Choice under uncertainty

: At the time Keynes published his A Treatise on Probability, all frequentists required all probabilities to be precise and exact numbers. Therefore, it appears that Keynes’s improved imprecise, logical, frequentist theory of 1921, which Keynes linked to Alfred North Whitehead’s previous approach, would have to have been rejected from any serious consideration due to the following boldfaced sentences that deal with Keynes’s  theoretical exposition:
“10. A proposition can be a member of many distinct classes of
propositions, the classes being merely constituted by the existence of
particular resemblances between their members or in some such way.
We may know of a given proposition that it is one of a particular class
of propositions, and we may also know, precisely or within defined
limits, what proportion of this class are true, without our being aware
whether or not the given proposition is true. Let us, therefore, call the
actual proportion of true propositions in a class the truth-frequency†
of the class, and define the measure of the probability of a proposition
relative to a class, of which it is a member, as being equal to the
truth-frequency of the class

The fundamental tenet  of a frequency theory of probability is,then, that the probability of a proposition always depends upon
referring it to some class whose truth-frequency is known within wide
or narrow limits. Such a theory possesses most of the advantages of
Venn’s, but escapes his narrowness. There is nothing in it so far which
could not be easily expressed with complete precision in the terms of
ordinary logic. Nor is it necessarily confined to probabilities which
are numerical. In some cases we may know the exact number which
expresses the truth-frequency of our class; but a less precise
knowledge is not without value, and we may say that one probability
is greater than another, without knowing how much greater, and that
it is large or small or negligible, if we have knowledge of
corresponding accuracy about the truth-frequencies of the classes to
which the probabilities refer.” (Keynes,1921, p.101;boldface and underline added)
Keynes has thus introduced a Boolean , relational, propositional logic ,as well as imprecise probability(Keynes used the verbiage approximate measures and/or inexact measurement or non numerical probability),into  his logical, frequentist theory. From Chapter VI, Keynes had already defined a measure about how the evidential weight of the argument would be measured in a frequentist approach:


“The same distinction may be explained in the language of the
frequency theory.∗ We should then say that the weight is increased
if we are able to employ as the class of reference a class which is
contained in the original class of reference.” (Keynes,1921, p.76-Keynes’s star footnote refers explicitly to chapter VIII).


Since the frequentists of Keynes’s time , following Venn, Peirce, Reichenbach or von Mises, rejected any other decision theoretic measure except for a precise  probability concept, it follows that they could not  accept Keynes’s construction of incorporating imprecise probability  along with  a second variable to measure evidential weight in a  decision theoretic context, which ,for instance ,Carnap later  called degree of  firmness and Savage called sureness(sure probabilities versus not sure probabilities). This means that Keynes’s  theoretical exposition would have been rejected, given that all frequentists of the time  accepted only some strict  version of a  limiting frequency approach to probability, which rejects any type of  interval valued probabilities or evidential weight  .(There are three papers that are relevant ,which appeared long after 1921.The first is Peter Walley and  Terrence L. Fine’s(1982) “ Towards a frequentist theory of upper and lower probability” ,published in the Ann. Stat. 10 (3) (1982) 741–761.
Two recent papers which attempted to put forth constructs similar in some ways to what Keynes tried to do in 1921 are Hubert’s (2021),” Reviving Frequentism”, published in Synthese and Fröhlich,  Derr, and Williamson(2024), “Strictly frequentist imprecise probability”, published in The Journal of Approximate Reasoning. These papers will not be dealt with in this paper).

Should military personnel (‘soldiers’) become selective conscientious objectors to an unjust war? This chapter argues, first, that in most cases the fog of war and politics makes it unreasonable to expect soldiers to make fact-intensive judgments about whether the war is just. Second, it argues that even a just-war tribunal, of the sort proposed by Jeff McMahan, will not do the job. It will inevitably lack the legitimacy and fact-finding capacity necessary to reassure soldiers in such a weighty decision. Third, the moral importance of maintaining civilian control of the military means that soldiers should generally obey orders to deploy. Fourth, however, absolute deference to leaders and commanders is morally unacceptable. The chapter defends an intermediate view advanced centuries ago by Cajetan, Suárez, and Vitoria: soldiers must not fight in an unjust war, but may defer to civilian leaders’ judgment of just cause unless the injustice is manifest.

Being in a social context influences risk-taking behavior. This study aims to identify the effect of an audience's presence on risk-taking while gambling. One hundred and thirtytwo university students played a computer roulette game. They were randomly allocated to one of our three conditions: (i) either they played alone; or (ii) in the presence of the experimenter; or (iii) in the presence of the experimenter, while being videotaped. Results revealed a significant effect on risk-taking in the participants with the presence of an audience, with more risk-averse behaviors in the two types of audience conditions than in the alone condition. No differences were found between the two audience conditions. Thus, an audience may prevent risk-taking and provide a social shield.

Should military personnel (‘soldiers’) become selective conscientious objectors to an unjust war? This chapter argues, first, that in most cases the fog of war and politics makes it unreasonable to expect soldiers to make fact-intensive judgments about whether the war is just. Second, it argues that even a just-war tribunal, of the sort proposed by Jeff McMahan, will not do the job. It will inevitably lack the legitimacy and fact-finding capacity necessary to reassure soldiers in such a weighty decision. Third, the moral importance of maintaining civilian control of the military means that soldiers should generally obey orders to deploy. Fourth, however, absolute deference to leaders and commanders is morally unacceptable. The chapter defends an intermediate view advanced centuries ago by Cajetan, Suárez, and Vitoria: soldiers must not fight in an unjust war, but may defer to civilian leaders’ judgment of just cause unless the injustice is manifest.

