The nature of capital and income

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Monograph

Identifikator:: 102659555X

URN:: urn:nbn:de:zbw-retromon-82920

Document type:: Monograph

Author:: Fisher, Irving http://d-nb.info/gnd/118533541

Title:: The nature of capital and income

Place of publication:: New York

Publisher:: The Macmillan Company

Year of publication:: 1923

Scope:: XXI, 427 Seiten

Digitisation:: 2019

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Introduction. Fundamental concepts

Collection:: Economics Books

Sec. 1] THE RISK ELEMENT 267 equally probable because the longer the trial is continued the more will the two tend toward equality. But they argue in a circle. It is not necessarily true that the longer the run the more closely will the frequency of the event approach its probability. For example, it is possible that though heads and tails have an equal chance, a run of heads may keep up for any given number of times, however long, a million, for instance; or that at first heads and tails may occur with equal frequency and as the ex- periment proceeds they may diverge more and more from such equality. No student of chance, whatever his theory of the philosophy of chance, would claim that these cases are vmpossible. The most that can be said is that they are extremely tmprobable. The statement, therefore, that the longer the run the more closely will the frequency of the event approach its probability turns out to be “the longer the run the more probably will the frequency correspond to the probability.” This is true as a proposition and it is in fact known as “Bernoulli’s Theorem ”’; but it cannot be made the basis of a sound definition of probability, for probability would be defined in terms of itself. It states that the probability of heads coming up is the frequency which heads will probably approximate in the long run! How else than in terms of probability can we formulate the conditions under which in the long run the coin “will ” fall according to its probability ? It is precisely at this point that the radical difficulty with the “long- run’’ theory is seen. It is said that in an athletic contest, the chance of winning is one half when two wrestlers are so nearly mated that in the long run “under precisely the same conditions,” each will win in half the contests. If the conditions are, literally speaking, precisely the same, then the same result will necessarily follow and the same man will always win. It is only as the conditions vary slightly from time to time in their unknown elements that there is a change of winner; and the instant the unknown-

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