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Simon DeDeo
Faculty, Carnegie Mellon University & the Santa Fe Institute. Runs the Laboratory for Social Minds.
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Simon DeDeo Dec 6
Replying to @johncarlosbaez
This seems related to theorems about random graphs as a function of edge probability—but now with (microcanonical) constraints!
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Simon DeDeo Dec 6
Twitter friends! I will be in London this Saturday afternoon, December 7th; and then again Sunday December 15th and Monday 16th. DM or e-mail if you are about. In between I will be completely off-grid on the east coast of Naxos, bringing apologies to Ariadne.
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Simon DeDeo retweeted
kambiandoelsistema Dec 5
Delphine Cossais
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Simon DeDeo Dec 5
Replying to @ROsorioX @ykallus and 2 others
Got it.
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Simon DeDeo retweeted
manu saadia 🖖 Dec 5
Anyways I really wished someone had the gumption to make another Trek movie with no villain and no fire shots and no violence whatsoever, only wits - like Star Trek IV: The Voyage Home
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Simon DeDeo Dec 5
Replying to @ROsorioX @ykallus and 2 others
Nope.
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Simon DeDeo Dec 5
Here's the version derived straight in Tweet form...
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Simon DeDeo Dec 5
this doesn't hold if the b_is don't have to sum to unity (i.e., if I'm allowed to with-hold money from the race.) That's when the odds start to matter. But the prediction under the "ergodicity economics" story is still totally-counterintuitive there!
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Simon DeDeo Dec 5
The puzzle is then... WTF? Why should I put even money on those two crazy horses? The answer is that yes, sure, I could have won bigger by shifting my bet to the horse with the better payoff... but that leaves me less to grow with if the horse with the worse payoff wins.
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Simon DeDeo Dec 5
that derivation works just fine as long as the o_i are all greater than zero.
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Simon DeDeo Dec 5
secretly, that just says "minimize the cross-entropy"; i.e., b_i should match p_i
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Simon DeDeo Dec 5
now notice that the log term decomposes, and you end up with a problem of maximizing p_i log b_i + C, with b_i constrained to sum to 1.
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Simon DeDeo Dec 5
you have the constraint that the b_is sum to unity, and you want to maximize the log-growth; so maximize p_i log (b_i * o_i), where you get to move around b_i
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Simon DeDeo Dec 5
So, expected winnings are b_i * p_i * o_i ; b_i is the fraction of money you put on horse i, p_i is the probability that that horse wins, o_i is the odds-payoff (e.g., 1.1 where you get 10% money extra if that horse wins.)
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Simon DeDeo Dec 5
Nope! Argh, I wish I could just photograph the page, but I can't find it. Every time I teach this I have to re-derive it because I don't believe it myself. Basically, the p and the o terms decouple because it's a log...
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Simon DeDeo Dec 5
You will understand what I'm saying if you read it!
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Simon DeDeo Dec 5
You have X dollars. You have to wager all X dollars on the outcome of a horse-race. P1, P2, P3... are the probabilities that the horses win; W1, W2, W3,... are the winnings. Assuming all W>0, you should spread your bets in proportion to the Ps, regardless of W values.
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Simon DeDeo Dec 5
...assuming you have to place the full amount on the race.
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Simon DeDeo Dec 5
Nope! Equal weight, determined solely by probability of winning.
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Simon DeDeo Dec 5
Replying to @peligrietzer
i will fight you
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