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Math Help - Brainteaser posed by colleague at work

  1. #1
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    Brainteaser posed by colleague at work

    This one has got me foxed. Please can someone help.....?!

    o Twenty five 'voters' in a voting contest
    o Each with 8 votes to cast - for now we'll assume all voters use all votes
    o Sixteen nominees from which to cast (choose) the 8 votes
    o The 8 nominees with the most votes - in rank order, would be the 'winners'

    o So on the basis that each nominee has, therefore, a potential maximum of 25 votes that could be received, and a minimum of 0 votes
    o What is a likely number of votes that would give x% confidence of being selected?



    Extension to the brainteaser: what if 5 voters only voted with 5 votes - what is the impact on the odds
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  2. #2
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    My feeling is that this problem is underspecified. What exactly are we assuming about voters behavior? Also, are we coming across partial information where voter behavior is random (in which case, we should be thinking in terms of conditional probabilities) or what?
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  3. #3
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    Sorry, you're right, please assume random voting
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  4. #4
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    I haven't worked on this at all, but out of curiosity, do you know for a fact that there is a nice solution to this? Or is this just some random question your coworker cooked up without knowing how to solve? I ask because I don't want to invest time in it if, when solved, it just turns into some terrible mess.
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  5. #5
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    Hi - its the latter. So please don't waste your time unless you want a challenge!!
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