system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What are and what is the difference between Pyramid Schemes, Ponzi Schemes, and MLMs?
gpt
Shortly after World War I, convicted forger Charles Ponzi came across and interesting and ostensibly legal way to make money. An international reply coupon (IRC) was a way for a letter mailed from abroad to provide return postage. The trick was, you bought them at the postage rate in the country of origin, but all countries would honor them, even if their rates were higher. Italy was suffering from severe postwar inflation, and IRCs could be bought very cheaply in US dollars, and exchanged for stamps worth five times as much.


This was all perfectly legal, so Ponzi formed a company to make these transactions and sought out investors, promising large returns within short time frames. Here he became a victim of his own success. While the math worked out, at some point, you actually had to redeem the IRCs for stamps, then find someone who wanted to buy those stamps. He wasn't able to cut through the red tape needed to get this done before he needed to pay out his first investors. Instead of making them wait, he just used money he got from later investors. That is the essence of a Ponzi scheme, instead of making money from a business or an investment, you pay off outgoing investors with the principal from incoming investors.    


The scheme was so popular that things soon got out of hand. People were mortgaging their houses and giving Ponzi their life savings, and he was in control of millions. Unfortunately,  even if he bought all the IRCs in Italy and sold every stamp in Boston, there was just no way to convert them into cash fast enough to give his investors a legitimate return. So he didn't bother, lived large and sued people who accused him of anything untoward. He also had a habit of not paying his debts, which eventually to his scheme being exposed for what it was. Investors demanded their money, Ponzi couldn't pay and was in fact deeply in debt. In the end, five banks collapsed, about $20 million in investors' money (over $200 million in 2015 dollars) was lost, and Ponzi went to jail and eventually died penniless.


A pyramid scheme is a similar but distinct beastie. Investors are encouraged and rewarded for recruiting new investors into scheme, often getting a cut of their investment. If the rewards are small and the underlying business or investment is sound, the pyramid aspect is merely considered an incentive, and is a legal multileveled marketing (MLM) scheme. More often, just about all the money is made through the rewards for recruiting of new investors. Since that number grows geometrically, it isn't long before they run out.  At that point, it is becomes a variation of a Ponzi scheme, where new investors are used to pay off old ones. Ponzi schemes can lack this recruiting element, so they are not always considered pyramid schemes.