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

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Paul

Posts: 393
Registered: 7/12/10
Re: Maximisation problem
Posted: Jul 27, 2013 5:33 AM
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On Saturday, July 27, 2013 10:14:46 AM UTC+1, 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, 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,
I agree with everything in your posting. 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? The reasonable choices seem to be n = 2, n = 3 or just leaving n as a variable. n >= 4 just seems to make the joke unnecessarily long-winded.

My preference is n = 2 though you would then say "both" instead of "all" as has been pointed out.

What do you think?

Thanks,

Paul



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