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“Suppose that you work in a restaurant…”

In relation to yesterday’s post on Monty Hall, Josh Miller sends along this paper coauthored with the ubiquitous Adam Sanjurjo, “A Bridge from Monty Hall to the Hot Hand: The Principle of Restricted Choice,” which begins:

Suppose that you work in a restaurant where two regular customers, Ann and Bob, are equally likely to come in for a meal. Further, you know that Ann is indifferent among the 10 items on the menu, whereas Bob strictly prefers the hamburger. While in the kitchen, you receive an order for a hamburger. Who is more likely to be the customer: Ann or Bob?

I just love this paper, not so much for its content (which is fine) but for its opening. “Suppose that you work in a restaurant…”

I get the feeling that econ papers always take the perspective of people who are more likely to be owners, or at least consumers, not employees, in restaurants. Sure, there was that one famous paper about taxicab drivers, but I feel like most of the time you’ll hear economists talking about why it’s rational to tip, or how much a restaurant should charge its customers, or ways of ramping up workers’ performance, etc. Lots about Ray Kroc, not so much about the people who prepare the fries. (When my sister worked at McDonalds, they let her serve customers and make fries—but not burgers. Only the boys were allowed to do that.)

Look. I’m not trying to pull out my (nonexistent) working-class credentials. I’ve been lucky and have never had to work a crap job in my life.

It’s just refreshing to read an econ paper that takes the employee’s perspective, not to make an economic point and not to make a political point, but just cos why not. Kind of like Night of the Living Dead.


  1. jd says:

    Nice point.

    I was following until the second to last paragraph. I won’t attempt to define “crap job”, but how sure are you that you’ve been “lucky” not to have those experiences? Does this make you a bit like one of those econ papers that is single perspective, that you just described in the paragraph before? ;)

    • Andrew says:


      OK, strike “lucky.” Change to “comfortable.”

      • jd says:

        Fair enough haha.

        I’ve had manual labor jobs, but not in a long time. Recently, I was rock climbing with a buddy of mine who is a lineman, and I was complaining about the heat. Knowing that I work in an office, he responded, “Why? Because the air conditioner blows too cold in your face?!” I laughed out loud. So true. He works in 100 degree heat all day, every day. My complaint was the inconvenience that it made recreation more difficult. So, these experiences really change one’s outlook and perspective.

    • jim says:

      Having worked innumerable sh*t jobs in my life, I’d say Andrew’s damned lucky to have never had to. If you think otherwise, read “Down and Out in Paris and London,” by George Orwell. No one wants those jobs. It’s no virtue to have had them. Does it give you a valuable viewpoint? Perhaps. But it’s not worth the cost.

      • Andre says:

        Interesting in “Down and Out…”, I’m writing this here in the case that readers don’t have time to read the book:

        “She was twenty years old old, perhaps; her face was the broad, dull face of a stupid child,
        but it was coated with paint and powder, her blue, stupid eyes, shining in the red light,
        wore that shocked, distorted look that one sees nowhere save in the eyes of these woman. She
        was a peasant girl, doubtless, whom her parents had sold her into slavery”

        This is a great example of the effects of poverty. It wasn’t her choice to be sold into
        sex slavery. I met someone working at a fast food restaurant at some state in America over the summer.
        I’m summarizing incorrectly, but my summary isn’t far from the truth. They, in some facet were above average
        intellect, due to extreme fluency in both Spanish and English, which is why I started a conversation with them.
        They were an immigrant from a Spanish speaking nation, father non-existent, mother also working. They had multiple siblings.
        The person was 18. They had been working at McDonalds for 2 years. They mentioned they were paying rent to help feed their siblings,
        one of which I vaguely remember was not of age to take care of themselves, (infancy, may be 1-3 years old). This
        person was also a student at community college.

        Point being, jobs like working at McDonalds, or Prostitution, are not choice for some people. If you think
        that, in most cases, someone chooses to work jobs like this, you are dissociated from the real world. I’m using
        the word “dissociate” in the psychological sense.

        I’m saying this here because time to pursue intellectual hobbies is, in many cases, an indicator of affluence.

        Great book by the way, thanks for the suggestions. Usually reading Non-fiction, I get to a point in the book and think,
        “Why am I reading this s***?”, but this keeps me interested.

  2. Christopher Marcum says:

    Hey Andrew,

    Thanks to the pointer on the paper; and you’re right that economists generally take the perspective of the upper class in these scenarios. It’s a little demeaning, however, to read that you consider food service a “crap job” since so many of us who haven’t had the same privileges as you started out working in restaurants and blue collar jobs. I, for one, have loved my experiences in those jobs (both of my parents continue to work in those sectors, and they value it a lot) and feel they’ve strongly shaped my work ethic and soft skills as an academic. I know you didn’t mean anything by the comment, though it comes across as flippant.

