Foreseeing the Past: Probability and Ancient Greek Decision-Making

The article explores the concept of probability in ancient Greece from a non-scientific perspective and shows how ancient decision-makers used historical data to make calculated decisions and speculate about the future. First, the paper considers how quantitative data was used by ancient Greek communities to make economic projections. It then shows how ancient Greek generals used the same conceptual tools to determine their odds of victory by tallying up and comparing the number and composition of armies and resources available to them and their enemy. In the third section, the paper examines how qualitative probability was articulated through the language of hope and likelihood to formulate chances of success in moments of crisis. Finally, the paper shows that ancient decision-makers implemented “power laws” to adapt to changing circumstances and the flow of new information, as they sought to improve their odds of success relative to their rivals.

John Maynard Keynes and Ludwig von Mises on Probability

The economic paradigms of Ludwig von Mises on the one hand and of John Maynard Keynes on the other have been correctly recognized as antithetical at the theoretical level, and as antagonistic with respect to their practical and public policy implications. Characteristically they have also been vindicated by opposing sides of the political spectrum. Nevertheless the respective views of these authors with respect to the meaning and interpretation of probability exhibit a closer conceptual affinity than has been acknowledged in the literature. In particular it is argued that in some relevant respects Ludwig von Mises’ interpretation of the concept of probability exhibits a closer affinity with the interpretation of probability developed by his opponent John Maynard Keynes than with the views on probability espoused by his brother Richard von Mises. Nevertheless there also exist significant differences between the views of Ludwig von Mises and those of John Maynard Keynes with respect to probability. One of these is highlighted more particularly: where John Maynard Keynes advocated a monist view of probability, Ludwig von Mises embraced a dualist view of probability, according to which the concept of probability has two different meanings each of which is valid in a particular area or context. It is concluded that both John Maynard Keynes and Ludwig von Mises presented highly nuanced views with respect to the meaning and interpretation of probability. JEL codes: B00; B40; B49; B53; C00. Key words: General Methodology; Austrian Methodology; Keynesian Methodology; Quantitative and Qualitative Probability Concepts: Meaning and Interpretation; Frequency Interpretation; Logical Interpretation; John Maynard Keynes; Ludwig von Mises; Richard von Mises. Resumen: Los paradigmas económicos de Ludwig von Mises por una parte, y de John Maynard Keynes por otra, han sido correctamente reconocidos como contradictorias a nivel teórico, y como antagonistas, con respecto a sus implicaciones políticas prácticas y públicas. Aún así, las respectivas visiones de estos autores con respecto al significado e interpretación de la probabilidad, muestra una afinidad conceptual más estrecha que los que se ha reconocido en la literatura. Se ha argumentado especialmente que en algunos aspectos importantes, la interpretación de Ludwig von Mises del concepto de probabilidad, muestra una más estrecha afinidad con la interpretación de probabilidad desarrollada por su oponente John Maynard Keynes, que con las maneras de ver la probabilidad respaldadas por su hermano Richard von Mises. Sin embargo, también existen grandes diferencias entre los puntos de vista de Ludwig von Mises y aquellos de John Maynard Keynes con respecto a la probabilidad. Uno de ellos destaca principalmente: cuando John Maynard Keynes aboga por un punto de vista monista de la probabilidad, Ludwig von Mises defiende un punto de vista dualista de la probabilidad, de acuerdo con el cual el concepto de probabilidad recibe dos significados diferentes, y en donde cada uno de ellos es válido en un área o contexto en particular. Se concluye que tanto John Maynard Keynes como Ludwig von Mises presentan puntos de vista claramente diferenciados con respecto al significado e interpretación de la probabilidad. Códigos JEL: B00; B40; B49; B53; C00. Palabras clave: Metodología General; Metodología austríaca; Metodología Keynesiana; Conceptos de probabilidad cuantitativos y cualitativos: Significado e Interpretación; Interpretación frecuencialista; Interpretación lógica; John Maynard Keynes; Ludwig von Mises; Richard von Mises.

