if I go into the casino with 67 bucks and make 1,5 times what I have, I will own 100 bucks.
If I go into the casino with 100 bucks and lose a third only (not 40%!) then I will own 67 bucks.
Thus, +50% and -40% are not the right arithmetic pairs. It should've been +50% and -33%. It's even more intuitive to say 3/2 and 2/3. Waiting for a matician who can explain better, but this whole story is more of a parlor trick than anything else.
> but this whole story is more of a parlor trick than anything else
I don't think it is really. You're right in saying that 2/3 and 3/2 are the right numbers to ensure that the population wealth stays the same. But the point of the exercise is to show that the population wealth can increase while the wealth of almost any individual in the population decreases.
This is the author's jumping-off point to argue that the standard arguments in economics about average welfare can be far removed from the experience of any single worker in the economy.
> You're right in saying that 2/3 and 3/2 are the right numbers to ensure that the population wealth stays the same.
Quick correction:
The article uses 0.6 and 1.5. In this setting, the population wealth increases and the wealth of almost any individual decreases.
In the comment you replied to, they propose 0.66 and 1.5. In this setting, the population wealth doesn't stay the same, it increases even more than before.
(In order for population wealth to stay the same, the payoffs should be 0.5 and 1.5)
Either wager (+50%/-40% or +50%/-33%) would be profitable wagers for a gambler in a casino to take. If you ever found a casino offering bets like that, you would never have to work again (unless they sued and won against you to get their money back). No casino would ever knowingly offer a wager with negative expected value for them.
It looks like those were chosen to get a opposite numbers for the comparison, +5% and -5%:
> the expected value ... grows by 5% in every round ... but, crucially, a head and a tail experienced sequentially is different from two different agents experiencing them ... we have lost ... approximately 5% per round
Thus, +50% and -40% are not the right arithmetic pairs. It should've been +50% and -33%. It's even more intuitive to say 3/2 and 2/3. Waiting for a matician who can explain better, but this whole story is more of a parlor trick than anything else.