by Will Clark

Well, what with holiday shopping, finals, and a raft of other time-vacuuming obligations, the interval between my posts here has lapsed to much more than two weeks once again. However, do not think that I have abandoned you, dear reader. Despite the crush of year-end commitments clamoring to fill my time, I have devoted some of it to the ongoing discussions here in Grammapolis, and as proof, I offer some snippets of data for your holiday perusal.

Several months ago I began a project far too ambitious for the time I had available, namely a simulation of a rogue investment group devoted to fostering equality through unpredictability. Needless to say the simulation is far from finished, but preliminary testing of the income distribution engine has revealed some interesting (and rather absurd) patterns.

The first tests I ran started as follows. Each of 300 participants received 33,000 dollars. Sixty percent worked to earn a five percent profit for the year. They were, in other words, gainfully, but not lucratively employed***. Twenty percent bet a random percentage of their money with a fifty-fifty chance of winning. These are regular Joes betting in the stock market. Ten percent of people ventured their capital with a ninety percent chance of losing ten percent of it, and a ten percent chance of an eighty percent return. These are capitalists who risk their money to attempt to create wealth. Naturally their success rate should be low. The rest did nothing. Then everyone was subject to an eighty percent chance of losing 2 percent of their wealth and a twenty percent chance of gaining two percent. Let’s call that an entropy tax. The universe is hostile.

Guess what happened? Repeat this for 100 years, and the steady earners soon have more money than almost anyone. The bettors and venture capitalists, with a few exceptions, settle into a truncated bell curve at the bottom of the income distribution, and occasionally some lucky soul becomes Richie Rich. This is absolutely not realistic. Nor is it what I expected. I figured that the number of winners in venture capital and the stock market would push the steady earners into the center of the income distribution, and it does, but only the short term. In the long run, steady returns outgrow everything else. In other words, steady, predictable returns result in an enormous, rich upper-middle class. Because my mathematical intuition is dismal, I did not see this coming. Still, some back of the envelope algebra makes everything pretty clear: A = P * 1.05^x should instantly outgrow something like A = P * ( 1.8^(0.1x) ) * ( 0.9^(0.9x) ), which, after all, is doomed to shrink over time as probability has its way with those betting against the house. In fact, unless anyone else can come up with a way to match exponential growth, that 5% per year will outstrip everything in pretty short order. Perhaps my probabilities were artificially inimical, (Ok, they definitely were.) but the point is clear enough.

The data provide evidence in favor of two of my basic tenets. First, random chance does generate a large middle class. Excluding the steady earners, those who risk their money on unpredictable bets fall into a pretty nice bell curve. Second, predictability is an extraordinarily powerful factor in determining who rises to the top of the income distribution.

When I next get around to this, I’ll set up a far more sophisticated model for economic growth and money flow, but I’ll post one round of histograms here just to give you an idea of what happens when a group has the power to earn a steady percentage year in and year out, with little risk to their capital. It’s pretty scary:

***Just realized why it's so scary. These "steady workers" are earning 5 percent on their assets. That makes them more like the aristocracy of nineteenth century Britain. No wonder they're trampling over everyone... Still, it just goes to show the power of reliable investment data.

Well, what with holiday shopping, finals, and a raft of other time-vacuuming obligations, the interval between my posts here has lapsed to much more than two weeks once again. However, do not think that I have abandoned you, dear reader. Despite the crush of year-end commitments clamoring to fill my time, I have devoted some of it to the ongoing discussions here in Grammapolis, and as proof, I offer some snippets of data for your holiday perusal.

Several months ago I began a project far too ambitious for the time I had available, namely a simulation of a rogue investment group devoted to fostering equality through unpredictability. Needless to say the simulation is far from finished, but preliminary testing of the income distribution engine has revealed some interesting (and rather absurd) patterns.

The first tests I ran started as follows. Each of 300 participants received 33,000 dollars. Sixty percent worked to earn a five percent profit for the year. They were, in other words, gainfully, but not lucratively employed***. Twenty percent bet a random percentage of their money with a fifty-fifty chance of winning. These are regular Joes betting in the stock market. Ten percent of people ventured their capital with a ninety percent chance of losing ten percent of it, and a ten percent chance of an eighty percent return. These are capitalists who risk their money to attempt to create wealth. Naturally their success rate should be low. The rest did nothing. Then everyone was subject to an eighty percent chance of losing 2 percent of their wealth and a twenty percent chance of gaining two percent. Let’s call that an entropy tax. The universe is hostile.

