Very, very fascinating article. I did not hit a paywall.
From the article, suppose you are offered a coin-flip game where you can win $20 or lose $17:
You might construct two arguments, both rather persuasive, to help you decide what to do. You may think, “I have a probability of ½ of gaining $20 and a probability of ½ of losing $17. My expected gain is therefore:
½ x ($20) + ½ x (-$17) = $1.50
which is positive. In other words, my odds of winning and losing are even, but my gain if I win will be greater than my loss if I lose.” From this perspective it seems advantageous to play this game.
Or, like a chess player, you might think further: “What if I stay for 10 flips of the coin? A likely outcome is that five of them will come up heads and that the other five will come up tails. Each time heads comes up, my ante is multiplied by 1.2. Each time tails comes up, my ante is multiplied by 0.83. After five wins and five losses in any order, the amount of money remaining on the table will be:
1.2 x 1.2 x 1.2 x 1.2 x 1.2 x 0.83 x 0.83 x 0.83 x 0.83 x 0.83 x $100 = $98.02
so I will have lost about $2 of my original $100 ante.” With a bit more work you can confirm that it would take about 93 wins to compensate for 91 losses. From this perspective it seems disadvantageous to play this game.
The mind-blowing part of this example is that a theoretically profitable gamble becomes a theoretically losing gamble if you take into account multiple trials and sequence of returns risk (although for some reason they don't call it that in the article). If we apply this reasoning to our daily marketplace decisions about whether we are underpaying or overpaying, we can see that the more transactions we do, the more wealth is probably leaving our hands and going to someone else.
Takeaways:
1) Reduce your number of consumer transactions if at all possible. Don't buy things or trade investments unless you absolutely must, because you are at a mathematical disadvantage with each trade, before you even account for transaction costs, taxes, or bid-ask spreads. There is some chance you have guessed the value wrong, and have created a utility-losing trade for yourself that concentrates wealth in the hands of someone else.
2) If money buys votes and influence, democracy might be unsustainable beyond a certain point on the Lorenz curve. Once one lives in an oligarchy, there is no reliable way to reverse the situation, because the oligarchs can buy more influence (and revolutions have a poor track record). Progressive taxation and an inheritance tax might be mandatory equipment for the maintenance of democracy and individual rights. Event these stalwarts are subject to influence, as we have seen for the past 40-50 years.
3) If you doubt #2, consider the effect of advertising on the bloated American lifestyle. Yes, we can be manipulated to transact against our interests. Why would we not also vote against our self interest?
4) Longer lifespans, and the inheritance of wealth essentially extend the game and increase the odds of oligarchy by increasing the number of transactions.
5) Monopoly is a strangely accurate game.
Criticisms:
1) Does the closed economic system of the computer model account for the gap between depreciation and inflation (i.e. if I buy a car for $20k, and the car depreciates $2k/year, but the cash depreciates 10% of a car per year, then my trading partner becomes relatively wealthier even though we both became poorer.)? It seems they are trading virtual currencies in the model, and nothing ever wears out. If the rich buy $50k cars and the poor buy $10k cars, depreciation would push the system back toward equality. Higher costs of living due to luxury would do the same.
2) Does the computer model account for growth of the economic pie (the force offsetting depreciation and inflation)? Is it assumed all participants contribute the same?
3) The study invents zeta as a factor to represent the increased advantages of being wealthy. But what if zeta is a curve instead of a constant? I.e. What if for some people, loss of wealth leads to increased productive effort (related to issue #2 above) and what if for some people, gain of wealth leads to retirement and a reduction in transactions? What if the curve is flat for the lazy middle class, and turns up at the ends for the industrious poor and the privileged rich?
