Sustainability - Part I

Fun with Tytler's Cycle

The problem

The recent US debt ceiling kerfuffle reminded me of something called “Tytler’s Cycle” attributed to Alexander Fraser Tytler (although the actual origin is in doubt). His central thesis is:

"A democracy cannot exist as a permanent form of government. It can only exist until the voters discover that they can vote themselves largesse from the public treasury. From that moment on, the majority always votes for the candidates promising the most benefits from the public treasury with the result that a democracy always collapses over loose fiscal policy, always followed by a dictatorship."

Maggie was more succinct:

"The problem with socialism is that eventually you run out of other people's money." ---Margaret Thatcher

To tighten up on Maggie's remark, the "you" are free riders and the "other people" are those pulling the wagon.

Since this newsletter is dedicated to measuring things, it seemed to me natural to look for a model in what Tytler said. If democracy is doomed in general, it might be fun to try to figure out just when the worst can be expected to happen.

The model

The [dismal] science of economics is about incentives. People act in accordance with incentives which benefit them (see Darwin for details). A rough sketch of Tytler’s claim looks like this:

It is natural to ask questions at this point. Is Tytler right? We will leave that for last. If he is even somewhat right, where are we on the time table? Also too hard. In the center at the top there is a HUGE change in direction. We will call that a tipping point. Are we on the right or left side of that at present? Still too hard. Let’s start with the easy stuff.

The curve on the left is just this equation, commonly known as a “growth rate”

Where:

e is the base of the natural log, a magic number approximately equal to 2.71828;

r is a rate, a positive number between zero and one. Since the average annual return in the US stock market has been about 9% for a century, for now we will use that as r;

t is time, a positive number represented by the x axis of the Tytler plot, going in the only direction it can; and

a is an “adjustment factor”, a number at the crux of our story

History

A very good book “The Birth of Plenty: How the Prosperity of the Modern World was Created” postulates that in about 1820 several things happened together to launch 150 years of growth and prosperity that changed the lives of humankind in ways that are nearly unimaginable. But here we are. Let’s examine that period as covering most of the left side of Tytler’s plot.

During those amazing 150 growth years a lot of good things happened but also some bad things. In the last third of that period we saw the introduction of all manner of laws intended to “right the wrongs of unbridled capitalism” and fix those bad things. We will not debate the wisdom of these laws now or whether they actually accomplish their stated purpose. That is just more polarizing rhetoric. For now, we are just studying history and reporting what happened.

The last plot above shows values along its vertical (y) axis. It also uses “1” as the value of “a” in the equation that creates the curve. Multiplying anything by “1” changes nothing so we will call using a = 1 the mathematical expression of unfettered capitalism.

So, what if the value of “a” is not “1”? An adjustment factor of less than 1 acts to dampen the rate of growth. As examples, here is what happens when “a” takes on three different values:

Note a few subtleties. One is that falling “a” adjusts the curve downward; another is that if you want an adjustment to 70% of the unfettered capitalism you once had, you must be willing to settle for less than half the Accumulation you would otherwise have over the same time period (compare the far right on the blue line with the far right on the green line).

[Next week: The composition of “a”]