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Psychophysics
This third edition of a classic text which was first published in 1976 is the only comprehensive, up-to-date presentation of psychophysics currently available. It has been used by undergraduate and graduate students, and scholars throughout the world and is consistently thought of as the best single source for learning the basic principles of psychophysics. The coverage of the field is comprehensive, including topics ranging from the classical methods of threshold measurement, to the modern methods of detection theory, to psychophysical scaling of sensation magnitude. The approach is one in which methods, theories, and applications are described for each experimental procedure.
New features found in this third edition
* methodological and theoretical contributions made in the field during this time period,
* descriptions of adaptive procedures for measuring thresholds, context effects in scaling, theory of quantal fluctuations, multidimensional scaling, nonmetric scaling of sensory differences, and the relationship between the size of the DL and the slope of the sensation magnitude function,
* new methods for measuring the observer's sensitivity of criterion and an expanded discussion of category scaling including the range frequency model and verbally labeled categories, and
* methods used to control the observer's nonlinear use of numbers in magnitude estimation such as line-length scaling, magnitude matching, master scaling, and category-ratio scaling.
New features found in this third edition
* methodological and theoretical contributions made in the field during this time period,
* descriptions of adaptive procedures for measuring thresholds, context effects in scaling, theory of quantal fluctuations, multidimensional scaling, nonmetric scaling of sensory differences, and the relationship between the size of the DL and the slope of the sensation magnitude function,
* new methods for measuring the observer's sensitivity of criterion and an expanded discussion of category scaling including the range frequency model and verbally labeled categories, and
* methods used to control the observer's nonlinear use of numbers in magnitude estimation such as line-length scaling, magnitude matching, master scaling, and category-ratio scaling.
446 pages, Hardcover
First published May 1, 1997
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May 8, 2021
that I may see and tell / Of things invisible to mortal sight.
--Paradise Lost, John Milton.
So, I'm going to do something a bit unusual here. And possibly confusing. I read Peter P. Wakker's Prospect Theory: For Risk and Ambiguity, then I read Psychophysics: The Fundamentals. It may seem odd, but these things are connected. Prospect Theory concerns how people make decisions, especially economic decisions, and especially decisions made when there is risk. It is therefore mostly studied by economists. "Psychophysics is the field of psychology that examines sensations generated by physical stimuli." (That quote is from Wakker's book.)
What is the connection? Here's another quote from Wakker's book that illustrates what both fields are about fundamentally:
Psychophysics, as Wakker said, is about the connection between physical stimuli and sensations. The subtlety here is that "sensations" are psychological, not physical. They are the same sort of subjective, intangible things as beliefs.
Psychophysicists and economists recognize the connection between their fields. That is why Wakker's book contains a definition of psychophysics. In fact, since the beginning psychophysicists have worked to extend their ideas beyond straightforward reactions to physical stimuli. Gustav Fechner, the founder of psychophysics, attempted to quantify aesthetics. Gescheider also mentions Daniel Bernoulli's 1738 paper as "one of the first attempts to formulate a psychophysical law". But Bernoulli's paper is about how people decide to make bets -- that is, it is about economic decisions under risk, which is precisely what prospect theory is about. And Bernoulli's main contribution was the idea of economic utility, still a fundamental concept in economics and prospect theory today.
So, if psychophysics and prospect theory are about mind-reading, how do they do it? Well, the first thing to realize is that, when your experimental subjects are humans, who can speak and answer questions, and whom you trust to be as honest as they can be, mind-reading is not such a trick. You ask them, "What do you think?", they answer, and presto! You're a mind-reader. The trick is that in both cases we're trying to answer questions that the people being questioned don't know the answers to. (Or at least, they don't KNOW they know the answer.) For instance, we try to answer questions like "How much louder is a 40 Pa 1000 Hz tone than a 5 Pa 1000 Hz tone?" or how much more valuable is $8000 than $1000? You might naively think that the answer is "eight times" in both cases, but you would be wrong. Deep inside your brain, without necessarily knowing it, you evaluate these things differently. For most people a 40 Pa tone sounds twice as loud as a 5 Pa tone -- so psychophysics tells us. And $8000 is more valuable to most people than $1000, but not by eight times. So economists tell us.
How much should you trust them? There is no physical ruler one can take to the magnitude of a sensation. This question is addressed by both authors. I was not impressed by Gescheider's answer (in section "The Measurement of Sensations" in chapter 14). He essentially passes on the ontological question of whether sensations are real things that can be measured and asserts that speaking of sensations as if they were real is just a linguistic convenience, sound and fury signifying nothing, and that we shouldn't bother our pretty little heads about whether they are real or not. Wakker is much better on this. He uses the axiomatic approach of a mathematician. He begins each of the several theories that his book presents by stating plausible axioms that are difficult to doubt. He then proves that, if these axioms hold, there must exist such things as utility functions and subjective probabilities. I found it quite convincing.
This is a good example of the differences between the two books. Gescheider is, for my taste, a little too elementary. Large parts of the book are not about psychophysics per se, but rather about basic statistical techniques. Now, to be fair, both Gescheider and Wakker are deeply concerned with the problem of measurement, and if you measure things and want to trust your measurements, you have to understand probability and statistics. But if you have already had a good stats education, Gescheider can be tedious. Wakker, on the other hand, is much more about the theory of measurement than the practice (although he does have things to say about the latter). Prospect Theory reads like an advanced mathematics textbook . (I just finished a PhD in Applied Mathematics, so I speak with some knowledge here.) It is not an easy read, even for a mathematician.
