Bounded vs. Unbounded

Lately I’ve been noticing a general phenomenon that strikes me as shady… comparing something unbounded against something bounded. The top quintile, decile, percentile, or whatever on, say, the income distribution is going to have no limit on the number. Which is why it is possible to have such a huge gap between the median and the mean when it comes to the top 1% in the income distribution, but unlikely at an n-tile beneath the top.

Or… The fact that happiness surveys lay a 1 to 4 or 1 to 10 scale on top of an in-principle unbounded income distribution, or in-priniciple unbounded growth in income over time, seems to me as a reason not to make a huge deal out of the fact that the average score on a bounded scale doesn’t necessarily rise with an essentially open-ended thing like economic growth. If growth is ongoing, and self-reported happiness rises with growth — even excruciatingly slowly — then it is just a logical necessity that there is some time in the future when everybody hits the ceiling of the scale. Even if income and happiness continues to grow, the scale will HAVE to report a flat average, and will HAVE to stop being fully informative. Now, if — as seems to be the case — people have a kind of aversion to putting themselves at or near the top of the scale (if I don’t know how happy I can get, I may not want to say that I’m already there, or even almost there), then you’ve got a case for totally banal scale re-norming that will also produce a flat trend over time, below the top of the scale — again, even if the effect of growth on happiness is ongoing. Perhaps someone can explain to me why this is not considered a huge problem.