...In general, hypothesis testing concerns trying to decide whether a parameter θ lies in one subset of the parameter space or in its complement...We also demonstrate an equivalence between hypothesis tests and confidence intervals...
Chapter 9, Testing Hypothesis
Risk or uncertainty?
In this textbook version of Raiffa and Schlaifer's statistical decision theory of experimentation combined with Savage's theory of statistics, the authors scratched the risk/uncertainty difference with a stroke:
...a number of economists have attempted to distinguish between risk and uncertainty, as originally proposed by Frank H. Knight. (1) Risk, Knight said, refers to situations where an individual is able to calculate probabilities on the basis of an objective classification of instances. For example, in tossing a fair die the chance of any single one of the six faces showing is exactly one-sixth. (2) Uncertainty, he contended, refers to situations where no objective classification is possible, for example, in estimating whether or not a cure for cancer will be discovered in the next decade...
...in this book, we disregard Knight's distinction. For our purpose, risk and uncertainty mean the same thing. It does not matter, we contend, whether an 'objective' classification is or is not possible. For we will be dealing throughout with a 'subjective' probability concept (as developed especially by Savage, 1954): probability is simply degree of belief. In fact, even in cases like the toss of a die where assigning 'objective' probabilities appears possible, such an appearance is really illusory. That the chance of any single face turning up is one-sixth is a valid inference only if the die is a fair one - a condition about which no one could ever be 'objectively' certain. Decision makers are therefore never in Knight's world of risk but instead always in his world of uncertainty. That this approach, assigning probabilities on the basis of subjective degree of belief, is a workable and fruitful procedure will be shown constructively throughout the book...
In a similarly direct manner, the authors defended analytic decision theory:
...the approach here does not allow for the psychological sensations of vagueness or confusion that people often suffer in facing situations with uncertain (risky) outcomes. In our model, the individual is neither vague nor confused. While recognizing that his knowledge is imperfect, so that he cannot be sure which state of the world will occur, he nevertheless can assign exact numerical probabilities representing his degree of belief as to the likelihood of each possible state. Our excuse for not picturing vagueness or confusion is that we are trying to model economics (/rational behavior), not psychology...The ultimate justification, for indifference-curve diagrams or for theories of decision under uncertainty, is the ability of such models to help us understand and predict behavior.
...a number of economists have attempted to distinguish between risk and uncertainty, as originally proposed by Frank H. Knight. (1) Risk, Knight said, refers to situations where an individual is able to calculate probabilities on the basis of an objective classification of instances. For example, in tossing a fair die the chance of any single one of the six faces showing is exactly one-sixth. (2) Uncertainty, he contended, refers to situations where no objective classification is possible, for example, in estimating whether or not a cure for cancer will be discovered in the next decade...
...in this book, we disregard Knight's distinction. For our purpose, risk and uncertainty mean the same thing. It does not matter, we contend, whether an 'objective' classification is or is not possible. For we will be dealing throughout with a 'subjective' probability concept (as developed especially by Savage, 1954): probability is simply degree of belief. In fact, even in cases like the toss of a die where assigning 'objective' probabilities appears possible, such an appearance is really illusory. That the chance of any single face turning up is one-sixth is a valid inference only if the die is a fair one - a condition about which no one could ever be 'objectively' certain. Decision makers are therefore never in Knight's world of risk but instead always in his world of uncertainty. That this approach, assigning probabilities on the basis of subjective degree of belief, is a workable and fruitful procedure will be shown constructively throughout the book...
In a similarly direct manner, the authors defended analytic decision theory:
...the approach here does not allow for the psychological sensations of vagueness or confusion that people often suffer in facing situations with uncertain (risky) outcomes. In our model, the individual is neither vague nor confused. While recognizing that his knowledge is imperfect, so that he cannot be sure which state of the world will occur, he nevertheless can assign exact numerical probabilities representing his degree of belief as to the likelihood of each possible state. Our excuse for not picturing vagueness or confusion is that we are trying to model economics (/rational behavior), not psychology...The ultimate justification, for indifference-curve diagrams or for theories of decision under uncertainty, is the ability of such models to help us understand and predict behavior.
