Torgerson’s conjecture and Luce’s magnitude production representation imply an empirically false property

Luce, R. Duncan

doi:10.1016/j.jmp.2012.02.002

Cited by 9 publications

(10 citation statements)

References 13 publications

(15 reference statements)

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“…Rather, they shift between the two scenarios in a yet unspecified manner (Steingrimsson & Luce, 2012b). A happy consequence of this seemingly novel characterization of the conjecture is that the data appear to simultaneously give a plausible account for the theoretically derived evidence against the Torgerson's (1961) conjecture based on the W function (Luce, 2012b) as well as of the inconsistency in the empirical record.…”

Section: Torgerson's (1961) Conjecturementioning

confidence: 80%

“…Luce (2012b) showed that when applied to eqisections and fractionation that the conjecture implies that the function W in the production representation (2) is the identity function. That W is the identity function is firmly rejected by existing data (Ellermeier & Faulhammer, 2000;Steingrimsson & Luce, 2005b;Steingrimsson, 2011Steingrimsson, , 2012cZimmer, 2005).…”

Section: Torgerson's (1961) Conjecturementioning

confidence: 99%

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Empirical and Theoretical Studies of Psychophysical Phenomena

Luce¹,

Steingrimsson²

2013

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Section: Torgerson's (1961) Conjecturementioning

confidence: 80%

Section: Torgerson's (1961) Conjecturementioning

confidence: 99%

Empirical and Theoretical Studies of Psychophysical Phenomena

Luce¹,

Steingrimsson²

2013

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“…1 suggest, instead, that W is a nonlinear function (Steingrimsson & Luce, 2007). Using this result, Luce (2012) concluded that Torgerson's conjecture is probably false. This conclusion implies that the above tests of Torgerson's conjecture were probably flawed.…”

Section: Objectionmentioning

confidence: 94%

“…Recently, Luce (2012) has objected that Torgerson's conjecture is probably false. His argument runs as follows.…”

Section: Objectionmentioning

confidence: 99%

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On the ability to directly evaluate sensory ratios

Masin

2012

Atten Percept Psychophys

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The study explored whether participants could directly evaluate sensory ratios. The results indicate that they did not exhibit this ability for the extensive continuum of length and the intensive continua of brightness and brightness difference. Functional measurement analysis, combined with a chronometric analysis of responses, indicated that participants used mental counting for length and used difference evaluation for brightness and brightness difference. The finding that participants evaluated brightness differences under instructions to evaluate brightness ratios suggests that difference judgments may be a general human capability. It resolves questions raised by prior tests of Torgerson's conjecture and by prior consistency tests of ratio evaluation.

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Model-Based Cognitive Neuroscience: A Conceptual Introduction

Forstmann

Wagenmakers

2015

An Introduction to Model-Based Cognitive Neuroscience

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This tutorial chapter shows how the separate fields of mathematical psychology and cognitive neuroscience can interact to their mutual benefit. Historically, the field of mathematical psychology is mostly concerned with formal theories of behavior, whereas cognitive neuroscience is mostly concerned with empirical measurements of brain activity. Despite these superficial differences in method, the ultimate goal of both disciplines is the same: to understand the workings of human cognition. In recognition of this common purpose, mathematical psychologists have recently started to apply their models in cognitive neuroscience, and cognitive neuroscientists have borrowed and extended key ideas that originated from mathematical psychology. This chapter consists of three main sections: the first describes the field of mathematical psychology, the second describes the field of cognitive neuroscience, and the third describes their recent combination: model-based cognitive neuroscience. IntroductionThe griffin is a creature with the body of a lion and the head and wings of an eagle. This mythical hybrid is thought to symbolize the rule over two empires, one on the earth (the lion part) and the other in the skies (the eagle part). The preceding six tutorial chapters may have given the impression that the field of model-based cognitive neuroscience is similar to a griffin in that it represents the union of two fundamentally incompatible disciplines. After all, the methods and concepts from B. U. Forstmann ( )

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Torgerson’s conjecture and Luce’s magnitude production representation imply an empirically false property

Cited by 9 publications

References 13 publications

Empirical and Theoretical Studies of Psychophysical Phenomena

Empirical and Theoretical Studies of Psychophysical Phenomena

On the ability to directly evaluate sensory ratios

Model-Based Cognitive Neuroscience: A Conceptual Introduction

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