In a silent room, you can hear a pin drop; in sunlight, the brightest torches seem dim. £100 is a lifeline to a starving man, but a trifle to a millionaire. Yet our politicians and news media go on obsessing over measures of the economy which bury this distinction - Gross Domestic Product (GDP) or its derivative, GDP growth. £100 counts for just the same whether it's money going from the wealthy to the poor, or a redistribution of wealth from the relatively poor to the already-rich, which is more likely.
There are many other problems with GDP, or the theoretically equivalent Gross Domestic Income, but this one at least admits a relatively simple solution. Just as pay rises are often expressed as a percentage of pay, we could be using a measure of income or consumption which counts any increase relative to how much someone already had. To do that, we just take the logarithm (or 'log') of one of those values.
For anyone who's not sure how logarithms work, the logarithm of 10 is 1, log 100 is 2, log 1000 is 3, and so on. In other words every time something gets 10 times bigger, its logarithm increases by 1. Every time something doubles, or increases by any fixed proportion, its log also increases by a constant amount.
That means that giving someone a 10% pay rise makes the same difference to log income regardless of their starting point: for example, giving £1,000 more to someone on £10,000 a year makes the same difference as giving £10,000 to someone earning £100,000. It raises the first from 4 to 4.041, and the second from 5 to 5.041. On the other hand, giving £1,000 to the person on £100,000 only increases their log income to about 5.004; we can raise the average log income (let's call it ALI) far more with a fixed amount of money by giving it to people with less to start with, just as we make far more difference to their lives that way. The ALI for existing economies ranges between about 2.5 and 4.5.
So what are the advantages of taking the average log income of a country, rather than just the average income, which is more-or-less what GDP per head measures? As noted, we would be accounting for income in a way that is more akin to how people think about pay rises, and the subjective meaning of wealth. In fact, there is strong reason to think that personal well-being is approximated far better by log income than it is by net income, and I would argue that the ultimate purpose of any economy is to further the well-being of people. ALI is far simpler to assess than attempts to measure well-being using surveys and similar instruments, like Bhutan's Gross National Happiness index, and less prone to disagreements over definitions and priorities.
ALI reflects the inequality of an economy, without directly measuring it; it doesn't suffer from what is often seen as a major pitfall of inequality measures like the Gini coefficient, which is that they tend to show a decrease in the income of the rich as a gain, even if it comes about without making the rest of the population any better off. Of course not everyone agrees this is a problem - there is a case for saying that inequality is inherently bad, and a related measure called the Social Welfare Function (SWF) generalises ALI to take this into account. Both measures also avoid the distortions that result from anything based on cut-off lines below which someone is declared to be sufficiently poor, and require little extra data to be collected.
As I mentioned earlier, there are many other problems with GDP that ALI doesn't attempt to directly address, but I think ALI has a strong claim to preserving all of its main advantages; GDP is a massively flawed statistic, but it is not totally worthless. That makes it likely that we will go on using some related measure, and it strikes me that ALI fits the bill nicely, while anything else we do to fix up GDP ought to transfer well to ALI. Don't take my word for it, though. I've never claimed to be an economist, and I am no doubt missing many subtleties here. Perhaps ALI has major flaws that I can't see - if you're an economist or just a thinker, or you know any you could ask, I would love to know if you can find any.
I first heard of this idea in this blog post, from which I drew the figures for existing ALI, and which eventually led me to this paper on happiness and income inequality, which backs up the point about log-adjusted income being much better correlated with well-being than plain income. It also led me to argue, in a blog entry which I haven't re-posted on Everything2, that ALI is the obvious solution to one of the four greatest mistakes our society is making, namely our obsession with GDP growth. The author of this thesis on social welfare pointed out that ALI is a special case of SWF, and the philosopher Tim Scanlon makes an excellent case against inequality based on both its negative consequences and other concerns in this 15-minute episode of 'Philosophy Bites'. For more inherent problems with GDP, here's a fine piece from the undercover economist, Tim Harford.