Vitalik on funding public goods

[psztorc]

Since prediction markets works better, why discuss DACs at all?

Your OP, which created this thread, referenced Vitalik's beliefs about financing public goods (as does the Thread Title). So that is literally what we are talking about.

Probably another key detail would be that DAC's are a years-old established concept, whereas the T-DAC smart contract I wrote about is an entirely new (untested) and theoretical concept. As it itself is an extension of a DAC, it would seem reasonable to move the conversation from AC to DAC to T-DAC.

[vbuterin]

Sorry, I did indeed use p in two contradictory ways. There is P, probability of participation, and p, probability of being pivotal. There is also the probability of success, but I've fixed that to 0.5 (since we can adjust the funding threshold up or down to make it so). Does that sound reasonable?

Or, when you say "everyone participating with some probability p" does that mean that everyone calculates the same probability [for example, p=15%], and then rolls a 100-sided dice and contributes if it comes up 15 or lower?

That is indeed my model.

that you intend to generalize from one DAC-project "build a lighthouse in New Haven, CT" to another "build a dam in Sandouping"?

There exist entrepreneurs, who calibrate DACs to have a 0.5 probability of success (so as to maximize each person's probability of being pivotal). There are going to be many of these games, with different thresholds. So I am seeing this as a situation where there are many different DACs constantly popping up around the world and people have plenty of experience seeing how often they end up succeeding and how often they end up having pivotal members.

Let's say it is the deadline. Will not all players donate (their marginal benefit - epsilon)? Their utility increases either way. In your framework, this is because they now believe that p1 = zero.

No, because everyone else is playing at the same time as them. At the deadline, the game is a single-round game, so the mixed-strategy-equilibrium model is the right one to take.

I intended to build a little "realism" into this: agents may try to save on their donations ('quasi-free-ride'), by attempting to generate additional interest/community in a market earlier, with a credible signal.

Sure, but priming the pump in this context is a public good. So we can't count on it to have that much of an effect.

I fully agree on heterogeneity of preferences, I just think that most public goods are NOT of the form where five people's utilities can add up to more than 30% of the total cost of a PG.

I know, my way is a little better because it encourages earlier donations and aggregates info on the project's feasibility.

Actually, I think prediction market-based incentivization is unfortunately worse, because at least DACs use the Gaussian distribution to create a leveraging effect where everyone's incentive is magnified by a factor of sqrt(N) due to the pivot effect, whereas the prediction market is basically just a donation scheme. A fully trustworthy donation scheme that has awesome anti-cheating and quality assurance properties, but a donation scheme nonetheless. People won't donate unless V > C, rather then the pV > C that DACs provide.

[vbuterin]

Actually, just to move this forward, how about I'll propose a formal model for the game that I am discussing, and we'll see what parts of it you disagree. We'll also limit ourselves to assurance contracts to simplify things; if we agree on the economics of the AC then we can move on to the DAC.

1. There exist N players, each of which receive $V utility from the production of a hypothetical public good.
2. An assurance contract is set up where people can contribute either $0 or $C.
3. If more than N/k people contribute, the funds are sent to the entrepreneur, otherwise they are sent back to the donors. k is set by the entrepreneur, because the entrepreneur knows from prior experience that each person has a probability of 1/k of contributing (the reason why the entrepreneur wants to set the threshold to N/k is so that the threshold is right at the top of the bell curve for the probability distribution of total contributions, maximizing the probability that someone is pivotal and therefore maximizing the incentive to contribute). As another consequence of this optimization on the part of the entrepreneur, the probability of success is 0.5.
4. The game lasts for R rounds, round 1 ... round R. People who have not yet contributed can become contributors during any round.

Note that there are plenty of simplifications here. If you think that given these simplifications my analysis is correct, but under your preferred simplifications my analysis is not correct, then we can focus on the simplifications. If you think that my analysis is not correct even given the simplifications, then we move on.

1. There is no incentive to contribute to rounds 1 ... R-1 (this is because you have more information in round R, and because contributing earlier means that you are pushing the probability of success toward the right side of the gaussian, where the derivative of the probability of success is lower, so fewer people will contribute)
2. Let p be the probability of being pivotal.
3. The utility of contributing is pV - C * 0.5. Hence, someone will contribute if 2pV > C.

The stable equilibrium is the one where 2pV = C, so some people contribute and some do not, and the equilibrium probability of contributing is 1/k. If more than 1/k people contribute, then the Gaussian will move to the right, so the threshold will no longer be at the top of the Gaussian, so p will be lower and thus 2pV < C so others will be less likely to contribute to compensate (so it would be the same result except you are expected to pay more); less than 1/k people contributing has the same result, except instead of compensating it drives the success probability to zero (which nobody wants).

This equilibrium does not exist if there are no values of C and k such that 2pV = C.

[psztorc]

Ok, I strongly believe in heterogeneous preferences, but I think your model setup might represent an AC reasonably well. I'm still not sure about your conclusions.

I was completely with you until this point:

3. The utility of contributing is pV - C * 0.5. Hence, someone will contribute if 2pV > C.

It seems to me that p has again shifted its meaning. You've asserted something-like: "people will independently derive the value of p, then roll a dice to decide if they will contribute", but here you say that "someone will contribute if 2pV > C". If everyone's p is the same, either everyone will contribute or no one will? It seemed before that everyone was indifferent to contributing (as long as enough people did), which implied the mixed strategy. Also V is always > C, so for p>=.5 everyone will contribute, seemingly.

