Paradox on rcor

Exposing Sleeping Beauty: Triggered or Induced?

Mon, 28 Sep 2026 00:00:00 +0000

Beauty wakes up on Monday morning.also on Tuesday, if Tails.with no memory, every time anew.when asked about her credence in Heads.

We have discussed before the distinction between a process being triggered and an outcome being induced. The distinction may look semantic at first sight, but it becomes probabilistically important whenever the observation available to an agent is produced by a mechanism that selects, filters, or repeats possible states.

Observation and Reporting in Conditional Probability — One Ace versus the Ace of Hearts

Tue, 02 Jun 2026 00:00:00 +0000

In practice, decision making rarely depends on the full information that was originally observed¹. Instead, decisions are often based only on the information that was eventually reported. This distinction is fundamental.

An observer may possess richer latent information than the information communicated through the reporting protocol. Consequently, two situations that appear equivalent at the reporting level may correspond to very different informational structures.

Conditional probability is usually introduced theoretically through abstract events and sigma-algebras. However, in practical applications, conditioning frequently depends on:

The 100 Prisoners Problem: Induced vs. Triggered Processes in Risk Management

Sat, 25 Apr 2026 00:00:00 +0000

In a previous post, we established a vital distinction: the difference between an induced event (arising from human intervention) and a triggered one (the release of pre-existing tension in a system).

A rigorous distinction between triggered and induced processes can be formalized using the 100 prisoners problem, as discussed in both the algorithmic literature Gál and Miltersen (2007)) and expository mathematical sources Pahor (2024), or even as a riddle video.

While there are many variations and related paradoxes, this formulation is particularly revealing from a structural perspective: it produces one of the largest known gaps between a naive triggered interpretation and a structurally correct induced one, leading to dramatically different outcomes.

Newcomb's Paradox — Global to local

Thu, 19 Mar 2026 00:00:00 +0000

Newcomb’s Paradox¹ is one of the most discussed thought experiments in decision theory, putting into tension two seemingly incompatible principles: expected utility maximization and the principle of dominance.

For an accessible introduction, see:

Standard discussions usually frame the problem in terms of:

Evidential Decision Theory (EDT)
Causal Decision Theory (CDT)

In this post, we propose an alternative structural formulation based on:

Zeno's Paradox Explained — From Math to Reality

Wed, 11 Mar 2026 00:00:00 +0000

Zeno’s paradox, in its classical form, suggests an apparently fundamental difficulty: to reach a target, one must first traverse half the distance, then half of the remaining distance, and so on. This results in an infinite succession of intermediate steps that seem to need to be completed before the final goal is reached.

Generalized Definition of Zeno’s Paradox Link to heading

A Zeno structure is a tuple:

Fair Split — the Current Solution to an Ancient Dilemma

Wed, 01 Oct 2025 00:00:00 +0000

Throughout history, people have wondered how to divide resources fairly.
From water shared among travelers lost in the desert to bread placed on the table for a hungry stranger, the dilemma remains the same: how much should each person receive if we want to be truly just?

This problem appears in many cultures. One of the oldest versions can be found in medieval Arabic manuscripts: two travelers had with them five and three loaves of bread. They meet a third traveler and decide that all three will eat from the pooled bread. After the meal, the newcomer, grateful, leaves eight coins for the meal received. How should the money be divided?

Crypto Paradox

Mon, 15 Sep 2025 00:00:00 +0000

I have often been asked questions about crypto investment. The following analysis aims to provide an elegant response.

In the world of traditional investments, the essential question is not only whether to enter, but also when to exit. Any prudent investor defines from the outset an exit strategy: price points, time horizons, risk levels.

But in the case of cryptocurrencies, this logic falters. Here emerges what we may call the Crypto Paradox:

Towards a Unified View of Probability

Fri, 29 Aug 2025 00:00:00 +0000

Probability is a fundamental concept that transcends disciplinary boundaries, including mathematics, statistics, physics, philosophy, and finance. Over time, different disciplines have developed distinct interpretations, each with specific strengths and limitations.

The table below offers a unified view of probability, presenting the main interpretations, associated formulas, contexts where they are appropriate, as well as the advantages and limitations of each. The aim is not merely to list the concepts, but also to highlight how some frameworks integrate or generalize others, thereby enabling a coherent perspective that is applicable across domains.

When Politics Fails

Sun, 04 May 2025 00:00:00 +0000

We present below a paradox popularized by Martin Gardner in October 1959 in his “Mathematical Games” column in Scientific American, under the title “The Two Children Problem.”

We will analyze a probabilistic problem related to a hypothetical policy where each family in a country has children until they have a boy, at which point they are required to stop. Our goal is to determine the resulting proportion of boys and girls in this country.

Understanding Statistical Tests

Tue, 29 Apr 2025 00:00:00 +0000

Introduction Link to heading

Misunderstandings around statistical tests are quite common, so we propose below an actuarial explanation. We’ll walk through a concrete example (independence testing) step by step.

This article explains how to choose the significance level α based on test accuracy , and how to interpret results using the concept of the acceptance region .

Step 1: Formulating Hypotheses Link to heading

Null Hypothesis (H₀): the data series are independent
Theoretical Alternative Hypothesis (H₁): the series are dependent

H₁ reflects the actual hypothesis of interest, but it is often difficult to state precisely or test directly. Therefore, we may introduce a more practical alternative hypothesis: