The Monty Hall Problem is not a Probability
نویسندگان
چکیده
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch
منابع مشابه
Maximum Entropy and Bayesian Inference for the Monty Hall Problem
We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian...
متن کاملProbability, Rational Single-Case Decisions and the Monty Hall Problem
The application of probabilistic arguments to rational decisions in a single case is a contentious philosophical issue which arises in various contexts. Some authors (e.g. Horgan 1995; Levy 2007) affirm the normative force of probabilistic arguments in single cases while others (Baumann 2005, 2008) deny it. I demonstrate that both sides do not give convincing arguments for their case and propos...
متن کاملPositive operator valued measures and the quantum Monty Hall problem.
A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.
متن کاملThe Monty Hall Problem
A range of solutions to the Monty Hall problem is developed, with the aim of connecting popular (informal) solutions and the formal mathematical solutions of introductory text-books. Under Riemann’s slogan of replacing calculations with ideas, we discover bridges between popular solutions and rigorous (formal) mathematical solutions by using various combinations of symmetry, symmetrization, ind...
متن کاملPersistent Cognitive Error in Performance on the Monty Hall Dilemma
The Monty Hall Dilemma is a probability puzzle that is notorious for eliciting suboptimal decisions from humans. A participant is given a choice from among three doors, one of which conceals a valuable prize. After an initial selection, one of the remaining, nonwinning doors is opened, and the participant is given a chance to switch to the other unopened door. The probability of winning is high...
متن کاملProbability, rational single-case decisions and the Monty Hall Problem
The application of probabilistic arguments to rational decisions in a single case is a contentious philosophical issue which arises in various contexts. Some authors (e.g. Horgan, Philos Pap 24:209–222, 1995; Levy, Synthese 158:139–151, 2007) affirm the normative force of probabilistic arguments in single cases while others (Baumann, Am Philos Q 42:71–79, 2005; Synthese 162:265–273, 2008) deny ...
متن کامل