Why do we change whatever amount we found in the first envelope: the Wikipedia "two envelopes problem" commented

We analyze the main arguments that attempt to explain why there is no point in changing the envelope. Most people confuse estimation and calculation, conditional and unconditional probabilities, random and non-random variables, modelling and reality, chance and uncertainty (or credence), whatever X known and whatever X unknown, personal and interpersonal estimates. Such confusions suggest that there would be no point in swapping the envelope. Our analysis is that if the first envelope is opened, whatever the amount, it is rational and consistent to think that it is worth changing it. If the first envelope is not opened, it is rational and consistent to believe there is no point in swapping the envelope.

Data and Resources

Additional Info

Field Value
Source https://hal.science/hal-00943573
Author Gerville-Réache, Léo
Maintainer CCSD
Last Updated May 7, 2026, 01:57 (UTC)
Created May 7, 2026, 01:57 (UTC)
Identifier hal-00943573
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Institut de Mathématiques de Bordeaux (IMB) ; Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
creator Gerville-Réache, Léo
date 2014-02-01T00:00:00
harvest_object_id e8ced051-ae0a-43fd-a770-0f51939e6a7e
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-03-17T00:00:00
set_spec type:UNDEFINED