Last Christmas I wrote about Santa’s present delivery process. This year, we’re going to talk about the Naughty and Nice List. So first, let’s examine what we know about the process: “He’s making a list. He’s checking it twice. Gonna find out who’s naughty and nice…” So from this we can assume that Santa himself is the administrator of the list and the list is apparently managed in real time — otherwise he would not have to check it twice. If there were a freeze date for list modification on say, December 22nd, the list at that date would be static and he could rely on its entries for delivery purposes. This also implies that Santa is getting real time data feeds as he’s delivering presents so each child’s aggregate score may be fluctuating even as Santa approaches his house or apartment. Clearly, though, once Santa is on your roof, he has to take the score as it’s computed at that time. If you’re doing something really, really naughty as he comes down the chimney, that won’t count against you this year.
The fact that he has to check it twice seems to indicate that Santa’s memory is faulty or that there is a real possibility of the list changing while he’s looking at it. Since Santa is really a wood spirit and wood spirits generally have good memories, we are pointed back to the probability of a highly volatile Naughty and Nice list.
The determination of being naughty or nice appears to be a transactional process. For the sake of argument, lets call the atomic transactions “behavioral transactions” or B-trans. To have a positive or negative effect, the B-trans must therefor have a scalar value of either positive or negative character and that value must be proportional to the naughtiness or niceness of the behavior being assessed– otherwise a really heinous act like burning down an orphanage could be wiped out but a relatively minor nice act, like not stepping on a petunia.
Thus, there is an aggregate score a child must earn to be termed naughty or nice. Since we have all observed known naughty kids receiving presents and known nice kids getting squat, we must assume that either or both of two additional factors are considered: confidence intervals and trending.
The confidence interval concept would allow a buffer zone for those whose aggregate score may be right around the naughty/nice boundary layer. How those children would be rated clearly must depend on additional factors. Probably the most reasonable is trending.
Trending would allow weighting for those who while right on the line between naughty and nice but who have tended to be nicer recently to be given the benefit of the doubt that they are on the road to niceness and that even though they have an aggregate score that puts them in the naughty category, they are treated as nice. Or conversely, a child who is generally nice but has been trending naughty could be categorized as naughty despite having an aggregate score that would be considered as nice.
For behavioral forecast accuracy, the most reasonable approach for trending adjustments would be an auto-regressive time series analysis — that is, a child’s behavior today is most likely influenced by their behavior yesterday, and less so by their behavior the day before, etc. Thus someone who was trending nice would probably continue toward nice, and one who was trending toward naughty should probably have the snot beaten out of them.
Clearly, the influence of the confidence interval and trending would only affect those children who were marginally naughty or nice. Genuinely nice children would have to do something pretty horrible to tip the scale to the naughty side; and genuinely naughty children would have to do something way out of character on the positive side to get to the nice category.
Given the above, it is probably safe to assume that by mid-year, your categorization as naughty or nice is pretty well sealed. So, by extension, for those solidly on the nice list by, say October, you’d pretty much have to turn axe-murderer to flip to the naughty side. And for those solidly naughty, you’d pretty much have to turn into Mother Theresa on steroids to get to the nice side.
So to all you truly nice kids out there, it’s too late to anything to make the naughty kids like you. And to the naughty kids, I can tell you where to go to buy beer.