Proof of stake: a stake-weighted proposer lottery (Peercoin 2012)

Weighting proposer selection by stake changes the resource used to allocate influence. This sampler isolates that one mechanism; it has no voting, slashing, randomness beacon, or finality and is not a full PoS protocol.

What to look for

Compare observed selection frequencies with stake proportions. More trials tend to bring them closer; splitting one stake among names does not increase its combined expected share.

Read cells in order. An assert that produces no output has passed. The final exercise asks you to change an input and explain the result.

The history behind this experiment: Breakthroughs in Consensus. See Exercises: consensus for a worked solution to the exercise.

from collections import Counter

import matplotlib.pyplot as plt

import blockchainkit as bk

stakes = {"alice": 10, "bob": 30, "carol": 60}
rounds = 10_000
proposers = bk.consensus.StakeSampler(stakes, seed=42).sample(rounds)
assert proposers == bk.consensus.StakeSampler(stakes, seed=42).sample(rounds)
counts = Counter(proposers)
expected = [stake / sum(stakes.values()) for stake in stakes.values()]
observed = [counts[name] / rounds for name in stakes]
print("Observed selection fractions:", dict(zip(stakes, observed, strict=True)))

Observed selection fractions: {'alice': 0.0938, 'bob': 0.2949, 'carol': 0.6113}

Stake concentration is visible even when the lottery is fair

fig, ax = plt.subplots(figsize=(7, 4))
xs = list(range(len(stakes)))
ax.bar([x - 0.18 for x in xs], expected, 0.36, label="Stake fraction")
ax.bar([x + 0.18 for x in xs], observed, 0.36, label="Observed proposer fraction")
ax.set(
    xticks=xs,
    xticklabels=list(stakes),
    ylabel="Fraction",
    title="Seeded proposer sampling over 10,000 rounds",
)
ax.legend()
fig.tight_layout()

Exercise

Split Carol’s stake across ten names. Does her total expected influence change? Why is choosing a proposer insufficient to decide between two conflicting blocks that proposer might sign? Why is a public seed unsuitable as the sole randomness mechanism for a live consensus protocol?