  3. jim says:

    Speaking to the larger point:

    Econ papers generally take the theoretical perspective that doesn’t exist in real life. :) That’s too bad because so much of economics is applicable to things that all of us do every day, and the average person who works in a restaurant could benefit a great deal from a cogent explanation – just as they might benefit from understanding the Monty Hall problem.

  4. AllanC says:

    I haven’t read the paper in detail but it seems interesting so I’ll be taking a gander this weekend. However, on my brief glance I did find the follow-up to the initial setup (that you quoted) less than satisfactory.

    The problem states the preferences of Ann and Bob but the explanation equates preference with necessary action, at least in the case of Bob. His preference for the hamburger (even if it is a “strict” preference) doesn’t mean he must order the hamburger, at least in the way I define preference. I can strictly prefer to go to my local rink and catch a hockey game on a Friday night but if the team isn’t in town……

    Also, the kitchen received an order for a hamburger…did they receive an order for another dish as well or just the one? If it’s just the one and we knew something about the days of Ann and Bob, which we just might if we have enough knowledge about them to know their food preferences, then that would change the calculus. Etc. Etc.

    Though this doesn’t detract from Bob being the more likely candidate if we have no other available information.

  5. Dzhaughn says:

    Perhasp for an oral exam? “Suppose you, gentle Ph.D. program candidate, are working as a fry cook and want to model the relationship between….”

  6. Nick Adams says:

    The Ann/Bob restaurant thing is the modus tollens (Fisher’s disjunction).
    If we change the number of items on the menu to 20 than this would be a pretty good way to explain a P-value of 0.05 to a neophyte.

  7. Andrew Halim says:

    Hi, anyone read the main article? (

    My question is about the last three paragraphs before the conclusion. The authors were talking about the ESP experiment where people can correctly predict coin-tosses >50%. The result of that study showed that out of the 1,000 students tested, 490 predict at a rate better than chance, 395 at a rate worse than chance, and 115 at the rate of chance.

    Then the authors wrote:
    “However, the researchers’ conclusion is premature, as the observed results can easily occur in the absence of precognition. In fact, this outcome is close to what would be expected if Zener had instructed his students to simply predict a tail whenever the previous three flips are heads—the equivalent of predicting a streak reversal (tails) in the setting of the streak reversal paradox.”

    My understanding is the probability of a tail after a three-streak head is still 50% right?
    The scenario is not restricted and the 4th flip is still an independent coin flip.

    Would anyone have good resources to understand more about this?


    • Carlos Ungil says:

      It’s due to the kind of sequences that will be generated. Looking at the bets, the success rate will be 50%. Looking at the participants, there will be more of them that have a (smaller number of) correct predictions and fewer of them that have a (larger amount of) incorrect predictions.

      For a simpler example, imagine there are two coin flips and the participant predicts head in the first flip. If he gets it right he passes in the second flip, if he was wrong he predicts head again in the second flip. At the end of the experiment 50% of the participants (assuming there are many and we observe the expected rates) will have done “better than chance” (1 sucess / 1 prediction ), 25% will have done “worse than chance” ( 0 / 2 ) and 25% will have done in line with expectations ( 1 / 2 ).

      • Exactly, the bias towards selecting misses when selecting shots after a streak of hits in a sequence of basketball shots is exactly this procedures. Start collecting shots whenever the previous three shots are hits, and stop whenever you get a miss. For a 50-50 shooter, half the time you get a miss immediately, and you stop (100% misses), 25% of the time you get a hit, miss then stop (50% misses), etc. So the starting rule is a random trigger of hitting three in a row, and the stopping rule is a miss. You can replace hits/misses with success/failure and apply to this problem.

  8. I worked around 8 different “crap” jobs during high school and college.

    At the time I didn’t recognize them as crap. I found it validating that they wanted to hire me, and pay me.

    On the other hand, I never kept any of these jobs for more that 3-6 months, so that says something.

    Also, I felt bad for some of the people older than me that were just trying to get by.

  9. Anoneuoid says:

    I have difficulty believing that people would answer something other than “Bob” unless they were severely mistrained to think incorrectly.

    The question is essentially asking whether you can distinguish between precise predictions and vague predictions.

    • Sort of, it comes down to whether you have some kind of jargony understanding of “strictly prefers”. Suppose Alice’s preferences are 1/N for all N items on the menu. Suppose Bob’s are 1/(N+epsilon) for every item on the menu except hamburgers which are (1+epsilon)/(N+epsilon).

      Suppose that on a given day this means Bob basically chooses at random but very very occasionally more often than equal chance, chooses the hamburger.

      Now, technically you should still answer Bob, but the advantage to doing so can be made infinitesimally small by assuming epsilon is small. This ambiguous part of the set-up is confusing.