On atom-swarming and Luce’s theorem for probabilistic beliefs

For qualitative probability spaces, monotone continuity and third-order atom-swarming are together sufficient for a unique countably additive probability measure representation that may have atoms (Mackenzie in Theor Econ 14:709–778, 2019). We provide a new proof by appealing to a theorem of Luce (Ann Math Stat 38:780–786, 1967), highlighting the usefulness of extensive measurement theory (Krantz et al. in Foundations of Measurement Volume I: Additive and Polynomial Representations. Academic Press, New York, 1971) for economists.

FORMAL QUALITATIVE PROBABILITY

Choices rarely deal with certainties; and, where assertoric logic and modal logic are insufficient, those seeking to be reasonable turn to one or more things called “probability.” These things typically have a shared mathematical form, which is an arithmetic construct. The construct is often felt to be unsatisfactory for various reasons. A more general construct is that of a preordering, which may even be incomplete, allowing for cases in which there is no known probability relation between two propositions or between two events. Previous discussion of incomplete preorderings has been as if incidental, with researchers focusing upon preorderings for which quantifications are possible. This article presents formal axioms for the more general case. Challenges peculiar to some specific interpretations of the nature of probability are brought to light in the context of these propositions. A qualitative interpretation is offered for probability differences that are often taken to be quantified. A generalization of Bayesian updating is defended without dependence upon coherence. Qualitative hypothesis testing is offered as a possible alternative in cases for which quantitative hypothesis testing is shown to be unsuitable.

A foundation for probabilistic beliefs with or without atoms

We propose two novel axioms for qualitative probability spaces: (i) unlikely atoms, which requires that there is an event containing no atoms that is at least as likely as its complement; and (ii) third‐order atom‐swarming, which requires that for each atom, there is a countable pairwise‐disjoint collection of less‐likely events that can be partitioned into three groups, each with union at least as likely as the given atom. We prove that under monotone continuity, each of these axioms is sufficient to guarantee a unique countably‐additive probability measure representation, generalizing work by Villegas to allow atoms. Unlike previous contributions that allow atoms, we impose no cancellation or solvability axiom.

Karakterisasi parameter model prediksi untuk eleviasi dari perangkap kemiskinan melalui intervensi kebijakan fiskal

The purpose of this study was to develop a model of poverty eleviation in the buffer zone of National Park through the optimization of the impact of the fuel subsidiary reallocation (BLT), statrted from April to October 2013 in three villages which representent ethnic culture in Lampung, Java, and the mixture of both, selecting 50 poor households (RTM) who received BLT (direct cash assistance) in 2005. In-depth interview was conducted to capture the economy performance of each household. Qualitative probability model was applied to the response variable (Yi) that were scored 1 for those have been exited from the poverty and scored 0 if not yet. The predictor variables used (Xij) including: fuel prices (Rp/liter), total of BLT (Rp), demographics (age, sex, family head education, as well as the number of dependents), the value of productive assets (Rp million/household), revenue from damar resin, and other sources (Rp million/household), access to public services, the distance to the border of BBSNP, the availlability of PNPM (national project of community empowermnent that scored 1 if any and 0 if not), the performance of social capital and the extention program conveyed. The Minitab Version 16 was employed for exzamining the goodness to the model and the significancy of the parameters pursued at the level of 5% and 10%. The conclusions were the exit capability against poverty were significantly affected by: fuel prices, the ammount of the BLT, the exisistency of PNPM, gender & education of household, number of dependents, the distance to central districts, the presence of electricity, the power of social capital, land ownership of both damar agroforest and paddy field acreages, the owner of productive assets such as ruminants. Accordingly, there were no culturetribe significantly affected by the existing from of poverty, which means that the poverty in this region was more structural cause than that of the cultural one.