The Procrastinator’s Clock

Someone has developed a procrastinator’s clock that is probabilistically inaccurate.  The idea behind the clock is that if you merely set your clock ahead by, say, 10 minutes then you know the clock is always ten minutes fast and so you will adjust accordingly.  But this probabilistic clock is always somewhere between 0 to 15 minutes fast.  Consequently, you never know the correct time and so can’t correct for the clock’s inaccuracies.  The clock, therefore, is supposed to increase your punctuality by deliberately introducing bias into your timekeeping.  Many bloggers have linked to it.  But I don’t think that the probabilistic clock will decrease the average cost to you of your tardiness. 

Let’s assume that you get a constant benefit for every second you procrastinate, but the cost of being late increases.  With an accurate clock you will procrastinate until at the margin the benefit of procrastinating another second equals the cost of being one more second late.

With the probabilistic clock you don’t know how late you will be, so you don’t know the exact cost of being another second late.  But you can estimate the time and so can estimate the lateness cost of procrastinating another second.  So with the probabilistic clock you will procrastinate until at the margin the benefit of procrastinating another second equals the estimated cost of being one more second late.  On average, therefore, the lateness costs you will suffer will be the same with the accurate and probabilistic clock. 

For reasons I haven’t detailed I suspect you will on average be less late with the probabilistic clock.  But because you will sometimes be extremely late with the probabilistic clock (more late than you would ever be with the accurate clock) the average lateness cost to you if you use the probabilistic clock equals the lateness cost to you if you use the accurate clock.

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  • anon

    the makers of the clock would assume that there is inherent irrationality in its users, otherwise there would be no need for one. if the subject is rationally judging the cost of procrastination, as you assume, they would be doing themselves a disservice by using anything other than accurate time.

  • anon: The “irrationality” we’re trying to overcome by using this kind of clock is the kind usually called (I think) time-dependent preferences. When it comes time to leave for an appointment, you don’t want to go as much as you want to keep doing some other thing, but ten minutes ago, you would have preferred your present self to be leaving now. That’s not strictly irrational, (nor a bias, incidentally,) so it’s compatible with the kind of accurate time cost judgment James describes.

  • Zhong Lu

    If you don’t have the discipline to leave for work on time, no clock is going to help you, probabilistic or otherwise.

    The probabilistic clock is for suckers who spend money to hide themselves from their personal flaws.

  • Andy

    You’ll be less late if the cost of lateness is concave up but the benefit is linear or concave down, no? Jensen’s inequality for time management…

  • Because the probabilistic clock requires you to estimate the time, it will make you better at estimating the time. This may make you less of a procrastinator. You still have to want to overcome the habit. I know, I did it.

    My incentive was workplace approval. Until my mid-30s, I had always been self-employed. My customers were so glad to see me arrive to fix their computer, they didn’t mind I was late. Yup, typical insensitive computer tech, I was. Once I became a management consultant, I had to be punctual because there were conference rooms full of people awaiting my arrival, people who had schedules. They were upset, and my bosses were upset, if I was late.

    I never did take to wearing a watch. But I became very punctual. Learning to have an “internal clock” to estimate time elapsed was key. Any gimmick that assists you in doing that should be helpful.

  • Zhong Lu

    But Bob, by your comment, “my incentive was workplace approval,” it appears you managed to become punctual without any gimmick at all.

    Who has become more punctual using a “procrastinator clock?” I think that’s the best way to settle the question of the usefulness of such a clock.

  • Alex H

    I think anon is on the right lines, whilst James Miller has cited the correct argument; though not given any time to the trap of a kind of “preselection”.

    Whilst it is true that the rational agent will procrastinate up until the point where the benefit of procrastinating exceeds the cost of being late no longer; the kind of person who would take the time in sourcing a “procrastinator’s clock” clearly recognises their time keeping issues and is thence seeking to always be on time. Acting rationally therefore; the owner of a procrastinator’s clock derives maximum utlilty from being on time.

    If the agent knows that the probabalistic clock is always between 0 and 15 mins fast, how he will act will depend on his preferences. The underlying assumption of this argument (i have assumed!) is that the utility from time spent procrastinating before leaving for an appointment is greater than time spent waiting on arriving early. How great the difference is unique to an individual. If negligible, an individual will make an estimate of the real time closer to 15 mins fast “to be safe”, whereas an individual who detests waiting will be more generous in their estimate of the clock speed and assume a lower average time gap.

    The interesting thing is that the more the individual knows about the workings of the clock, the less useful it will be. If your girlfriend is always late, best switch her clock with a probabalistic clock and not say anything!