Ponzi Schemes and Sigmoid Curves

Steven Dutch, Natural and Applied Sciences, Universityof Wisconsin - Green Bay
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A Note to Visitors

I will respond to questions and comments as time permits, but if you want to take issuewith any position expressed here, you first have to answer this question:

What evidence would it take to prove your beliefs wrong?

I simply will not reply to challenges that do not address this question. Refutabilityis one of the classic determinants of whether a theory can be called scientific. Moreover,I have found it to be a great general-purpose cut-through-the-crap question to determinewhether somebody is interested in serious intellectual inquiry or just playing mind games.Note, by the way, that I am assuming the burden of proof here - all youhave to do is commit to a criterion for testing.It's easy to criticize science for being "closed-minded". Are you open-mindedenough to consider whether your ideas might be wrong?


Growth Curves

The real "Inconvenient Truth" for many people is that unlimited growth is impossible in a finite world. Many people prefer the illusion that exponential growth can continue forever, at an ever accelerating rate.

Real growth curves are sigmoid - they look like highly slanted S's (hence the name), integral signs (�ˆ�) or italic f's. The early part of the growth curve does indeed look exponential, and in many cases it's the product of positive feedback in which every change acts to produce more of the same. Introduce rabbits to an uninhabited lush island and they will have baby rabbits. Those in turn will mean even more rabbits having litters, which will mean more rabbits ....

But sooner or later negative feedback kicks in. Every change strengthens some factor that opposes change. On our island above, the rabbits will eventually eat all the vegetation. Every new rabbit makes life harder for all the others. Mortality increases as undernourished rabbits with weakened immune systems succumb to disease. Fertility declines as rabbits are weakened by hunger, and infant mortality increases. Maybe the population will tend toward a steady limit. More likely the rabbits will have one last bumper crop of babies before the crunch comes, overshoot the carrying capacity of the island, and die off en masse. Or maybe the die-off will be moderate and set the stage for another overshoot and die off in an ongoing cycle.

It can be possible for growth to continue sustainably - for a short time - if the system itself grows. If sea level drops and the rabbits' island becomes bigger, or waves keep piling sand on the shore. But this sustainability can only last a short time. Sooner or later sea level will stabilize, and in any case exponential growth accelerates ever more, and eventually outstrips any growth in the size of the system.

The point where the growth curve stops accelerating and starts decreasing is called the inflection point. It is our dubious good fortune to be living near the inflection point of many of our growth curves. One real instance is thedemographic transition, where population growth levels off as children become economic burdens rather than assets. Most developed countries are at or beyond this point.

Pretty much every con game is built around some deep seated refusal to face an inconvenient truth. The chances of getting rich quickly and without effort are negligible? No, says the con man, let me show you how. It takes time and hard work to succeed? Have I got a deal for you. You're not very talented or attractive? The real people around you may not be impressed, but there's a supermodel in a chat room waiting to talk to you.

And one fabulous sucker game is to promise lavish, guaranteed returns. Let the market go up and down; my investment only goes up, and faster than the market. Of course it can. You pay off early investors with money paid in by later ones. The more lavishly you pay out, the more new investors clamor to get aboard, and the more likely the old ones are to stay in the game. Eventually, the scheme crashes because you can't haul in enough suck investors fast enough to deliver the promised growth, or someone wants out and there isn't enough left to pay him. This, of course, is a Ponzi scheme. Some Ponzi schemers, like the namesake Charles Ponzi, were simple con men, but others like Bernie Madoff probably resorted to cutting corners when their schemes didn't work out. Bernie Madoff probably genuinely believed he could outperform the market, at least at first.

The essence of a Ponzi scheme is the charade of unlimited growth. Let's say you convince someone to pay you $100, which you will invest and pay him $50 a year indefinitely (50% return per year? Not too shabby). A year later, he comes to collect his money, but he's so enthusiastic he brings a friend along. You pay your investor $50 but the friend gives you $100 to buy in. You now have $150. A year later each of your investors brings in another friend each. They pay you $200, you pay your two investors $50 each, a total of $100. You now have $250. The following year your four investors each bring in a friend. You pay out $200, rake in $400, and have $450, and so on. This can go on only as long as you can bring in new investors. Next year, none of your eight investors recruits anyone, but they still come to collect their $50. That will leave you with $50, assuming you haven't spent the pot in the meantime, which of course you have.

Any scheme founded on indefinite exponential growth will eventually crash against the finite nature of reality. Pyramid franchising schemes may be legal in that participants are selling something of value and have real ability to recruit new members (which is where all the incentives are), but morally they're indistinguishable from Ponzi schemes in that, sooner or later, someone in the lower levels is left holding the bag.

The Gambler's ruin scheme isn't a Ponzi scheme, but it embodies the same principle of exponential growth colliding with finite reality. The idea is to bet, then double the bet each time. Say you bet $1, lose, bet $2, then $4, and finally bet $8 and win. You have bet $7 but won $8. Inevitably, when you win, you will get $1 more than you lost. If you don't run out of money first, or hit the house limit. Sooner or later it is inevitable that you will hit one of those limits, in which case you lose everything.

What is a Ponzi Scheme?

