The Oligarch Game: use coin-tosses to demonstrate "winner take all" and its power to warp perceptions

I suspect it’s an unhelpful confluence of several factors:

Obviously people in good situations have an interest(certainly as a pragmatic PR matter; but likely psychologically as well) in the idea that they are where they ought to be/earned it/etc. (And this perception is reinforced by the fact that the successful often do work hard for it; they just don’t see all the people working as hard or harder and getting nothing for their pains).

People generally, successful or not, are not intuitively good at statistics(even statisticians have bad instincts; they just know the math that they ought to use); and the idea that outcomes are substantially impersonal dumb luck is not one that squares well with our socially oriented cognition: people resist the idea that things just happen without any sort of moral logic or agent behind them in all sorts of areas, from economics to evolution to medicine.

There’s also massive survivorship bias: successes tend to be massively more visible than failures(unless they are of the…discrete…school of fortune-building); so while they are the exception rather than the rule their visibility is massively out of proportion with their frequency.

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Taking a broad spitball look at history I’d be inclined to suspect that the moral of the story is that sufficient growth can mask issues with your wealth distribution(whether market, state; or a combination) so long it they last; but leave you vulnerable to extra consequences if it starts to slow down; or stop/reverse.

Unless everyone is judging their wealth exclusively in comparison to others(which doesn’t seem to be the case, especially along people on the lower end; where the marginal utility of money is still high and all changes in wealth can mean significant differences in living standards, not just a change in the scoreboard); a ride rising fast enough to lift more or less all boats can put off uncomfortable questions about how fast some boats are being lifted; but if the tide starts to go back out the distribution among the boats comes to the fore.

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It’s funny, I do remember considerations of dumb luck, and I know economists and if you bring it up they’ll tell you a lot of what happens is luck. I think the problem is that they essentially see humans as a fungible commodity. It’s okay if someone is lucky because we all might be that someone.

Assign an interest rate. At the end of every round everyone’s wealthy grows by that rate. It is trivial to observe this doesn’t change how the game plays out unless the new money is unequally shared, with more going to the poorer players. But note in that reality returns on investment are unequally shared with more going to the richer people.

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I wonder if you could modify the game. Give one person 1 or 2 cards (representing a certain privilege) at the start to let them re-flip a coin toss. Or give another couple of people a card or two that allows them to force another person to re-flip a count.

I bet even just a single card could tip the balance a lot of the time.

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This is an interesting article. The game itself relies on a 0 expectation, i.e. 50% chance of winning or losing the lower of the two bankrolls. So by definition, this is not a wise bet to do once (let alone repeatedly). In a business setting, you’re looking for a positive expectation or to create one structurally that is repeatable.

It would interesting if the automated game would let you vary the bet size and the payoff so that it gives an advantage to one of the participants to see if there are stable arrangements. As it is, it is mostly a demonstration of the notion of risk of ruin used by gamblers/investors to set bankroll and bet sizes to stay in a game with a positive expectation, but a low rate of payout. One idea would be to try a payout like they use in chess (Elo ratings). If a low rated (bankroll) player beats a high-rated player, the payout is more favorable.

UPDATE: There is now a version that does a redistribution step. https://hackerfactor.com/oligarchy-game.php?soc

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A friend of mine is a trader with a huge agribusiness firm - essentially his job is to invest all the profits. He explained to me how his hedge fund worked - essentially guaranteeing double digit returns to rich people (minimum of $10,000,000 to invest) by combining loans into tranches, then taking the “best” tranche (with all the good investments, high payouts, etc.) and giving it to the hedge fund investors with guaranteed returns, while the other tranches are purchased by insurance companies, pension funds, whatever, who are satisfied with a 3% return. (my terminology may be off a bit, conflating terms from “The Big Short”)

I asked him how this was legal or why you had to have $10,000,000 to get in on it, why can’t I get in on this? His answer was “transaction costs - if you let everyone do it, then it will get bogged down with too many shareholders, etc.”

In other words, because it’s a private club you clown - who the fuck do you think you are to get the same deal as these billionaires?

We’re not friends anymore - for this and other reasons, mostly related to his lack of a soul.

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3 to 5% is very fast GDP growth in a mature economy. You could hand out $5 to each player each round in the game outlined above, and it wouldn’t change the outcome in the slightest.

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This has been an enlightening conversation. Here are the two concepts I’m still struggling with. First, how to define oligarchy when the total value of an economy is unbounded (i.e. does defining it as the ratio of everyone’s “stuff” even make sense as the amount of “stuff” available goes to infinity); and second, along the lines of “all models are wrong, some are useful”, how to capture the intuition that economic transactions are not zero sum in the model, because if transactions really are zero sum, then as jhritz points out no rational actor would have an incentive to undertake them. So I’m not convinced this model applies to the economy that closely (i.e., when I pay for lunch, it really is with the belief that both myself and the restaurant are better off than if I did not).

Right now America throws 40% of it’s groceries in the trash and 1 in 7 children live with hunger (and it’s similar where I live but America is the country that gets the most helpful infographics to google). So we’ve already “gone to infinity” for food, but still somehow not everyone gets a share.

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That’s definitely the wrong direction to try to find a definition.

If a small minority of people can dominate a society due to wealth, including capture of law, justice, & regulation, then you’ve got an oligarchy.

