Weight Map Abstraction

Proof-of-Stake
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This is a specific proposal on how to implement some of the “PoW in PoS protocols” described in Delayed Protocols. Shout out to @drstone for the inspiration for this scheme.

NOTE: there are probably better ways of doing this, but this is what fell out of trying to shove PoW into the CBC Casper framework. The better way might be something like “provide a PoW on some random number and get new coins,” but I think this is more fun :slight_smile:

One main criticism of PoS consensus algorithms it that of the “initial distribution question.” For example, imagine Bitcoin had started with PoS instead of PoW - Satoshi would have just ended up with all the coins, and it all would have ended there. So here’s an attempt to solve the initial distribution question w/in the current PoS frameworks we have - namely Casper FFG, CBC, and Tendermint.

In all the above systems, we have some set of validators V, and a function W : V \to \mathcal{R}+, where W is the weight function. Usually, we think about defining a validators weight as the number of tokens they have staked. However, it may be possible to think about defining these weight maps in other ways. For example, validators (really, miners) could do non-outsourceable PoW on their own address, where their weight is the PoW on their address.

If these miners do more PoW on their address, then they have to “deposit” this PoW in the same way we handle validator set changes currently within the above-mentioned protocols (usually: it has to happen under consensus).

From there, the miners run any of the consensus algorithms mentioned above as usual: in Tendermint, making blocks and pre-voting + pre-committing; in FFG: making blocks and voting; in CBC: making blocks. This means we don’t have a “traditional PoW” protocol, in the sense that the forkchoice is not a longest-chain rule. Also, we are required to make a weak subjectivity assumption as well.

With this, we can have a protocol that avoids the initial distribution question, seemingly as much as regular PoW does.

However, there’s one major issue with the above scheme. Essentially, as soon as a miner decides they don’t want to mine/validate anymore, all the PoW they’ve done on their address is worthless. This is because the PoW is only worth the discounted future rewards it allows the miner to receive (which is 0 when they no longer plan on mining/validating). This is different from PoS, where their coins have value even after they’ve stopped validating (and so it hurts them to be slashed).

To fix this (and where the delayed protocols come in), we just have to delay giving the validator their rewards until the end of the withdraw period. Now, they can’t equivocate w/out losing their rewards from their time as a miner.

There are two problems remaining, one is due to the nature of delayed rewards, and the other due to the nature of PoW:

  • Delayed rewards might make it harder for validators/miners to exist, as these validators/miners may have upkeep costs they need to pay in real time (and they can’t exactly borrow against their future rewards :stuck_out_tongue: )
  • This scheme is less secure than a PoS protocol that pays the same amount of rewards - as there’s significantly less at stake for some validator.
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If these miners do more PoW on their address, then they have to “deposit” this PoW in the same way we handle validator set changes currently within the above-mentioned protocols (usually: it has to happen under consensus).

Perhaps, the minimum amount of PoW required scales (linearly?) with the stake that a validator puts into the system. It doesn’t need to be wholly taxing, but in order to be a big fish you can imagine you’d have to put in some extra work.

I think these schemes more or less touch on some notion of reputation in the protocol. These delayed schemes encode a short-term reputation in the protocol.

To that end, I think something that could be worth investigating is also on the “decay” side. In mechanism design, you usually have two functions: A choice function X:V^n\longrightarrow A and a payment function P:V^n\longrightarrow \mathbb{R}^n. If we consider a validator’s weight as a random variable W(t) that decays at a rate inversely proportional to the PoW you complete with respect to your designated mininum, then nodes will be incentivized to complete this PoW entirely (if these rates check out). Both rules could incorporate these weights into their selection and, in both this and the delay case, not sticking around corresponds to a reduction in rewards.

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Perhaps, the minimum amount of PoW required scales (linearly?) with the stake that a validator puts into the system. It doesn’t need to be wholly taxing, but in order to be a big fish you can imagine you’d have to put in some extra work.

I’m not sure I totally follow. I was proposing that only stake that a validator (really: miner) has is the PoW they do on their own address and the rewards that they haven’t received yet. In which case, the PoW will scale linearly w/ the weight of a validator - b/c it is their weight.

I think these schemes more or less touch on some notion of reputation in the protocol.

Why is reputation necessary? We can define weight as the number of leading zeros on the “largest” PoW on an address - in which case I don’t think we need reputation at all. For that matter, I think it’d be best to keep reputation out - it’s a fairly large attack surface in any case.

If we consider a validator’s weight as a random variable W(t) that decays at a rate inversely proportional to the PoW you complete with respect to your designated mininum, then nodes will be incentivized to complete this PoW entirely

I don’t totally follow. What’s the designated minimum here? The weight (aka, PoW) decaying over time might be reasonable to simulate the depreciation of mining equipment overtime - but I’m think I’m missing something :slight_smile: