionally transcranial magnetic stimulation (Chapter 5) and computational modelling (Chapter 6) are used as tools to investigate the CR. It is concluded in this thesis that the associative explanation of the CR in the Perruchet effect cannot be dismissed, although the strength of such an effect has perhaps been overstated in previous research. Evidence from autonomic conditioning provides the strongest evidence for an influence of CS-US association in the Perruchet effect as removal of the CS abolishes the CR in this thesis (Chapters 2 and 3). However, evidence from the eyeblink (Chapter 3) and RT (Chapters 4 and 5) variants of the effect suggest that there is undoubtedly a non-associative contribution to these effects. Although the exact mechanistic nature of this non-associative mechanism is unknown, priming is given as a possible explanation, and it is confirmed that such effects cannot be explained propositionally (Chapter 5). Overall a single processing system explanation of learning is not sufficient to explain the Perruchet effect.ESR

An Investigation of the Perruchet Effect

The single versus dual processing systems debate is one that has taken centre stage in the human learning literature. The existence of a propositional reasoning system is not disputed in this thesis, but whether a secondary processing system is required is. This is specifically tackled by investigating the mechanisms which underlie the Perruchet effect, an effect which is used widely to support a dual processing systems stance. During the Perruchet paradigm a single conditioned stimulus (CS) is partially reinforced by an unconditioned stimulus (US). Conditioned responding is found to dissociate from conscious expectation of the US across runs of reinforced (CS-US) and non-reinforced (CS-noUS) trials. US expectancy ratings typically fluctuate in accordance with the gambler’s fallacy. Conversely associative mechanisms are postulated to govern the variable strength of the conditioned response (CR). The associative nature of the CR is the subject of this thesis as it is queried whether a non-associative mechanism might explain this result. Three different methodological strands of the Perruchet effect are studied in this thesis: autonomic conditioning (Chapters 2 and 3), eyeblink conditioning (Chapter 3) and reaction time (RT) studies (Chapters 4 and 5). Additionally transcranial magnetic stimulation (Chapter 5) and computational modelling (Chapter 6) are used as tools to investigate the CR. It is concluded in this thesis that the associative explanation of the CR in the Perruchet effect cannot be dismissed, although the strength of such an effect has perhaps been overstated in previous research. Evidence from autonomic conditioning provides the strongest evidence for an influence of CS-US association in the Perruchet effect as removal of the CS abolishes the CR in this thesis (Chapters 2 and 3). However, evidence from the eyeblink (Chapter 3) and RT (Chapters 4 and 5) variants of the effect suggest that there is undoubtedly a non-associative contribution to these effects. Although the exact mechanistic nature of this non-associative mechanism is unknown, priming is given as a possible explanation, and it is confirmed that such effects cannot be explained propositionally (Chapter 5). Overall a single processing system explanation of learning is not sufficient to explain the Perruchet effect.ESR