If billionaires can buy law, buy justice, and buy regulation, that’s all you need.

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Humans desire to put things in a perceived order. even when it makes no sense to put them in the order they are in, it will do, to allay the fear of chaos. Although Mammal brains are not binary computers they share problems with dealing with the truly random. its why gods, stereotypes, and hope plague our world.

The game is not, nor attempts to be, a model of how economies work. It serves to demonstrate bugs in human perception of chance outcomes. It contributes to understanding of social wealth discourse. But not of how wealth, or distribution of wealth, arises.

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Aside from the question of whether it’s a good idea to bring ‘unbounded’ into the picture(both because the economy consists only of activity within a few light-minutes of earth, judged according to the standards of entities who need to eat today and will be dead within a few decades, maybe a century for the young ones, so ‘the long term’ is actually under a time limit; and just because “very large but finite” is vastly more mathematically tractable than anything non-finite); I’d consider a focus on marginal utility when trying to decide what an ‘oligarchy’ looks like.

Unless you are a profoundly weird entity that uses money purely for keeping score; its marginal utility is going to decline as you obtain more of it(probably not perfectly evenly, I’d expect bumps as you reach various objectives with fixed lower bounds on cost, housing in a desirable location, your first airplane, whatever; but diminishing marginal utility). This allows the amount of utility in an economy to decline, even if all interactions are at least zero sum or better: all that’s required is distribution rules result in money flowing to people who derive increasingly little utility from it fast enough to get ahead of gains from trade.

It’s an incomplete picture; but I think it captures one element of what, intuitively, separates an unequal but prosperous society from an ‘oligarchy’:

If the flow of resources remains on the side of continuing improvements in utility concerns about inequality and reports of oligarchs are likely to remain substantially theoretical because the only way for utility to increase is if enough of the gains accrue to people with relatively high marginal utility for money and away from people whose marginal utility for money closely approaches zero.

If this threshold is crossed, and wealth increasingly ends up in places where its marginal utility is negligible at the expense of people whose would derive much more utility from it, the question of “If we’re so rich; why are we so poor?” starts to take on a burning urgency; and the economic role of people with vastly more money stops looking largely theoretical and starts looking like an ugly fight over a shrinking pie.

Even if we assume that the pie, in absolute terms, must necessarily be expanding; it’s readily possible for the utility derived from it to be shrinking; and that’s ultimately what people notice.

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I really like what you’ve written, with one exception. An oligarchy inherently means a system of government (official or unofficial) run by the wealthy. What you describe doesn’t have a feedback loop through control of law or regulation. I think it’s implied, but one could imagine a system where there are obscenely wealthy people aggregating money at marginal utility approaching zero, where those same people have no actual power in the government.

Heck, the British monarchy is a real-world example - near zero influence on government and extreme wealth.

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I call bullshit on this however. it DOES show the wrong perceptions that is true but in the current market of billionaires who hoard this game represents it quite well. you want it fixed? fine create a cost that all have to pay keep it, lets say every 12 rounds players pay a buck. the game will still end the same or end up there faster.

I’d agree with that, which is the main reason I described the picture as incomplete; and in real-world cases it seems like the attractive arbitrage opportunities between money and influence and back again always seem to overwhelm people’s force of habit, or noblesse oblige or pragmatic concern that inspiring a proletarian uprising would be bad for business; so I definitely wouldn’t dispute that, as a matter of history, as well as definition, an oligarchy involves the economic rules being distorted in a variety of ways for the advantage of the already rich.

That said, I’d say that the issue of the perception of oligarchy and its connection to the trend in overall utility within a society likely exists independent of(though obviously closely connected in practice to, since oligarchy is both an efficient means of moving wealth to low marginal utility parties and what people call the outcome when wealth is flowing to low marginal utility parties) an operational oligarchy:

If a hypothetical oligarchy decided that a clean, civilized, welfare state with favorable human development indices and such was really the best way to keep the heat off while they made real money; I strongly suspect that the result would, except to all but the most principled anti-corruption campaigners, generally be read as “unequal but prosperous”(I suspect that this is not particularly hypothetical, unfortunately, in the case of some of the world’s dodgier tax shelters: if you spread just a smidgeon of the good fortune around locally you can enable monstrous oligarchical abuses on a vastly greater scale abroad without facing popular condemnation for them, since your policy doesn’t read as oligarchical at home).

On the other side, you could likely have a perception of oligarchy with a functional oligarchy if, say, an agrarian society suffered a few bad harvests. Regardless of their existence, or ability to control commodity prices in the face of the weather, I’d expect that a sinister cabal of commodity hoarders would soon come to exist in popular imagination.

Since people seem to have difficulty keeping their hands out of the cookie jar forever; I’d agree that the distinction between societies where utility is trending down despite absolute wealth remaining constant or increasing and societies where oligarchical tendencies are distorting the flow of wealth is mostly a matter of theoretical elucidation rather than something you’d generally find in the wild.

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Good points.

An oligarchy can avoid an uprising if, 1. they conceal their true wealth and/or 2. bread and circus.

money=power=corruption=money=power=corruption…

Which makes the proposed wealth tax so important in combination with returning the highest marginal income tax in the US back to 1950s levels. The only way to keep from having to whack the mole every couple of years is to disarm the billionaires of their main weapon of power - billions.

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