Title: Probability, Complexity, and the Real World

Abstract: Probability is often presented as a mathematical framework for modeling and understanding uncertainty or (apparent) randomness in the world. But Probability is a much larger and more complex concept than a mere mathematical calculus that falls out of Kolmogorov's axioms. Aside from its mathematical content, there are practical, psychological, and ethical considerations that are often as or more important in many applications, especially when making complex decisions in complex domains.

Practically, the existence of a sound mathematical model is far from sufficient to properly identify the situations to which it applies and subsequently implement it to achieve the desired end goal. Psychologically, there is a difference between understanding the math and experiencing the emotional swings of its real world implementation. There is always volatility and risk, even with flawless execution and a perfect model. Ethically, probabilities are often used to justify scientific conclusions and influence policy.

Using examples from advantage gambling, the scientific replication crisis, and election forecasting, I'll illustrate how the academic conception of probability as a mathematical artifice disregards these additional components in a way that misleads, misinforms, and misrepresents many real world components of risk and uncertainty.

The talk will touch on elements from prior work on these topics:

H. Crane. (2018). Probabilistic Foundations of Statistical Network Analysis. Chapman-Hall.
H. Crane. (2018). The Fundamental Principle of Probability. Researchers.One, https://www.researchers.one/article/2018-08-16.
H. Crane. (2018). Logic of Probability and Conjecture. Researchers.One, https://www.researchers.one/article/2018-08-5.
H. Crane. (2018). Polls, Pundits, or Prediction Markets: An assessment of election forecasting. Researchers.One, https://www.researchers.one/article/2018-11-6.

Bio: Harry Crane is Associate Professor and Co-Director of the Graduate Program in Statistics and Biostatistics, and Affiliated Faculty in the Graduate Program in Philosophy at Rutgers University. He is co-founder of Researchers.One, an innovative platform for peer review and scholarly publication and initiative for intellectual reform. Crane is currently Chancellor's Excellence Scholar (2018-2020) at Rutgers University and Fellow at the London Mathematical Institute, and has previously held positions as a Visiting Scholar in Mathematics at UC Berkeley, Research Associate at the RAND Corporation, and Research Fellow at the Foreign Policy Research Institute. Harry received his PhD in Statistics from the University of Chicago and BA in Mathematics and Economics from the University of Pennsylvania.

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