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Remarkable revisions of the Wikipedia article "Two envelopes problem"

Remarkable revisions

Some of the revisions of the English language Wikipedia article 'Two envelopes problem' surprised me.

Replacement of the wording

(Added on June 30, 2019)

The wording of the problem presented in the original revision (August 25, 2005) was the opened version problem.
About one month later, at the revision 22:05, 3 October 2005, the wording was replaced with the wording presented in the article "Envelope paradox" changing to the closed version problem.
And at the same revision the opened version problem became called "A Second Paradox".

Changing meaning of the opened version problem

At the revision 18:42, 8 October 2008, the opened version problem became not described.
At the revision 20:37, 8 April 2011, in the section "Extensions to the problem", the opened version problem became presented as the subject of the switching strategy rather than the two envelope paradox. (← Revised on January 12, 2020)
At the revision 18:36, 1 May 2011, the new section "Randomized solutions" that describes Cover's principle was added. (Reference : Cover, T. M. (1987). )
At the revision 17:23, 13 February 2012, the section "Extensions to the problem" was rewritten to present only calculating formula of conditional expected value.

A new expectation formula which was regarded as equivalent to the known expectation formula

In a section created at the end of 2014 on the talk page of the article "Two envelopes problem", many editors discussed about quotation of a new expectation fomula. (Even now in January 2019, we can read that section on the talk page, thanks to an editor who NACed the section.)

The new formula is a calculation on the two pairs of amounts, so, it is essentially different from the DivideThreeByTwoian's formula. And the calculated expectated value does not have a dimension of a usual quantity.
To my eyes, the new formula is comparing the ratio of the losing (case of the lesser pair) and the ratio of the gaining (case of the greater pair) to the each mean value, despite the mean values are different.

However, none of the participants of the discussion (except the proposer) did not discuss the actual meaning of the formula, while discussing notability or benefit of the formula and the reliability of information source.
In addition, some of the participants of the discussion (except the proposer) including the major editors said that it has essentially same meaning as the known DivideThreeByTwoian's formula, with no explanation how to verify it.

Such a tone of discussion may have influenced the later editings of the article, and even now in February 2019, we can see traces in the article.

Removed picture of two envelopes

A picture of two envelopes was pasted at the revision 11:42, 27 August 2009.
To my disappointment, it was removed at the revision 22:34, 18 January 2016 after no less than 6 years have passed.

Complete removal of the "Randomized solutions" section

On December 28, 2019, with a title "An alternative randomized solution", a new strategy was written in the section "Randomized solutions". The strategy is to use a monotonically increasing function as the probability not to switch. I think such strategy is one of the most common randomized switching strategies.

However, to my surprise, just after the edition, on December 29, 2019, the section "Extensions to the problem" and this section "randomized solutions" were replaced by completely different section "Conditional switching".

The new section "Conditional switching" does not mention the effect of randomizing. And the term "Conditional switching" seems to only mean that the player is allowed to open the chosen envelope before deciding whether to switch.

On May 1, 2011, the section "Randomized solutions" was created by one of the major editors of the article "Two envelopes problem". And main parts of the content were written by him in May 2011.
Anyway, the article "Two envelopes problem" has lost the section describing randomized switching strategies.

Reference

• Cover, T. M. (1987).
  Pick the largest number.
  In Open problems in communication and computation (pp. 152-152). Springer New York.
   
  

Terms

• NAC
  About NAC, please see the page "Wikipedia:Non-admin closure" in the English language Wikipedia.
   
  
• opened version problem
  In the opened version problem of the two envelopes problem, the player will be given the opportunity to switch envelopes after opening the selected envelope.
   
  
• closed version problem
  In the closed version problem of the two envelopes problem, the player will be given the opportunity to switch envelopes before opening the selected envelope.
   
  
• DivideThreeByTwoian
  Some people think that thinking of two pairs of amounts of money is the cause of the paradox of the two envelopes.
  In other words, they think that it is wrong to simultaneously use the amount x/2 and 2x in the expectation formula.
  And most of them think that the correct expectation formula is "E=(1/2)a+(1/2)2a".
  I call them DivideThreeByTwoian because (1/2)a + (1/2)2a = (3/2)a.
   
  

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