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 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)	Δf_min (DCR/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	9.5	13.31	2.70%
0.1	0.625	2.475	2.475	396.0%	0.0310	~0.50	12.375	13.31	2.70%
0.5	3.125	4.975	4.975	159.2%	0.0686	~1.10	24.875	13.31	2.70%
1.0	6.25	8.10	8.10	129.6%	0.1435	~2.30	40.5	13.31	2.70%
10.0	62.5	64.35	64.35	102.96%	1.2685	~20.30	321.75	13.31	2.70%
50.0	312.5	314.35	314.35	100.592%	6.2685	~100.30	1571.75	13.31	2.70%
100.0	625.0	626.85	626.85	100.296%	12.5185	~200.30	3134.25	13.31	2.70%

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.