My feeling is still that in the last round, people will contribute the C. They may experience regret either way (donating or otherwise). Imagine V = 100 and C is 2. Then regret for the success case ("too many" people donated) is -2 ("I could have saved that 2!") but for the fail case is -98 ("I really needed that lighthouse, why didn't I just donate the 2!?"). Thus it seems that even your constrained model would have everyone donating when C < V/2. Possibly, even when C > V/2 everyone would donate (as, by definition, agents do act to maximize their utility).

[psztorc]

There exist entrepreneurs, who calibrate DACs to have a 0.5 probability of success (so as to maximize each person's probability of being pivotal). There are going to be many of these games, with different thresholds. So I am seeing this as a situation where there are many different DACs constantly popping up around the world and people have plenty of experience seeing how often they end up succeeding and how often they end up having pivotal members.

I'm feeling very confident that you are going to want to abandon this premise. Entrepreneurs may fund many DACs, but this will drive C down, and (V-C) up (increasing the likelihood of success, but decreasing your "p"). More importantly, this assumes that you can look at how people feel about {V1, C1, "Digging a gigantic hole in the Atacama Desert and then filling it back up."} and generalize it to {V2, C2, "Building an Earth Asteroid Deflector to protect the planet from destruction."}, which I feel is pretty much impossible.

[vbuterin]

Ok, I strongly believe in heterogeneous preferences, but I think your model setup might represent an AC reasonably well. I'm still not sure about your conclusions.

I was completely with you until this point:

3. The utility of contributing is pV - C * 0.5. Hence, someone will contribute if 2pV > C.

It seems to me that p has again shifted its meaning. You've asserted something-like: "people will independently derive the value of p, then roll a dice to decide if they will contribute", but here you say that "someone will contribute if 2pV > C". If everyone's p is the same, either everyone will contribute or no one will? It seemed before that everyone was indifferent to contributing (as long as enough people did), which implied the mixed strategy. Also V is always > C, so for p>=.5 everyone will contribute, seemingly.

My feeling is still that in the last round, people will contribute the C. They may experience regret either way (donating or otherwise). Imagine V = 100 and C is 2. Then regret for the success case ("too many" people donated) is -2 ("I could have saved that 2!") but for the fail case is -98 ("I really needed that lighthouse, why didn't I just donate the 2!?"). Thus it seems that even your constrained model would have everyone donating when C < V/2. Possibly, even when C > V/2 everyone would donate (as, by definition, agents do act to maximize their utility).

Your case had a very high value for V/C, so your DAC in my model would work up to ~2500 people. Note also that regret for the fail case is -98 only when a member is pivotal; in the case where the contract would have failed with or without them, there is no regret.

this assumes that you can look at how people feel about {V1, C1, "Digging a gigantic hole in the Atacama Desert and then filling it back up."} and generalize it to {V2, C2, "Building an Earth Asteroid Deflector to protect the planet from destruction."}, which I feel is pretty much impossible.

V1 ~= 0. V2 ~= ∞. And there will be many cases in between. People will probably figure out the values in between using linear regression.

So, on the main point, I guess the main impasse is how to reconcile:

1. The probability of contributing is 1/k
2. A person contributes if 2pV > C, and does not otherwise

The only tool that game theory has for solving this class of problems is the mixed-strategy Nash equilibrium, ie. a set of probabilities such that there is no benefit from unilateral deviation from everyone's strategy. So, intuitively, the goal is to prove (or disprove) that if everyone contributes with probabilty 1/k, then 2pV = C. My explanation for that is that that situation is the situation that an entrepreneur wants, since anything else is not a stable equilibrium.

What alternative equilibrium do you propose in my model? One where k ~= 1? In that case, p will be the inverse square root of the number of irrational people, which certainly is more manageable by a constant factor, and what we should really focus attention on is not the model of "there exist N people" but rather "there exists an infinite number of people with a power law distribution of V values for the public good"; I think that might be more where the uncertainty that I am getting at comes from. But in that case, I am pretty convinced that a p ~= 1/sqrt(N) factor is going to appear in there for similar reasons.

[psztorc]

Note also that regret for the fail case is -98 only when a member is pivotal; in the case where the contract would have failed with or without them, there is no regret.

That does seem like the case, doesn't it? But, in a world of homogenous preferences, where everyone shares the same V, would pay the same C, and independently constructs the same p, each of these individuals is empirically a copy of the same person. If they all share exactly the same preferences and cost/benefits, and the same reasoning (in construction of p), they might all be simultaneously and equally responsible for the contract's success or failure. Even if no one contributed, "everyone" might be pivotal. This might be what, for example, Eliezer Yudkowsky would argue. I don't think it is particularly important either way.

So, on the main point, I guess the main impasse is how to reconcile:

1. The probability of contributing is 1/k
2. A person contributes if 2pV > C, and does not otherwise

Yes, because there is a clear contradiction between "a probability of contributing" and "contributes if".


Six pure outcomes, V ranking highest, V-C ranking second, and getting nothing the lowest:

	No Donate	Donate
No Lighthouse	0	0
Pivotal Lighthouse	0	1
Lighthouse	2	1

In this setup, someone would care about their likelihood of being in the "Lighthouse" state, but not in the "Pivotal Lighthouse" state (under trembling-hand, you'd donate as long as you weren't in "Lighthouse"). I think it is your obsession with 'being pivotal' which explains why your ideas are so different.

Edit: I had mislabeled the rows. Fixed now.
Edit 2: Elaborated "In this setup..." point.