There is another reason I feel more comfortable about prospect theory than psychophysics. Psychophysics, it turns out, relies heavily on the basic mind-reading technique I outlined above: you ask people what they think, and they tell you. Can you trust them? No: a recurring theme of Psychophysics: The Fundamentals is that psychophysical measurements are biased in various ways that are difficult to fully correct. And animal studies are virtually impossible. Prospect theory, in contrast, is about decisions. To make a measurement in prospect theory, you present the subject with two (or more choices) and see which one they select. You can trust them to the extent that you can trust the subject to do what is in his/her/its perceived best interests. Such experiments can be done on animals as well as humans, and have been.
But the good news is that there are large commonalities between the two disciplines. For instance, psychophysical laws are generally power functions, and economic utility functions are also well fit by power laws.
--Paradise Lost, John Milton.
So, I'm going to do something a bit unusual here. And possibly confusing. I read Peter P. Wakker's Prospect Theory: For Risk and Ambiguity, then I read Psychophysics: The Fundamentals. It may seem odd, but these things are connected. Prospect Theory concerns how people make decisions, especially economic decisions, and especially decisions made when there is risk. It is therefore mostly studied by economists. "Psychophysics is the field of psychology that examines sensations generated by physical stimuli." (That quote is from Wakker's book.)
What is the connection? Here's another quote from Wakker's book that illustrates what both fields are about fundamentally:
De Finetti's (1972) first chapter, written in a thought-provoking manner, opened up to me the technique of behavioral foundations, and the possibility of defining something as seemingly intangible as one's subjective degree of belief, in a tangible manner. De Finetti showed how we can read the minds (beliefs, i.e. subjective probabilities) of people. I felt electrified by his ideas, and decided that I wanted to work on them. I hope that the readers will also sense some of the magic of these ideas.
Psychophysics, as Wakker said, is about the connection between physical stimuli and sensations. The subtlety here is that "sensations" are psychological, not physical. They are the same sort of subjective, intangible things as beliefs.
Psychophysicists and economists recognize the connection between their fields. That is why Wakker's book contains a definition of psychophysics. In fact, since the beginning psychophysicists have worked to extend their ideas beyond straightforward reactions to physical stimuli. Gustav Fechner, the founder of psychophysics, attempted to quantify aesthetics. Gescheider also mentions Daniel Bernoulli's 1738 paper as "one of the first attempts to formulate a psychophysical law". But Bernoulli's paper is about how people decide to make bets -- that is, it is about economic decisions under risk, which is precisely what prospect theory is about. And Bernoulli's main contribution was the idea of economic utility, still a fundamental concept in economics and prospect theory today.
So, if psychophysics and prospect theory are about mind-reading, how do they do it? Well, the first thing to realize is that, when your experimental subjects are humans, who can speak and answer questions, and whom you trust to be as honest as they can be, mind-reading is not such a trick. You ask them, "What do you think?", they answer, and presto! You're a mind-reader. The trick is that in both cases we're trying to answer questions that the people being questioned don't know the answers to. (Or at least, they don't KNOW they know the answer.) For instance, we try to answer questions like "How much louder is a 40 Pa 1000 Hz tone than a 5 Pa 1000 Hz tone?" or how much more valuable is $8000 than $1000? You might naively think that the answer is "eight times" in both cases, but you would be wrong. Deep inside your brain, without necessarily knowing it, you evaluate these things differently. For most people a 40 Pa tone sounds twice as loud as a 5 Pa tone -- so psychophysics tells us. And $8000 is more valuable to most people than $1000, but not by eight times. So economists tell us.
How much should you trust them? There is no physical ruler one can take to the magnitude of a sensation. This question is addressed by both authors. I was not impressed by Gescheider's answer (in section "The Measurement of Sensations" in chapter 14). He essentially passes on the ontological question of whether sensations are real things that can be measured and asserts that speaking of sensations as if they were real is just a linguistic convenience, sound and fury signifying nothing, and that we shouldn't bother our pretty little heads about whether they are real or not. Wakker is much better on this. He uses the axiomatic approach of a mathematician. He begins each of the several theories that his book presents by stating plausible axioms that are difficult to doubt. He then proves that, if these axioms hold, there must exist such things as utility functions and subjective probabilities. I found it quite convincing.
This is a good example of the differences between the two books. Gescheider is, for my taste, a little too elementary. Large parts of the book are not about psychophysics per se, but rather about basic statistical techniques. Now, to be fair, both Gescheider and Wakker are deeply concerned with the problem of measurement, and if you measure things and want to trust your measurements, you have to understand probability and statistics. But if you have already had a good stats education, Gescheider can be tedious. Wakker, on the other hand, is much more about the theory of measurement than the practice (although he does have things to say about the latter). Prospect Theory reads like an advanced mathematics textbook . (I just finished a PhD in Applied Mathematics, so I speak with some knowledge here.) It is not an easy read, even for a mathematician.
There is another reason I feel more comfortable about prospect theory than psychophysics. Psychophysics, it turns out, relies heavily on the basic mind-reading technique I outlined above: you ask people what they think, and they tell you. Can you trust them? No: a recurring theme of Psychophysics: The Fundamentals is that psychophysical measurements are biased in various ways that are difficult to fully correct. And animal studies are virtually impossible. Prospect theory, in contrast, is about decisions. To make a measurement in prospect theory, you present the subject with two (or more choices) and see which one they select. You can trust them to the extent that you can trust the subject to do what is in his/her/its perceived best interests. Such experiments can be done on animals as well as humans, and have been.
But the good news is that there are large commonalities between the two disciplines. For instance, psychophysical laws are generally power functions, and economic utility functions are also well fit by power laws.
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