A key reason Bitcoin works is because of its participation incentives.
The whitepaper provides little enlightenment about how/why this works
- the proof in the paper assumes that more than half the participants
*are* honest, without explaining how the incentive structure *leads*
to this outcome. I'm developing a theory for how this might work, but
it's taken a strange turn, so I want to the idea by you all.

I think most people are familiar with the "expected utility" approach
to prescribing decision making under risk. If you are risk-neutral,
then you should take a bet if it has a positive expected profit. If
the house has an edge, then it's a loser's game. (For now exclude
games like poker involving skill)

Assuming miners make decisions like this leads to a bad outcome for
Bitcoin. The reason is that due to economies of scale, computational
power is cheaper in bulk (i.e., the Cloud). Since you earn more the
more computing power you put in, the only equilibrium is where the
most efficient entities (large scale mining operations with custom
hardware) drive the marginal profit down to zero, and in that case
it's *unprofitable* for anyone else to participate at all.

An easy way out is to say "well people mine Bitcoins because they're
altruistic," and while this may be true for some people, it's not a
useful design heuristic overall - it suggests Bitcoin might work just
as well if there were no mining rewards at all.

As it turns out, the expected utility theory does not describe very
well how people actually make risky decisions. People play at casino
slots and state lotteries, even though those have negative expected
profit (it's similarly not useful here just to call them altruistic,
though). The Allais paradox (see wikipedia) is a really compelling
counterexample - you can try it on yourself, it describes two options
to choose from and almost everyone consistently makes a choice that
violates EU.

Behavioral economists since the 80s have used an alternate model than
EU to better describe how people participate in lotteries and gambles,
the best of which is Cumulative Prospect Theory [1]. It says you can
predict how people play lotteries by assuming they overweight very
small probabilities.

This leads to an unintuitive design criteria for Bitcoin's incentive
scheme, in order to prevent centralized mining. The trick is to make
it *unprofitable for everyone*. Individuals will participate in a
lottery, even at negative expected value, as long as it has
positive-skewed *jackpots*. On the other hand, if gamblers keep the
expected value quite low, then large firms may behave closer to EU
agents, and not participate at all.

Bitcoin doesn't just compete with the state monopoly on currency, it
competes with state monopoly on lotteries!

This theory is really appealing to me, because I think it gives an
explanation for why Bitcoin isn't a perpetual motion machine, where
the "money from nothing" source of motivation comes from. It harnesses
a human psychological trait that systematically deviates from
(standard EU) rationality. A tendency to gamble on long shots may be a
feature of the human psyche, not a bug, as it potentially leads to a
desirable outcome where infrastructure (mining power) is diffused
widely.

Can you imagine accepting "overweight small probabilities, rather than
maximizing expected value" as a rational/prescriptive rule for making
decisions? Would Bitcoin participants tolerate the explanation that on
average mining is unprofitable, and it's *supposed* to be that way?

[1] http://psych.fullerton.edu/mBIRNBAUM/psych466/articles/Tversky_Kahneman_JRU_92.pdf


--
Andrew Miller