9 lines
2.4 KiB
Markdown
9 lines
2.4 KiB
Markdown
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The general idea of this implementation of Casper is as follows:
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1. There exists a deterministic algorithm which determines a single proposer for each block. Here, the algorithm is simple: every validator is assigned an ID in the range `0 <= i < NUM_VALIDATORS`, and validator `i` proposes all blocks `NUM_VALIDATORS * k + i` for all `k ϵ Z`.
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2. Validators perform a binary repeated betting procedure on every height, where they bet a value `0 < p < 1` for the probability that they think that a block at that height will be finalized. The bets are incentivized via logarithmic scoring rule, and the result of the bets themselves determines finalization (ie. if 2/3 of all validators bet `p > 0.9999`, the block is considered finalized, and if 2/3 of all validators bet `p < 0.0001`, then the state of no block existing at that height is considered finalized); hence, the betting process is self-referential.
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3. From an incentive standpoint, each validator's optimal strategy is to bet the way they expect everyone else to be betting; hence, it is like a schellingcoin game in certain respects. Convergence in either direction is incentivized. As `p` approaches 0 or 1, the reward for betting correctly increases, but the penalty for betting incorrectly increases hyperbolically, so one only has the incentive to bet `p > 0.9999` or `p < 0.0001` if they are _really_ sure that their bet is correct.
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4. If a validator's vote exceeds `p = 0.9`, they also need to supply the hash of the block header. Proposing two blocks at a given height is punishable by total deposit slashing.
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5. From a BFT theory standpoint, this algorithm can be combined with a default strategy where bets are recorded in log odds (ie. `q = ln(p/(1-p))`), if 2/3 of voters vote `q = k` or higher for `k >= 1`, you vote `q = k+1`, and if 2/3 of voters vote `q = k` or lower for `k <= -1`, you vote `q = k-1`; this is similar to a highly protracted ten-round version of Tendermint (log odds of p = 0.9999 ~= 9.21).
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6. If 2/3 of voters do not either vote `q >= 1` or `q <= -1`, then the default strategy is to vote 0 if a block has not yet arrived and it may arrive close to the specified time, vote `q = 1` if a block has arrived close to the specified time, and vote `q = -1` if a block either has not arrived and the time is far beyond the specified time, or if a block has arrived and the time is far beyond the specified time. Hence, if a block at a particular height does not appear, the votes will converge toward 0.
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