• Dagwood222@lemm.ee
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    6 months ago

    Great Hollywood story about the curse of Ishtar.

    They send a team ahead of the main unit to set things up. One of their tasks is to buy an ugly camel, because the script calls for them to have the worst camel ever. The team goes to the camel market and the first camel they see is hideous, the the guy in charge says that they can’t just buy the first camel they see. Over the next few days they see dozens of camels, and everyone agrees that the first was by far the ugliest. The boss admits his error and goes back to the first seller.

    “Sorry, you can’t have that camel.”

    “Why not?”

    “We ate him”

    The moral of the story is “Buy the first camel.”

    • tal@lemmy.today
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      6 months ago

      The moral of the story is “Buy the first camel.”

      Nah, there’s information to be gained via the selection process.

      https://en.wikipedia.org/wiki/Secretary_problem

      The secretary problem demonstrates a scenario involving optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan’s dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also known as the 37% rule.

      The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of n rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.

      The shortest rigorous proof known so far is provided by the odds algorithm. It implies that the optimal win probability is always at least 1/e (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality. The optimal stopping rule prescribes always rejecting the first ∼n/e applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the 1/e stopping rule, because the probability of stopping at the best applicant with this strategy is already about 1/e for moderate values of n. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.