[jon_gunnarsson]

Yes, I agree. Just add “non-empty” before “proper subset” in the lemma and you’re golden.

[jon_gunnarsson]

I thought Bernoulli’s approach was about diminishing marginal utility, not risk aversion. And while Bernoulli’s choice of a logarithmic utility function does not generalise to all possible games of chance, his approach does generalise if we choose a different function. Nor do we have to choose something silly like a constant function. Consider the following simple utility function (where X is the amount of money you have and negative values of X are not allowed):

X/(X+1000)

This is a strictly monotonously increasing function (satisfying the assumption that extra money is always at least a little bit useful) with an upper bound of 1, so no matter the payout structure, the expected utility can’t possibly exceed 1. This is also a more realistic utility function than the one offered by Bernoulli since it seems intuitively obvious that money alone can’t make you arbitrarily happy or satisfied.

[jon_gunnarsson]

Starts at around 15:30.

[jon_gunnarsson]

Thank you for the reply. Is there any way to tell whether Crassus’s fire brigade was actually profitable? And if it was, why didn’t anyone undercut him by offering fire fighting services on a saner business model, such as selling subscriptions or just charging fees on an individual basis?

[jon_gunnarsson]

Thank you, I will take a look at the diary. Could you also give me a recommendation for something broader?

[jon_gunnarsson]

Thanks Aristocra. However, that quote doesn’t really touch on what Eisenhower thought of all this.

[jon_gunnarsson]

I’ll add another vote for a course on the history of the Middle East.

I would also very much like to see a course on Far Eastern history. Given that Eastern (and especially Chinese) Civilization has for most of pre-modern history been on par with or superior to Western Civilization, and yet has remained largely separate, there is much to be learned about the Far East. However, I, along with most Westerners, am embarassingly ignorant about this topic. And what better time than now, when Asia has woken up from it’s centuries-long stagnation and a number of East-Asian countries have caught up or are in the process of catching up to the West?

[jon_gunnarsson]

AaronRobert, it’s not really news that Abraham Lincoln was a racist. Even Obama acknowledged that when he praised Lincoln at his first inauguration. But we can hardly condemn Lincoln for that, given that practically everyone back then was racist.

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