On logic
First, the author considers the postulates he made about preference relations on acts to have both an empirical interpretation - as a 'prediction about the behavior of people' - and a normative one - as a 'logic-like criterion of consistency'.
Then some discussion of the role of logic in general:
Then some discussion of the role of logic in general:
...logic itself admits an empirical as well as a normative interpretation...to summarize (the empirical interpretation), logic can be interpreted as a crude (since people make mistakes and have limited computing power) but sometimes handy empirical psychological theory...(not very successful though)
...the principle value of logic, however, is in connection with its normative interpretation...as a set of criteria by which to detect, with sufficient trouble, any inconsistencies there may be among our beliefs...'not appropriate' here to discuss 'why and in what contexts we wish to be consistent'. We simply 'often do wish to be so'.
Implication of reducing multi-stage to single-stage
Defining acts as functions from states to consequences, reduction of many multi-stage actions to a single action follows naturally, bringing up a surprising implication for research planning though:
...the great majority of experimentalists...suppose that the function of statistics and of statisticians is to decide what conclusions to draw from data gathered in an experiment or other observational program...
...but statisticians hold it to be lacking in foresight to gather data without a view to the method of analysis to be employed...they hold that the design and analysis of an experiment should be decided upon as an articulated whole...The author then went on to propose the main theme of the discussion as the 'Look before you leap' type, as is opposite to 'You can cross that bridge when you come to it'. I wonder whether the precautionary principle amounts to 'Look and be cautious before you leap' or 'You can cross that bridge when you come to it but be cautious'. The latter would seem more widely applied.
Savage on Schlaifer
(preface to Dover edition)...the (personalistic) movement itself has other sources apart from those from which this book itself was drawn ...one with great impact on practical statistics and scientific management is a book by Robert Schlaifer...his ideas were developed wholly independently of the present book, and indeed of other personalistic literature...they are in full harmony with the ideas in this book but are more down to earth and less spellbound by tradtions...
The honorably working Bourgeois
Many essays start by quoting dictionaries and definitions, but few can be much more revealing than the dictionaries and encyclopedia themselves, as is the one done by McCloskey in Chapter 2 to start talking about the Bourgeoisie, plural of a Bourgeois whose female partner would be a Bourgeoise, not to be distinguished in spoken language from its plural form Bourgeoises, who all share ancestry with the German Bürger and Bürgerinnen, the hard-working "towns-man-ly" people, what McCloskey tries to portray as a virtuous class.
One thing peculiar about her portrait is the inauthenticity and the lack of creativity of the Bourgeois class, whose greatest drives for hard work are freedom and the ability to imitate, rather than any pure profit maximization with resolution nor logic. I wonder what economics would be like if such a homo socius becomes the protagonist.
One thing peculiar about her portrait is the inauthenticity and the lack of creativity of the Bourgeois class, whose greatest drives for hard work are freedom and the ability to imitate, rather than any pure profit maximization with resolution nor logic. I wonder what economics would be like if such a homo socius becomes the protagonist.
Sufficiency of self-interest in cooperation
The author argues that self-interested m-Cooperate strategy is unstable and easily afflicted by chance events of for example one m-Cooperator turning to Defect. Why couldn't the strategies also adapt to become stochastic and tolerant to chance events? The author admits himself that this doesn't exclude the possible existence of strategies immune to chance events. Nevertheless, such partial results are commonly used as arguments for inefficiency of self-interest and for the necessity of exogenous factors such as institutions.
The other argument using implausibility of self-interested cooperation in large groups instead of in a dyadic setting is also debatable. Individuals in large groups are not isolated from each other. There is the social network structure connecting group members and graph theory has shown that it is possible to connect most individuals in the world with one another within a very small number of links (social networks theory, 6 degrees of separation). This makes reciprocal actions not unlikely, and reciprocal altruism not unlikely, if the individuals realize this connectivity.
The other argument using implausibility of self-interested cooperation in large groups instead of in a dyadic setting is also debatable. Individuals in large groups are not isolated from each other. There is the social network structure connecting group members and graph theory has shown that it is possible to connect most individuals in the world with one another within a very small number of links (social networks theory, 6 degrees of separation). This makes reciprocal actions not unlikely, and reciprocal altruism not unlikely, if the individuals realize this connectivity.
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