UvA-DARE is a service provided by the library of the University of Amsterdam () "A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth-and early twentieth-century probability theory, mathematics and logic Verburgt, L.M. Citation for published version (APA): Verburgt, L. M. (2015). "A terrible piece of bad metaphysics"? Towards a history of abstraction in nineteenth-and early twentieth-century probability theory, mathematics and logic. It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website.

Abstract: Some authors have signalled a realist orientation in Keynes's thought (although many times assigning different meaning to this label). This paper will maintain that Keynes held an ontological, epistemic and logical-semantic realism. As recognized by those scholars, ...

Purpose Gambling is increasingly a global phenomenon, derided by some as exploitative and viewed by others as entertainment. Despite extensive research into gambling motivations, previous research has not assessed whether gaming choice is a function of one’s personal motivations or simply a desire to gamble in general, regardless of game choice among recreational gamblers. The purpose of this study is to explore this theme by considering “illusion of control” where luck and skill may moderate gambling motivation. Design/methodology/approach This study applies two motivation theories, hedonic consumption theory and motivation disposition theory, and examines heuristic perspectives related to gambling. Three stages of qualitative data collection were undertaken. Findings The findings indicate that for recreational gamblers, gaming choice is a function of personal motives. Hence, gamblers chose games that reflect their needs or motives, focusing on the game or games that best allow the...

This paper focuses on Keynes's understanding of individual decision-making under uncertainty and tries to address a question left mostly unexplained in the critical literature. On re-reading Keynes after the recent surge of interest induced by the financial crisis, a number of scholars have placed emphasis on well-known excerpts from the General Theory dealing with the " state of long-term expectations. " Keynes evidenced that future events conditioning economic activity in general, and investment in particular, " can only be forecasted with more or less confidence, " and that " the state of confidence, as they term it, is a matter to which practical men always pay the closest and most anxious attention, " while economic theory does not. In these instances, Keynes argued, people may fall back on " conventions, " which give them assurance that they are doing the right thing. As a result, " to behave in a manner which saves our faces as rational, economic men … we have devised for the purpose a variety of techniques. " But Keynes's main message is that under uncertainty " [a]ll these pretty, polite techniques, made for a well-panelled Board Room and a nicely regulated market, are liable to collapse. " For instance, conventional behaviour easily turns into herd behaviour, and financial markets are pervaded by alternating currents of euphoria and panic. So a question remains: how should Keynesian agents behave in markets continuously on the brink to fail? Are there, rephrasing Keynes, " impolite techniques " to be used under uncertainty or must we end up admitting that " we simply do not know, " and behave in a conventionally understood fashion? The paper offers a reading of Keynes suggesting that the thread going from Keynes's Treatise on Probability to the General Theory and its defence provides a positive analysis of decision-making under uncertainty, and argues that placing emphasis on this positive analysis simply means adhering to Keynes's long-standing commitment to interpret reasonable judgement in a (surely unconventional) probabilistic setup .

Two experiments examined the relationships between the knowledge that another person has won in a gamble, the illusion of control and risk taking. Participants played a computer-simulated French roulette game individually. Before playing, some participants learnt that another person won a large amount of money. Results from a first experiment (n = 24) validated a causal model where the knowledge of another person’s win increased the illusion of control, measured with betting times, expectancy and self-reports on scales, which in turn encourages risk taking. In the second experiment (n = 36), some participants were told the previous player acknowledged the win to be fortuitous. The suppression of the belief that the previous winner had himself exerted control over the outcome resulted in lower rates of risk-taking behaviors. This suggests that it was not the knowledge of another person’s win in itself that increased risk taking, but rather, the belief that the other person had some control over the gamble’s outcome. Theoretical implications for the study of social mechanisms involved in gambling behavior are discussed.

The thesis of this paper is that Keynes wrote A Treatise on Probability in opposition to the frequentist theory of probability, systematised by John Venn, which denied any role for probability in decision theory. Keynes was interested in finding an alternative conception of probability that could be utilised as a guide of life. To analyse this point, the paper considers Keynes's criticisms of frequentist tradition in the two versions of his Fellowship dissertation, and in the published edition of his Treatise. Keynes's project is then illustrated with the famous example of whether or not to go out with one's umbrella in the situation in which the pressure is high and the clouds are black.

Some authors have signalled a realist orientation in Keynes's thought (although many times assigning different meaning to this label). This paper will maintain that Keynes held an ontological, epistemic and logical-semantic realism. As recognized by those scholars, Moore's philosophy has had a deep influence in Keynes´s realism. However, nobody has developed the possible influence of Franz Brentano. Instead, they have appraised the issue of Keynes's realism from different traditions, frequently alien or posterior to Keynes. The paper will show that Brentano's influence helps to arrive at a clarifying interpretation of Keynes's realism and of his key notion of intuition. It will also maintain that this is the central contribution of Keynes's epistemology.