Thread by @oliverbeige

Here's #HalFinney's back-of-the-envelope calculation from January 2009. Let's update that and turn it into a collective decision problem.

I'm starting with a bunch of simplifying assumptions:
1. The "ultimate payoff of world domination" is fixed at $10m per coin.
2. All-or-nothing scenario: world domination or bust. (I actually disagree with that.)
3. No interest rate or NPV accounting.

In that case we have a simple lottery. For one lottery ticket, you get a payoff of ε * $10M + (1-p) * 0, or simply $10M times ε. So what's your estimate for the world domination probability ε?

To keep everything simple, let's use a current $BTC price of $10,000. In that case, a risk neutral player should invest if ε > 0.1%. This is two orders of magnitude lower that the success rate from the Satanic Verses.

Still, a 0.1% chance of making a big buck isn't all that bad, right? But there's a reason why I used ε for this probability and not the standard p. In calculus, ε is an arbitrary small number >0. This is what we're guessing.

In collective (i.e. human-powered) decision scenarios, this ε has three empirical characteristics:
1. Naive estimates tend to be off by orders of magnitude,
2. usually biased upwards.
3. Trying to counter this upward bias often leads to an estimate of ε = 0. This is also wrong.

So even in isolation, this is a tricky decision problem. But we're not in acting isolation. Our own estimate depends on the estimates (and actions of others), and vice versa. So let's turn this into a signaling game.

You'll probably not signal your actual value of ε, but much rather your current action contingent on your private ε, say "HODL" or "NODL"...

...where HODL means "under my current private ε, I expect a positive return on investment" (feel free to risk-adjust this according to your private risk preference), and NODL means the opposite.

Keep in mind we don't have the luxury of running this experiment a thousand times, so we're out of the frequentist world and deep in the muck of Bayesian updating.

So your ε turns from an initial, private, "naive" scalar to a function based on everyone else's ε, or more exactly their HODL/NODL signal from which you try to impute their ε's.

Also, in a large population, you will not factor everyone's signal in equally, but you will give more weight to signals you consider credible.

Empirical interlude: humans have a persistent habit to assign more credibility to signals that match their own, ceteris paribus. If you do that, you're well on your way into a filter bubble.

So even in this simple scenario we have a signaling feedback mechanism where my ε depends on the ε's of those people I trust and vice versa,

We could make this a bit more complicated and also allow you to signal your trust weights by calling others "EXPERT", "SHILL" or "NOICOINER". We now have a very simple model of #cryptotwitter.

We also have a decentralized population model where the equilibrium outcome is completely independent of any underlying "true value"...