Decred Censorship Computations

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

Input Data

0. Stake Share (α): 0.50 (20,480 tickets, T=40,960 ticket pool).
1. Ticket Price: ~211 DCR (stake value ≈ 4,320,256 DCR, ~$69.12M at $16/DCR, varies 100–300 DCR).
2. Block Subsidy (R_m): ~0.0616 DCR (PoW, 1% of ~6.16 DCR total subsidy).
3. Vote Reward (R_v): ~1.0965 DCR (PoS, 89% ÷ 5 votes/block).
4. Current Fees (F_other): ~0.05 DCR/block (~0.0005 DCR/TX, ~100 TXs/block).
5. Base Reward (R_base): R_m + F_other ≈ 0.0616 + 0.05 = 0.1116 DCR.
6. Veto Probability (p): ~0.50 (α=0.50, ≥3/5 votes).
7. Inclusion Probability (q): 0 to 1 (fraction of blocks with targeted TXs).
8. Miner Margin (m): >0.50 (assumed ~0.6 for Δf_min, typical 0.5–0.8).
9. Blocks/Hour: 12 (5-minute block time).

Censor’s Cost

• Veto Cost: k=3 votes withheld, cost = k × R_v = 3 × 1.0965 ≈ 3.2895 DCR/veto.
• Loss Rate: q × p × 3.2895 × 12 ≈ 19.737q DCR/hour.
  • q=1: 19.737 DCR/hour (~172,896 DCR/year, ~$2.77M at $16/DCR).
  • q=0 (self-censorship): 0 DCR/hour.
• Annual Cost: q=1: 172,896 ÷ 4,320,256 × 100 ≈ 4.00% 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 × 0.1116 ≈ 0.0558 DCR/block.
• Break-Even Fee Delta: (1 - p)(R_base + Δf) ≥ R_base → Δf ≥ R_base = 0.1116 DCR.
  • New fees: 0.05 + 0.1116 = 0.1616 DCR/block.
  • Fee increase: 0.1116 ÷ 0.05 × 100 ≈ 223.2%.
• Per-TX Impact: ~100 TXs/block, fees rise from 0.0005 to 0.001616 DCR/TX (~223.2%, ~$0.026 at $16/DCR).
• Targeted TX Fee: Δf_min = (p × R_base)/(m - p) ≈ (0.5 × 0.1116)/(0.6 - 0.5) ≈ 0.558 DCR/TX (~$8.93, m=0.6).

Cost Dynamics

• Censor Advantage: Low cost (0–4.00% APR) enables sustained vetoes, especially if q→0. Censor tolerates ~$2.77M/year (DCR=$16).
• Miner Pressure: 50% revenue loss (0.0558 DCR/block) pushes self-censorship unless Δf ≥ 0.1116 DCR/block (~223.2% block fee hike).
• Fee Realism: ~223.2% increase or ~0.558 DCR for targeted TX may be impractical, favoring self-censorship.
• Defection: Non-censoring miners lose ~0.0558 DCR/block, driving defection to q=0 or exit, reducing censor costs to 0% APR.

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	0.1116	0.1116	223.2%	0.001616	~0.026	19.737	4.00%
0.1	0.625	0.6866	0.6866	109.856%	0.013116	~0.21	19.737	4.00%
0.5	3.125	3.1866	3.1866	101.971%	0.063616	~1.02	19.737	4.00%
1.0	6.25	6.3116	6.3116	100.986%	0.126116	~2.02	19.737	4.00%
10.0	62.5	62.5616	62.5616	100.098%	1.251116	~20.02	19.737	4.00%
50.0	312.5	312.5616	312.5616	100.020%	6.251116	~100.02	19.737	4.00%
100.0	625.0	625.0616	625.0616	100.010%	12.501116	~200.02	19.737	4.00%

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 of non-conformance. However this is counter-incentive. Any miner that censors earns twice the reward by experiencing 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 Multi-Player Stag Hunt, miners cooperate for a high collective payoff (resisting censorship, akin to hunting a stag) or defect for a safer individual payoff (self-censorship, akin to hunting a hare).

Payoff Matrix (Two-Player Example)

	Cooperate (C)	Defect (D)
Cooperate (C)	0.0558, 0.0558	0.0558, 0.1116
Defect (D)	0.1116, 0.0558	0.1116, 0.1116

• Cooperate: (1 - p) × R_base ≈ 0.0558 DCR/block (requires all cooperate).
• Defect: R_base ≈ 0.1116 DCR/block.
• Full cooperation (q=1) resists censorship but is unstable; defection drives q→0.

Miners face a Multi-Player Stag Hunt with a 50% stakeholder censor (α=0.50, p≈0.50) vetoing blocks with targeted TXs. They choose to cooperate (non-censoring, q>0) or defect (self-censoring, q=0). Payoffs are expected revenue (DCR/block) for individual choices, coordination allowed. Full cooperation (q=1) resists censorship but is unstable; any defection drives q→0, sustaining censorship.

• Equilibria: Full cooperation (all C, q=1) resists censorship but risky; full defection (all D, q=0) is stable, risk-dominant.
• Mixed Strategy: Cooperation probability q ≤ 0.5 due to risk dominance.
• Dynamics: Non-censoring miners lose ~0.0558 DCR/block (revenue vs. ~1.90 DCR/block costs), driving defection.
• Outcome: Self-censoring miners earn 0.1116 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 severely limited against a 50% stake censor (α=0.50). Low cost (0 - 4.00% APR) and fee increases push censor cost toward 0%. A 60% stake censor (p≈0.683) increases cost upper bound (0 - 4.56% APR), raises miner loss rate (~68.3%) and therefore fees required for offset (~704.2%), significantly increasing censor advantage. Critically, there is no mechanism by which a majority censor can be evicted by the economy.