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2015/01/17 23:21:27
First edition 2014/07/26

The Mental Models for the Wallet Game

Caution
I who am Japanese wrote this page in English, but I am not so good at English.

Different mental models and different illusions make the same expectation formula for the Wallet Game. But there are two different 'Wallet Game Paradoxes'.

The Wallet Game

According to some documents, the paradox of the Wallet Game seems to have following scenario.

The Rule Part of this Paradox The Paradox Part of this Paradox

Mental Models for the Two Envelope Paradox and the Wallet Game

Some people make following mental model about the Two Envelope Problem.



In the following sections , the people with this mental model are called 'DoublePairian'.

If a DoublePairian think about the Wallet Game, he or she probably have a mental model such as follows.



In the following sections , the people with this mental model are called 'ManyPairian'.



Some people make following mental model about the Two Envelope Problem.



In the following sections , the people with this mental model are called 'SinglePairian'.

If a SinglePairian think about the Wallet Game, he or she probably have a mental model such as follows.


(This figure was revised on December 26, 2014)

In the following sections , the people with this mental model are called 'WinLosePairian'.

Each pairians make same expectation formula

If a ManyPairian has been caught by probability illusion, he or she may think as follows. If a WinLosePairian has been caught by the Inconsistent Variable, he or she may think as follows. The mathematical problem for the ManyPairians is far different from the mathematical problem for the WinLosePairians.

But if the ManyPairians have been caught by a probability illusion and the WinLosePairians have been caught by the Inconsistent Variable,  they may make same expectation formula as above.

Even if such a thing happened., their paradoxes are different each other.

Is there a chance that a WinLosePairian be caught by the Inconsistent Variable?

I think that a SinglePairian of the Two Envelope Paradox will hardly be caught by the Inconsistent variable.
(Please see the page "Inconsistent Variable Theory on The Two Envelope Paradox")

But I think that a WinLosePairian of the Wallet Game will easily be caught by the Inconsistent Variable.

Reason

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