The roses in your garden are dead and your gardener tells you that there are bugs that have to be killed if you want the next generation of roses to survive.  So you pay him to plant new roses and spray poison to keep the bugs away.

Each week he comes back and tells you that the bugs are still threatening to kill the roses and you will need to pay him again to spray the poison to keep them away.  This goes on and on.  At what point do you stop paying him to spray poison on your roses?

Keep in mind that if there really are bugs waiting to take over once the poison is gone, you are going to lose your roses if you stop spraying.  So you are taking a big risk if you stop.  On the other hand, only he really knows for sure if the bugs are threatening, you are just taking his word for it.

Now add to that the possibility that the poison is not guaranteed.  You may have an infestation even in a week where he sprays.  Of course this only happens if the bugs are a threat.  If you spray for many weeks and you see no infestation this is a pretty good sign that the bugs are not a threat at all.

If you do stop spraying at some point, on what basis do you make that decision?  Assuming he is spraying vigilantly you would optimally stop after many weeks of no infestation.  You would continue for sure if one week the bugs return even though he was spraying.

But you don’t know for sure that he is actually spraying.  You are paying him to do it, but you are taking his word for it that he is actually spraying.  If you assume that he is doing his job and spraying vigilantly, and you therefore follow the decision rule above, and if we wants to keep his job then he won’t be spraying vigilantly after all.

So what do you do?