The Math Predicts 225 Times More Income Buys About 3 Points of Happiness
Happiness tracks how many times income multiplies, so it takes ever larger fortunes to feel much better.
Astral Codex Ten · Contra Pritchard On Liberal HappinessAmerican output per person is roughly 225-fold what it was in Europe in the year 1000. The math predicts that vast fortune should add about three points of happiness on a one-to-ten scale.
The reason is that happiness rises with the logarithm of income, not with income itself. In plain terms, what counts is how many times income multiplies, not how many dollars are added. Doubling from a small sum adds as much happiness as doubling from a large one, so each extra point of happiness costs more than the last.
In one large American survey, from $10,000 a year to more than $500,000 a year, average happiness rose almost in a straight line when plotted against that multiplied scale. The group averages lined up almost perfectly with the multiplied-income scale, for both momentary joy and overall satisfaction with life.
Apply that line to history, and a 225-fold rise in income predicts about a three-point gain. Suppose the average person in the medieval world would have rated life at three out of ten, if such a rating had been possible. The line would then predict six out of ten for the average person today.
Today we can check this against a poor country. Economic historians in the Maddison Project, a long-running effort to estimate past incomes, put England around the year 1000 at $1,151 per person. The closest modern match is Burundi, at $1,031. When asked to rate their lives, most Burundians answer three or four, while most Americans answer six or seven.
That match is between countries, not between people within one country, which is what rules out the explanation that happiness comes only from being richer than your neighbors. And researchers find no sign that the effect flattens out near American incomes. More money can still buy more happiness, perhaps indefinitely, but it takes ever larger multiplications to feel it.
Questions people ask
Does this mean a raise does nothing for happiness?
No. A raise still helps, and the studies suggest the benefit does not stop at high incomes. It just means equal dollar raises matter less as you earn more, while equal proportional raises matter about the same.
Why use Burundi as a stand-in for medieval England?
Because average income is similar, about $1,000 per person per year, which makes it a useful rough comparison for material life. It is not a perfect match, since medicine, technology, and culture differ, but it gives a real-world check on what low income plus modern survey methods looks like.
Could we ever reach 10 out of 10 happiness?
On this math, it would require enormous further income growth, because each point takes a larger multiple than the last. In practice, the one-to-ten scale also compresses differences at the top, so surveys may understate very high or very low well-being.