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

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quasi

Posts: 9,903
Registered: 7/15/05
Re: Maximisation problem
Posted: Jul 27, 2013 6:16 AM
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pepstein wrote:
>quasi wrote:
>>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


I'm no longer so sure of my claim below about infinitely many
levels of recursion.

>>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.


A1 and A2 seem necessary, but I don't now see any need for
further levels. I don't know what I was thinking.
>>
>> (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.


Once again, as far as I can see, B1 and B2 are needed, but I
don't see a need for further levels. Then again, right now I'm
very tired, so maybe I'm not thinking it through all the way.

>> (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,
>
>I agree with everything in your posting.


I think you agreed too quickly.

I now think the stuff about infinitely many levels is nonsense.

>Would you be so kind as to answer the question I opened the
>thread with? Which value of n do you think makes the joke work
>best?


I like n = 3 best.

n = 2 wraps up too quickly, with no suspense.

n = 4 or higher is too long-winded.

Leaving n unknown is too abstract, suggesting more conceptual
depth than is actually there.

quasi



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