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Topic: Maximisation problem
Replies: 10   Last Post: Jul 27, 2013 6:16 AM

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quasi

Posts: 10,450
Registered: 7/15/05
Re: Maximisation problem
Posted: Jul 27, 2013 5:30 AM
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pepstein5 wrote:
>Peter Percival wrote:
>> Paul wrote:
>>

>> >Let n be a fixed integer > 1. n logicians walk into a bar.
>> >The barwoman says "Do all of you want a beer?" The first
>> >logician says "I don't know." The second logician says
>> >"I don't know." ... The n-1st logician says "I don't know."
>> >The nth logician says "Yes please."

>>
>> That doesn't answer the question correctly.

>...
>
>Please could you state your objection? Everyone is narrowly
>focusing on the yes/no question: "Do all of the n logicians
>want a beer?"


It's not exactly a yes/no question since some of the answers
have been "I don't know".

>Everyone saying "I don't know" clearly wants a beer because,
>if they didn't want a beer, they would know that not everyone
>wants a beer and would answer "no" instead of "I don't know."


The joke has the implicit assumption that each logician would
answer yes or no if asked individually as whether or not
they want a beer. With that assumption, together with
infinitely many levels of recursion about that assumption,
the logic of the joke works.

To eliminate that issue, the joke could be stated as follows.

BEGIN JOKE

Let n be a fixed integer > 1. n logicians walk into a bar.
The barwoman says "Do all of you want a beer?"

Assume that

(A1) Each logician either wants a beer or doesn't want a beer.

(A2) Each logician knows that each of the others either wants
a beer or doesn't want a beer.

(A3) Each logician knows that each logician knows that ...

and so on, for infinitely many levels.

(B1) Also assume that each logician will answer either
"Yes","No", or "I don't know", and will only answer "I don't
know" if they can't deduce the preferences of the others.

(B2) Each logician knows that each logician will answer
either "Yes","No", or "I don't know", and will only answer
"I don't know" if they can't deduce the preferences of the
others.

(B3) Each logician knows that each logician knows that
each logician will answer ...

and so on, for infinitely many levels.

With those assumptions,

The first logician says "I don't know." The second logician
says "I don't know." ... The n-1st logician says "I don't
know." The nth logician says "Yes please".

END JOKE

Of course, the joke should be left as it is, so as not to
ruin it. The goal is humor, not precision.

quasi



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