      The answer is still Bob, but there’s a confusion as to how much information you have because we don’t know what “strictly prefers” means. Someone might thing it’s very very obvious that there’s N:1 odds in favor of Bob, but others might think it’s still very very close to 1:1

      • Anoneuoid says:

        I assumed it means he always orders a hamburger. Ie, p(Hamburger|Bob) = 1

        • That might be what was meant but if so they should have said “Bob always orders a hamburger” because strictly prefers seems to apply to the case where epsilon is greater than but not equal to zero. Your interpretation applies when epsilon is infinite.

          • AllanC says:

            This was the explanation in the paper:

            “By contrast, once we do account for how they choose, then the correct intuition emerges right away: because ordering a hamburger is more consistent with Bob (who must order it) than with Ann (who may order it), the order is more likely to have been placed by Bob.”

          • Anoneuoid says:

            I read on and they say:

            To illustrate, in the Ann and Bob restaurant example, the prior odds in favor
            of Bob being the customer (relative to Ann) are 1:1. However, once a hamburger
            has been ordered, because Bob is more likely to order the hamburger than Ann
            is, the odds in favor of Bob must increase. In particular, if Ann is equally likely to
            order each of the 10 items, then because Bob orders the hamburger for sure, he is
            10 times more restricted to choose the hamburger than Ann. Therefore, the odds
            in favor of the customer being Bob increase by a factor of 10 upon learning that
            the customer ordered a hamburger. Thus, the posterior odds in favor of Bob are

            It is like asking people which person they would listen to about celestial matters after seeing a comet:

            A) Someone who predicted the exact date and time this comet would appear
            B) Someone who predicted a comet will appear sometime in the future

            Obviously A is the more impressive feat.

  10. jim says:


    I think it’s great that you acknowledge that you’re lucky to have avoided working “crap” jobs. You are, and that’s great. Power to ya, you did well by it.

    I understand Christopher’s POV, but as a veteran of many food service jobs the rule is that they are crap jobs. It’s no better as a manager than as a dishwasher.

    My exploration of the broader crap job universe landed me in the hospital several times. Whatever you do, stay in school, kids. :)

    • Andrew says:


      Perhaps the larger point is that events in our life are neither all good or all bad.

      For example, I was unlucky enough (or showed enough poor judgment) to be in an unsupportive work environment for several years, but on the plus side, having colleagues treatment me with disrespect was good in that it gave me a more pluralistic perspective, along with a better understanding of when bad things happen to people. The experience of being disrespected, screwed over, and lied about gave me insights that I don’t think I ever would’ve had, if that job had gone more smoothly.

      For another example, I lost a bit of $ in the 2008 stock market crash. The funny thing is, a few months before the crash, I’d thought about taking my money out of the stock market, but I hadn’t gotten around to doing it. The result was bad for my bank account but it was good for my understanding of the world. Had I happened to have timed my withdrawal effectively, I think I’d’ve ended up with an incorrect and smug view that the crash was easily predictable by the general public. Having the crash happen to me made the challenges much more clear.

      • jim says:

        “I lost a bit of $ in the 2008 stock market crash”

        :) Yeah that was a pretty widespread learning experience! Thankfully I was stupid enough to keep at it and hallelujah the market gods shined on me on the upside. (H/T Warren Buffet).

        Definitely we all should make the most use of whatever experiences we have and for sure the worse the experience the more important the lesson.

        Just the same, why not benefit from being part of a well endowed species? Opposable thumbs are pretty cool, but language is even better. The benefit of language is that it communicates experience across individuals, space and time. (actually, if you think about it opposable thumbs communicate objects across individuals, time and space, right?). So why not make the most of others’ experience? Goodness knows, there are plenty of unpredictable opportunities to screw up.

        In Taleb’s Black Swan I remember him making some argument on the basis of the old adage “if it doesn’t kill me it makes me stronger”. Taleb was wrong: sometimes true. Sometimes not. Tangle with handful of U238 and you will never be stronger because of it. Some things leave permanent marks. We’re better off without them.

  11. Terry says:

    Here be the beginnings of wisdom: “Had I happened to have timed my withdrawal effectively, I think I’d’ve ended up with an incorrect and smug view that the crash was easily predictable by the general public. Having the crash happen to me made the challenges much more clear.”

    Another way to bring home this point is to explicitly try to predict the future about something that will have a clear outcome. Force yourself to actually state that there is an x% chance that y will happen. Will the market go up or down in the next month? Are the claims in this breaking story actually true? Who will win the Texas senate race? What will be the point spread in the Steeler’s game next Sunday? When you do this, the uncertainties swim up at you, and you are often unwilling to make any firm prediction at all.

    You have to do this exercise ex ante. Hindsight bias is so ferocious that it is pretty much impossible to remember all the uncertainties ex post. You tend to remember only certain “premonitions”. Take your stock market example. You probably had many thoughts over your lifetime that you should do x or y with your investments, but the 2008 “premonition” is the one your remember vividly.

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