Decred Censorship Computations

This is a response to Is Decred censorship-resistant?, pertaining to the Hybrid Mining Fallacy.

Input Data

1. Stake Share (α): 0.50 (20,480 tickets, T=40,960 ticket pool).
2. Ticket Price: ~211 DCR (stake value ≈ 4,320,256 DCR).
3. Block Subsidy (R_m): ~1.85 DCR (PoW, 30% of ~6.16 DCR total subsidy).
4. Vote Reward (R_v): ~0.74 DCR (PoS, 60% of total subsidy, by 5 votes/block).
5. Current Fees (F_other): ~0.05 DCR/block (~0.0005 DCR/TX, ~100 TXs/block).
6. Base Reward (R_base): R_m + F_other ≈ 1.85 + 0.05 = 1.90 DCR.
7. Veto Probability (p): ~0.50 (α=0.50, ≥3/5 votes).
8. Inclusion Probability (q): 0 to 1 (fraction of blocks with targeted TXs).
9. Miner Margin (m): >0.50 (assumed ~0.6 for Δf_min).
10. Blocks/Hour: 12 (5-minute block time).

Censor’s Cost

• Veto Cost: k=3 votes withheld, cost = k × R_v = 3 × 0.74 = 2.22 DCR/veto.
• Loss Rate: q × p × 2.22 × 12 = 13.31q DCR/hour.
  • q=1: 13.31 DCR/hour (~116,592 DCR/year).
  • q=0 (self-censorship): 0 DCR/hour.
• Annual Cost: q=1: 116,592 ÷ 4,320,256 × 100 ≈ 2.70% APR; q=0: 0% APR.

Miner’s Cost and Fee Requirement

• Orphaning Loss: p=0.50 reduces revenue to (1 - p) × R_base = 0.5 × 1.90 = 0.95 DCR/block.
• Break-Even Fee Delta: (1 - p)(R_base + Δf) ≥ R_base → Δf ≥ R_base = 1.90 DCR.
  • New fees: 0.05 + 1.90 = 1.95 DCR/block.
  • Fee increase: 1.90 ÷ 0.05 × 100 = 3800%.
• Per-TX Impact: ~100 TXs/block, fees rise from 0.0005 to 0.0195 DCR/TX (~3800%).
• Targeted TX Fee: Δf_min = (p × R_base)/(m - p) ≈ (0.5 × 1.90)/(0.6 - 0.5) ≈ 9.5 DCR/TX (m=0.6).

Cost Dynamics

• Censor Advantage: Low cost (0–2.70% APR) enables sustained vetoes, especially if q→0 (self censorship). Censor tolerates ~$1.86M USD/year (DCR=$16).
• Miner Pressure: 50% revenue loss (0.95 DCR/block) pushes self-censorship unless Δf ≥ 1.90 DCR/block (~3800% fee hike for the block).
• Fee Realism: ~3800% increase or ~9.5 DCR for a targeted TX may be impractical, favoring self-censorship.

Impact of Fee Levels

Decred has a block size limit well below that of Bitcoin (BTC). As a result, with a similar demand for confirmations, we would expect to see significantly higher than Bitcoin per tx average fees. Bitcoin has experienced sustained fee levels over $50. This table shows the 50% orphan rate miner break-even derived from an average non-censored tx fee level. Notice that the fee delta grows significantly with confirmation demand, with no change to the censor's cost.

Avg. Market Fee (USD/TX)	F_other (DCR/block)	R_base (DCR/block)	Δf (DCR/block)	Fee Increase (%)	Per-TX Fee (DCR/TX)	Per-TX Fee (USD/TX)	Censor Loss Rate (DCR/hour, q=1)	Censor APR (%, q=1)
0.008	0.05	1.90	1.90	3800.0%	0.0195	~0.31	13.31	2.70%
0.1	0.625	2.475	2.475	396.0%	0.0310	~0.50	13.31	2.70%
0.5	3.125	4.975	4.975	159.2%	0.0686	~1.10	13.31	2.70%
1.0	6.25	8.10	8.10	129.6%	0.1435	~2.30	13.31	2.70%
10.0	62.5	64.35	64.35	102.96%	1.2685	~20.30	13.31	2.70%
50.0	312.5	314.35	314.35	100.592%	6.2685	~100.30	13.31	2.70%
100.0	625.0	626.85	626.85	100.296%	12.5185	~200.30	13.31	2.70%

Zero Sum

Above assumes a hypothetical worst case for the censor - that all blocks/miners include censorable txs. In this case difficulty would eventually adjust and eliminate the cost. However this is counter-incentive. Any miner that censors earns twice the reward by halving half the orphan rate. At that point non-censoring miners are half as efficient and will therefore eventually all go out of business due to the zero sum nature of PoW mining. This is only overcome by a compensating fee differential in censorable txs. This is similar to PoW censorship resistance, however in this case the differential is disproportionate to censor offset, as shown above.

Stag Hunt Game

In a Stag Hunt, players cooperate for a high payoff (e.g., hunting a stag, akin to all miners resisting censorship) or defect for a lower but safer payoff (e.g., hunting a hare, akin to self-censorship).

Payoff Matrix

	Cooperate (C)	Defect (D)
Cooperate (C)	0.95, 0.95	0.95, 1.90
Defect (D)	1.90, 0.95	1.90, 1.90

• Cooperate: (1 - p) × R_base ≈ 0.95 DCR/block.
• Defect: R_base ≈ 1.90 DCR/block.

Miners face a Stag Hunt game when a 50% stakeholder censor (α=0.50, p≈0.50) vetoes blocks with targeted TXs. They choose to cooperate (non-censoring, include TXs, q>0) or defect (self-censoring, exclude TXs, q=0). Payoffs are expected revenue (DCR/block). The choices are individual, coordination allowed. Global non-defection is the only case in which the censor does not win, but that is an unstable/untenable outcome.

• Equilibria: (C, C) resists censorship but risky; (D, D) is stable, risk-dominant.
• Mixed Strategy: Cooperation probability q ≤ 0.5 due to risk dominance.
• Dynamics: Non-censoring miners lose ~0.95 DCR/block (revenue vs. ~1.90 DCR/block costs), driving defection to q=0 or exit.
• Outcome: Self-censoring miners earn 1.90 DCR/block, pushing censor costs to 0% APR.

Streak Misapplication

The Is Decred censorship-resistant? analysis incorrectly applies "any-streak" probability in probRunAtLeastL(N, P, L) to assess a censor's ability to sustain vetoes for L consecutive blocks when miners persistently include targeted transactions (q=1). This calculates the chance of at least one L-length veto streak occurring anywhere in 288 blocks (1 day), overestimating the censor’s success (e.g., ~90.36% for L=6, α=0.50). In reality, censoring a specific transaction requires vetoing consecutive blocks starting from its inclusion, governed by a geometric probability (p^L ≈ 0.50^6 ≈ 1.56% for L=6). This misapplication actually increases the perceived effectiveness of censorship under the assumptions. However, as the above analysis shows, streak analysis is not relevant.

Conclusion

Censorship resistance is limited against a 50% stake censor (α=0.50). Low cost (0 - 2.70% APR) and large fee increases (~3800%) make self-censorship likely, pushing actual 50% censor cost toward 0%. A 60% stake censor increases p to ~0.683, increasing cost upper bound (0 - 3.07% APR), raising miner losses (~68.3%) and therefore fees required for offset (~11,980%), significantly increasing censor advantage. Critically, there is no mechanism by which a majority censor can be evicted by the economy.