Financing an investment by using proceeds from new suckers to pay off the old ones is the classic Ponzi scheme, but we can recognize many other schemes that share the same logic as a Ponzi scheme even though they may be entirely legal. The essence of a Ponzi scheme is paying off present obligations using illusory future income. Note the word illusory. Taking out a loan to expand a business and using the increased income to pay off the loan is not a Ponzi scheme. The business may or may not grow, and the lender may or may not get his money back, but if everyone's done their homework, it should work out. Both the businessman and the lender are taking a rational risk. Projecting future computing trends based on Moore's Law is also not a Ponzi scheme. Computers do double in capability about every two years, there are lots of promising lines of research that promise to keep the trend going for some time yet, and most important, nobody denies there's a limit somewhere. And when we do hit the limit, we will still have all our computing power. The world will not crash when we hit the ultimate speed limit for downloading porn.

What is a Bubble?

After the housing market collapsed in 2009, many economists criticized the concept of a "bubble." Actually the term is intuitively accurate. Something continues to expand with nothing really behind it until the thin shell eventually pops. Every bubble is fundamentally a Ponzi scheme. Investments grow in value because not because they become intrinsically more valuable, but merely because people think they will be able to sell them to someone else, who in turn thinks he will be able to sell them off. Sooner or later someone is left holding the hot potato.

The Ponzi Psychology

It's perfectly possible to run a Ponzi scheme that masquerades in - almost - every respect as a legitimate investment scheme. It offers yields that are in line with the market, yields fluctuate up and down, and the fund takes occasional losses. The only difference is the con man simply takes all the money. In fact, it happens all the time even in legitimate enterprises. There's a word for it: embezzlement.

But where's the fun in investing in something that offers only competitive yields and maybe even losses? No, the lure of a Ponzi scheme is fast and easy growth. Ponzi schemes appeal to certain psychological fantasies:

Physical Resources

It's astonishing that people who chant "there's no such thing as a free lunch" when it comes to social programs behave like it's a free all you can eat buffet when it comes to resources.

Economic Resources

Everyone can see that Bernie Madoff ran a Ponzi scheme, but I haven't seen many people notice that American society has been rife with Ponzi schemes for many years. Even fewer have noticed the embarrassing fact that many of these schemes profited the middle class rather than the rich.

"Will You Crucify Mankind on a Cross of Gold?"

There may have been Ponzi schemes before this one, but with the 19th century demand for "easy" money, I believe we entered an epoch where some sort of Ponzi scheme was operating almost continually. The push for "easy" money was effectively a demand for controlled inflation, allowing small debtors to borrow money and pay it off with cheaper dollars in the future. This, in itself was not necessarily a bad thing in that it offset the increasing concentration of wealth at the upper levels of society. In a world where technology was rapidly creating wealth, gold was simply not a realistic token of wealth any more. Instead, inventors and entrepreneurs could increase the wealth of the society, while hoarders of gold could grow richer by merely holding onto unproductive metal.

The much maligned William Jennings Bryan, so viciously caricaturized in Inherit the Wind, was actually a progressive in his prime and delivered his famous line about "Will you crucify mankind on a cross of gold?" during a campaign speech at the Democratic National Convention in 1896. Bryan captured the nomination and ran on a platform of "easy money" (actually using both gold and silver as currency standards), but lost.

Benign as its intent was, the notion of easy money planted the seeds of an expectation that growing income was inevitable and even a right.

The Roaring Twenties

The Roaring Twenties, with growth fueled by stocks purchased on margin, effectively turned the U.S. economy into a grand Ponzi Scheme. It was possible to purchase stocks with just a fraction of their value down, with investors counting on paying the rest as their portfolios grew. In principle you could build a sound portfolio for long term investments this way. In practice, people paid off their stock purchase installments and used any extra money to buy more stocks on margin.

Status Symbols and the Installment Plan

We can forgive people of the World War II generation for going just a little bit nuts after the war ended. Many had not enjoyed prosperity since 1929, plus the U.S. had built the world's largest industrial complex and unleashed it on the civilian economy.

First thing they did was have babies. Wow, did they ever have babies (I was one). Seventy million of them over 15 years. And to think the Sixties generation thought they invented sex. This population pulse, moving through the age pyramid like "a pig through a python," first created a boom in building schools, then a boom in building colleges, then a boom in housing, and finally it is making Social Security and pension plans groan at the seams. In a decade or so, the first Baby Boomers will begin dying of old age. A decade after that enough will have died off that the Boomers will have lost a lot of their political clout. Then we could very likely see deep cuts in elder programs. It could get ugly as frustrated post-Boomers try to protect their retirements.

But back to the Fifties. American mass production was turned to building suburban tract homes and filling them with refrigerators, washing machines, and televisions. Black and white, and you actually had to get up and walk across the room to change channels. It was a cruel age. And to sell all this stuff quickly, many retailers offered installment plans. Now all these plans were finite in duration and everyone involved knew it. Still, consumerism on the installment plan reinforced the idea of unlimited growth. You'd get a new gizmo now, pay it off later, get a newer gizmo, and so on.

Credit Cards

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Wage-price spiral of 1970's

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Outsourcing

Social Resources

If conservatives are in deep denial about the finite nature of physical resources, liberals are at least equally bad in denying the expendability of social resources.


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Created 6 September 2009; Last Update 24 May, 2020

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