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Ergodicity: Difference between revisions
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=== Ensemble probabilities and time series probabilities === | === Ensemble probabilities and time series probabilities === | ||
In fact, the group as a whole ''won’t'' make money each round. | [[File:Ensemble vs time.png|frameless|left]]In fact, the group as a whole ''won’t'' make money each round. | ||
Why? Because the ensemble average ''means nothing for any single player''. ''No one'' scores a constant 105% return. Players score ''either'' 150% ''or'' 60% and then invest their winnings in the next round. Their expected payoff through time is therefore not the snapshot ''average'' of the winning payoff and the losing payoff — that is a return the player certainly won’t get — but the ''product'' of the winning payoff ''multiplied by'' the losing payoff (i.e., 90%). | Why? Because the ensemble average ''means nothing for any single player''. ''No one'' scores a constant 105% return. Players score ''either'' 150% ''or'' 60% and then invest their winnings in the next round. Their expected payoff through time is therefore not the snapshot ''average'' of the winning payoff and the losing payoff — that is a return the player certainly won’t get — but the ''product'' of the winning payoff ''multiplied by'' the losing payoff (i.e., 90%). | ||
This is the amount over time, each player should expect to win. Or, in this case, lose | This is the amount over time, each player should expect to win. Or, in this case, lose: | ||
This is the logic of the casino: the more you play, the more, inevitably, your investment will tend to zero. | This is the logic of the casino: the more you play, the more, inevitably, your investment will tend to zero. | ||
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=== Salaries === | === Salaries === | ||
So, therefore if we all pool our resources and lead an anarcho-syndicalist community existence we will all be rich, rich, rich? | [[File:Ensemble vs time 2.png|frameless|left]]So, therefore if we all pool our resources and lead an anarcho-syndicalist community existence we will all be rich, rich, rich? | ||
No. Put away ''Das Kapital''. | No. Put away ''Das Kapital''. | ||
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=== The Bill Gates fallacy === | === The Bill Gates fallacy === | ||
All this is because, the snapshot average ''across'' a group of salaries doesn’t tell ''you'' anything about ''your'' own expectation through time. An “average salary” is an emergent property whatever group you choose to average: it is arbitrary. You can’t see it in any single salary. | [[File:Career expectations.png|right|frameless]]All this is because, the snapshot average ''across'' a group of salaries doesn’t tell ''you'' anything about ''your'' own expectation through time. An “average salary” is an emergent property whatever group you choose to average: it is arbitrary. You can’t see it in any single salary. | ||
This is why, when Bill Gates hops on a London bus, he makes everyone on board, on average, a billionaire, even though 79 other people on the bus earn exactly what they did before he arrived and the bus average was £25,000. | This is why, when Bill Gates hops on a London bus, he makes everyone on board, on average, a billionaire, even though 79 other people on the bus earn exactly what they did before he arrived and the bus average was £25,000. | ||
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That initial difference in money, after three years, is small in the context of a lifetime’s earnings: £31,000. | That initial difference in money, after three years, is small in the context of a lifetime’s earnings: £31,000. | ||
But the compounding effect afterwards, even though both are making the same 5% return, is massive: after 40 years their salaries are nearly £100,000 apart, and over the 40 years, the aggregate earnings differential between them is £1.7 ''million'' | But the compounding effect afterwards, even though both are making the same 5% return, is massive: after 40 years their salaries are nearly £100,000 apart, and over the 40 years, the aggregate earnings differential between them is £1.7 ''million'': | ||
Try not to have a slow start to your career, folks. | Try not to have a slow start to your career, folks. | ||