Sunday, November 29, 2009

The Paradox of Happiness

Disciplines are always most interesting when they cross with other disciplines and the economics of happiness is no exception. Talking to some of my friends the other day (one versed in anthropology and another in psychology), we noted how much people value a sense of genuine accomplishment and is probably why, in some cases, wealthy people aren't as happy as less wealthy people. (Setting aside the lower mortality rates in poorer societies.)

For example, the people of the indigenous tribe that must work every day to get a meal are going to be happier (assuming they are successful) than the middle management who, while isn't concerned about getting his next meal, has no sense of accomplishment and feels as though his life is wasted. (This, by the way, is how many mid-life crises take root.) Indeed, people who have the option to leave their tribe in favor of modern life tend not to take it (I know this is very common among the Amish, and I'm sure a similar story can be told for other groups).

However, I argue that the wealthier, accomplished person will be happier than the less wealthy accomplished person ("accomplished" being defined as the standard of the society...for example, getting a book published in the wealthier society versus bringing home a kill in the less wealthy one). Some expressed doubt to the claim, so here's my reasoning.

First definitions: p (probability of achieving an accomplishment); S (happiness from achieving survival); s (happiness from surviving); A (happiness from achieving something else); and a (happiness from that something else). This draws the distinction, for example, between the sense of achievement from a book published and the royalties received from getting a book published. Note I'm also assuming it's equally likely to achieve something in a rich society and in a poorer society. This is primarily to make the math easier.

A person would be indifferent between two societies if:

p(S+s) = p(A+a)+s,

where the right-handed side is the wealthier society (they get the benefits of survival without trying) and the left-handed side is the indigenous society. Simplifying reveals:

S-A = a+((1-p)/p)s

In other words, there must be a larger sense of accomplishment from surviving than from other accomplishments to make a person indifferent. To make a person prefer the less wealthy societies (which I strongly doubt), the premium (S-A) would have to be greater than a+((1-p)/p)s, which I doubt since both values are positive and a might well be quite large.

Now consider the scenario when p=1, or when you are comparing people in each society who have made achievements (either in survival or in something else). The equation becomes:

S-A = a

If we think of such individuals in each society as sharing common traits (intelligence, drive, etc), then this means that more capable people are less likely to prefer modern society compared to less capable people--it all depends on the additional satisfaction derived from achieving survival versus achieving something else. While I imagine this premium to be quite small, the fact that this (simple) model predicts "stronger" people are more likely to prefer an environment that is more dangerous seems to be quite the paradox.

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