Thursday, December 12, 2013

The mathematics of being a jerk

On Tuesday I was heading into the subway when I was faced with a snap decision - the doors were closing and I could leap towards the train and probably end up being caught in the doors or just stand there and wait.  In a move that should surprise no one I made the leap and the doors closed on me as I was halfway through.  They opened again of course as I squeezed myself onto the train and then a few seconds later we all chugged on our merry way south.  Then I began thinking about whether or not this makes me a jerk for making everybody else wait a few extra seconds to get on their way.

Obviously the inconvenience I cause to others is small but there are a lot of others being inconvenienced.  I estimated that there were two hundred people on the train and that my little escapade delayed their travel by about four seconds.  Eight hundred seconds of delay is roughly thirteen minutes of wasted time and since the next train is likely to come along in six minutes or so I wasted seven minutes of total human time.  Mathematically speaking it looks like I am a jerk.

There are complications of course.  If there is already somebody else getting caught in the doors and delaying the train then my aggressive move costs nothing and is entirely pragmatic.  This scenario seems highly unlikely given the particulars of the platform I was on but is not out of the question.  The more relevant issue is the probability that I make it just in time and avoid catching myself on the doors.  Clearly in retrospect that probability is 100% but when making the decision I did not know that; I knew for sure that I would get on that train but not how clean the entry would be.

I wonder if I am the only one who reacts to getting caught in train doors by counting the other passengers so I can determine if I am a bad person or not.


  1. I do similar things while driving. I make no claims that this makes you normal though....

  2. I don't agree with your analysis. Just because people end up spending an extra 4 seconds here does not mean that the cost to them is 4 seconds. You may make someone miss a connecting train by 2 seconds and have to wait 6 minutes, so you've cost that person 6 minutes. Or maybe someone is going to an appointment and are just going to be waiting around at the doctor's office instead. You've just changed where they are waiting. If the person is headed into work, you've robbed their company of 4 seconds of time, not them personally. I would expect that with high probability you're impact is negligible (likely even net positive, counting your time) and with small probability you're a huge jerk.

  3. It is certainly true that I didn't rob each person of 4 seconds. Most of them I robbed of nothing and some I robbed of more than that due to connections, appt times, etc. However since I can't possibly evaluate those things I think a reasonable approximation is to use the amount of time I delayed the train. If you have a better method I would be happy to use it, but I doubt one such exists.

  4. There's also another part of this equation. The shiny new subway trains, the Toronto Rockets, have a "safety feature" (read flaw). If the doors on a train are blocked 3 times from closing, then the door system goes into a failsafe mode, and need to be reset, and useally that happens at a yard.

  5. Define "better method". We can certainly come up with a more accurate calculation of how much your selfish action wasted the time of others, but to do so we would need more data. Consider just the question of missed connections: if you could gather some information about what routes people were taking on transit at that particular time of day, then that gives you a rough distribution for how many people on your particular train are going where. Then checking that against the various bus schedules at the "downstream" stops, you can get estimated probabilities that people are going to be missing their buses.

    Alternatively, you could consider this a tragedy of the commons-type scenario: the cost to the population as a whole is minimal in the case of one infraction, but what if this was the norm? If everyone did the same thing, then the guy who was three seconds behind you gets to do the same thing when the doors bounce for you... and then the woman four seconds behind him... and so on. (Some queuing theory could be applied to determine the mean length of such chains, I suppose.)

  6. I make similar calculations with the elevator and whether to hold it for someone and/or whether I should I rush it. The added variance of which floor people are going to makes it fun. If they're below 15, holding costs me, but rushing doesn't really cost them.

    The new trains no longer get disabled when the doors jam 3 times.

    Using math, you're a jerk. But much like you can tax everyone a small amount for a special interest and they don't really mind/notice, I suspect you can get away with it without feeling too bad.

  7. There's a big assumption in your calculations: that the "best" solution is the average time taken. As a regular commuter, reliability (the standard deviation if you will) is far more important to me than the average time or rather, I insist that I have a >99% chance of arriving on time. While most of the time, aggressive actions might have minimal effect, when they do the delay is prolonged. It's unlikely, but getting caught in the door could mean a much larger delay should an injury or malfunction occur.

    In order to account for a greater standard deviation (even in the car driving situation where a shorter average time occurs) I have to leave much earlier in order to guarantee a sufficiently accurate result. This means I'm wasting far more time waiting around than would be necessary with passive people despite a lower average speed.

  8. I think LeBKC has it. We can't calculate the actual time wasted by any given person without knowing a lot about their circumstances, but we can observe the wide effect on people's behaviour that results from knowing that people, in general, cause jams in order to get on trains/elevators/off-ramps, etc.

    But there is an extra complicating factor. If a train I personally catch is significantly delayed in the morning then I might get to work late Then if someone notices I'll say, "Sorry, the subway had problems." By making me 5 minutes late you've actually *saved* me from 5 minutes of being at work. On the other hand, assuming this is a normal morning for me, you've also replaced those 5 minutes with 5 minutes of wrangling a toddler who doesn't understand why things are happening.

    I'm not sure which I prefer.

  9. You're also forgetting those people who will get on the train later who would otherwise have MISSED their connection. You are delaying your train so theirs will catch up...