Guess what happened? Repeat this for 100 years, and the steady earners soon have more money than almost anyone. The bettors and venture capitalists, with a few exceptions, settle into a truncated bell curve at the bottom of the income distribution, and occasionally some lucky soul becomes Richie Rich. This is absolutely not realistic. Nor is it what I expected. I figured that the number of winners in venture capital and the stock market would push the steady earners into the center of the income distribution, and it does, but only the short term. In the long run, steady returns outgrow everything else. In other words, steady, predictable returns result in an enormous, rich upper-middle class. Because my mathematical intuition is dismal, I did not see this coming. Still, some back of the envelope algebra makes everything pretty clear: A = P * 1.05^x should instantly outgrow something like A = P * ( 1.8^(0.1x) ) * ( 0.9^(0.9x) ), which, after all, is doomed to shrink over time as probability has its way with those betting against the house. In fact, unless anyone else can come up with a way to match exponential growth, that 5% per year will outstrip everything in pretty short order. Perhaps my probabilities were artificially inimical, (Ok, they definitely were.) but the point is clear enough.

The data provide evidence in favor of two of my basic tenets. First, random chance does generate a large middle class. Excluding the steady earners, those who risk their money on unpredictable bets fall into a pretty nice bell curve. Second, predictability is an extraordinarily powerful factor in determining who rises to the top of the income distribution.

When I next get around to this, I’ll set up a far more sophisticated model for economic growth and money flow, but I’ll post one round of histograms here just to give you an idea of what happens when a group has the power to earn a steady percentage year in and year out, with little risk to their capital. It’s pretty scary:

***Just realized why it's so scary. These "steady workers" are earning 5 percent on their assets. That makes them more like the aristocracy of nineteenth century Britain. No wonder they're trampling over everyone... Still, it just goes to show the power of reliable investment data.

Iteration 0 :

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As you can see, one round of betting puts the lucky guys on top, the unlucky guys at the bottom, and the hard working, salt-of-the-earth types right smack in the middle. This is intuitive. Now, wait thirty years:

Iteration 30 :

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There is now exactly one man in the top bracket. The steady earners are dominating the economy, each with assets worth 93% as much as the top earner's. Even the do-nothings have assets only worth about 20% as much as the top earner, and many of the the bettors have fallen into the single digits.

And after ninety years?

Iteration 90 :

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Society is completely stratified. The steady earners in the upper middle class have become the upper class. Everyone in it has about the same worth. The bettors have all fallen to asset levels that are only a few percent of that owned by the steady earners.

The lesson here? Predictable returns can lead to startling inequality between classes, while at the same time fostering high levels of equality within classes. Is the solution to attack the predictability of these people's returns? Or will that drive everyone into the sort of decay curve we see the bettors trapped in? Clearly much will depend on probabilities, which I promise to represent increasingly accurately.

For now, though, interesting stuff, but utterly unrealistic. Stay tuned for a more true-to life simulation next time, in which half the people the economy are not Warren Buffet.

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As you can see, one round of betting puts the lucky guys on top, the unlucky guys at the bottom, and the hard working, salt-of-the-earth types right smack in the middle. This is intuitive. Now, wait thirty years:

Iteration 30 :

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There is now exactly one man in the top bracket. The steady earners are dominating the economy, each with assets worth 93% as much as the top earner's. Even the do-nothings have assets only worth about 20% as much as the top earner, and many of the the bettors have fallen into the single digits.

And after ninety years?

Iteration 90 :

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Society is completely stratified. The steady earners in the upper middle class have become the upper class. Everyone in it has about the same worth. The bettors have all fallen to asset levels that are only a few percent of that owned by the steady earners.

The lesson here? Predictable returns can lead to startling inequality between classes, while at the same time fostering high levels of equality within classes. Is the solution to attack the predictability of these people's returns? Or will that drive everyone into the sort of decay curve we see the bettors trapped in? Clearly much will depend on probabilities, which I promise to represent increasingly accurately.

For now, though, interesting stuff, but utterly unrealistic. Stay tuned for a more true-to life simulation next time, in which half the people the economy are not Warren Buffet.