Sunday, June 05, 2005
Log-rolling

When the news turns to economics, we hear great wailing and gnashing of teeth over the "widening gap" between rich and poor, while both rise. This is not a bad thing but a natural consequence of human perception and behavior.

Most of our senses run on the basis of percentage or multiplication. This flies against intuition or common sense, because we don't often have an opportunity to compare our 'common' sense with actual measurement. What we feel as an addition is actually a multiplication, or a rise by percent.

There are only a few situations where we can spot the distinction without using an instrument for comparison. Here's one.... At night, you turn on a 100-watt interior light. This gives you about the same illumination as an open window in daytime, so we can estimate that the sun coming through the window is about 100 watts as well.

You certainly notice the difference between on and off at night. But what happens when you turn the light on in the daytime?

You know that its illumination is about the same as the portion of sunlight that comes through the window, so you'd think that 100 watts of sun + 100 watts of bulb should equal 200 watts, or twice as much light as either one by itself. But in fact, turning on the lamp in daytime makes almost no difference. You'd need to multiply the total by about 10 to give your eyes the feeling of adding another unit.

Though it's less familiar, you can do the same with sound. Take two equal sources, like two portable radios set to the same station and volume, or two electric razors. Run one and estimate the level. Turn on the second one. Should be twice as loud, right? No, it's just a little more. You'd need about 10 sources to get the feeling of twice the sound.

If our perception of economic matters works the same way, we should need a multiplication to sense a step in income or wealth. Not necessarily 10; I'd guess it's around 3. If I make 10K dollars, my neighbor with 30K is one step above me. If I make 120K, my neighbor with 360K is one step above me. This process automatically widens the gap as the base rises.

Look at the stairways. Consider step 1 and step 2 as the 'poor and rich' in an earlier time; then after an overall increase in national wealth, the gap from poor to rich is now between step 2 and step 3. If wealth is measured in an additive way, as on the left stairway, each of these gaps is the same number of dollars.

But on the percentage stairs (right) each gap is the same rise in percentage terms, which means that the gap from poor to rich increases in dollars over the years. This looks strange because we're accustomed to using the actual numbers when dealing with money. With light, sound, or pain, we don't ordinarily use the actual amounts; we only use our senses, which automatically translate the percentage scale into equal steps. So we don't realize that we're using the percentage scale.

Some economists agree with this point, at least in a rather arcane and indirect way. They maintain that 'utility' (i.e. satisfaction) moves by percent. For example, if you have 10 units of happiness right now, it will take 30% more wealth to give you 11 happies. But I can't find evidence that they've done any controlled experiments to prove this. Anybody out there know more about economics?

Moral of the story: Any time you hear an economic report or discussion, notice whether it's based on raw numbers or percentages. If raw numbers, be careful. The reporters or discussers are either ignorant or intentionally trying to fool you.