In the proof-of-stake (PoS) paradigm for maintaining decentralized, permissionless cryptocurrencies, Sybil attacks are prevented by basing the distribution of roles in the protocol execution on the stake distribution recorded in the ledger itself. However, for various reasons this distribution cannot be completely up-to-date, introducing a gap between the present stake distribution, which determines the parties current incentives, and the one used by the protocol. In this paper, we investigate this issue, and empirically quantify its effects. We survey existing provably secure PoS proposals to observe that the above time gap between the two stake distributions, which we call stake distribution lag, amounts to several days for each of these protocols. Based on this, we investigate the ledgers of four major cryptocurrencies (Bitcoin, Bitcoin Cash, Litecoin and Zcash) and compute the average stake shift (the statistical distance of the two distributions) for each value of stake distribution lag between 1 and 14 days, as well as related statistics. We also empirically quantify the sublinear growth of stake shift with the length of the considered lag interval. Finally, we turn our attention to unusual stake-shift spikes in these currencies: we observe that hard forks trigger major stake shifts and that single real-world actors, mostly exchanges, account for major stake shifts in established cryptocurrency ecosystems.
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