Financial Mathematics Text

Tuesday, November 20, 2012

On the Existence of Santa Claus

While this is a very broad topic which this one blog cannot do justice, I would like to consider one argument against the existence of Santa Claus in more detail. The strategy will be to show that this argument is inadequate given two considerations.

The crucial piece of evidence for this argument is a statistical tendency for children of wealthy families to receive gifts totaling a higher value than children of poor families. This leads to two general claims.

1) The divergence of gift values between rich and poor can be explained by the general income/wealth divergence of the families to which they reside.

2) If the gifts came from Santa Claus we would not expect to see this anomaly.

Therefore, the distribution of gifts is best explained as richer parents giving more/expensive gifts than poorer parents. As such, Santa Claus does not exist. 

To be perfectly clear, I do not dispute the fact that the difference in wealth and income could explain why rich children tend to receive a higher gift value than poor children. So I will leave the first premise alone. The remainder I shall discuss two workarounds for the second premise of the argument.

The general insight is this: Premise (2) supposes that Santa Claus is "egalitarian"; in other words, Santa Claus distributes gifts equally. I claim this may be, in fact, false given two considerations.

Observation 1

It is clear from what we know about Santa Claus that he rewards good behavior with good gifts and bad behavior with bad gifts. It is even said that naughty children will receive a lump of coal. Even when the price of coal peaked in 2008 at around $150/ton, that's still less than 10 cents per pound.

As a result, it may be the case that rich children are simply better behaved than their naughty poor counterparts.

Observation 2

Another reason Santa Claus may not be egalitarian is that he may subscribe to a view I dub trickle-down giving. The idea is quite simple; there are many ways in which giving more to rich children actually benefits poor children. Here are two examples:

1) After a rich child is done playing with a toy, that toy can be given to a place like Good Will where poor children will have the opportunity to purchase the item at only a small cost.

2) But even while a rich child has possession of the gift, they may invite their poor friends over to enjoy the toy with them. And since rich children may be better behaved, they may be more likely to share their toys.

Given these two observations, I have reason to doubt the second premise in the argument above. As a result, I conclude that the argument fails to rule out the existence of Santa Claus. Both the relative merit of rich versus poor children and trickle-down giving provide insight as to why rich children tend to receive more gifts than poor children.

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