Distribution Curve Design

Abstract

ECIP-1120 proposes distributing base fees to miners using a backward-looking "ℓ-smoothing" mechanism rather than burning them. This research determines the optimal parameters for this distribution: the number of ancestor blocks to consider (BACKWARD_FEES_BLOCK_COUNT) and whether to use a uniform or decay curve. The goal is to maximize manipulation resistance while ensuring miners receive timely compensation for securing the network.

Research Objectives

1. What is the optimal value for BACKWARD_FEES_BLOCK_COUNT (the smoothing window)?
2. Should fees be distributed uniformly across ancestor blocks or follow a decay curve?
3. How do different distribution parameters affect miner incentives during low-activity periods?
4. What is the minimum window size needed to adequately resist manipulation?

Background

The Distribution Problem

In EIP-1559, base fees are burned to prevent off-chain agreements (OCAs) between miners and users. However, burning is not viable for Ethereum Classic where:

• Miner revenue is essential for chain security
• ECIP-1017's fixed emission schedule must be preserved
• Fees become increasingly important as block subsidies decline

ℓ-Smoothing Theory

Roughgarden's analysis (Section 8.3.1) describes ℓ-smoothing as an alternative to burning: instead of paying fees to the current block's miner, distribute them across multiple blocks.

This works because:

1. Dilutes manipulation incentives: A miner manipulating the basefee only receives 1/L of the benefit
2. Preserves miner revenue: All fees eventually go to miners
3. Stateless calculation: Distribution computed from existing block headers

Backward vs Forward Looking

ECIP-1120 proposes backward-looking distribution for its simplicity and robustness.

Death Spiral Prevention

A critical motivation for fee smoothing is preventing a "death spiral" as block subsidies approach zero under ECIP-1017. Without smoothing:

1. Empty blocks offer no reward: Miners have no incentive to mine blocks with no transactions
2. Irregular block times: Mining becomes sporadic during low-activity periods
3. Transaction discouragement: Users face unpredictable confirmation times
4. Feedback loop: Lower activity → lower revenue → fewer miners → worse UX → even lower activity

Fee smoothing breaks this cycle by ensuring miners receive distributed fees from ancestor blocks even when their block is empty. This maintains a floor of mining incentive regardless of immediate transaction activity.

Stateless vs Stateful Design

ECIP-1120 proposes a stateless backward-looking mechanism rather than a stateful forward-looking accumulator. This design choice has significant implications:

When a reorg occurs, stateful data would require rolling back previous operations and tracking the history of changes to correctly restore state on the canonical chain. The stateless approach simply recomputes from the new canonical chain's block headers—no rollback logic needed.

Distribution Curve Options

Uniform Distribution: Each of the L ancestor blocks contributes 1/L of its fees.

Block N receives: Σ(ancestor[i].baseFee × ancestor[i].gasUsed) / L

Decay Curve: Recent blocks contribute more than older blocks.

Block N receives: Σ(ancestor[i].baseFee × ancestor[i].gasUsed × weight[i])
where weight[i] decreases with distance

Methodology

Approach

1. Theoretical Analysis: Model manipulation resistance as a function of window size
2. Historical Simulation: Replay ETC transaction history with different parameters
3. Game-Theoretic Analysis: Model miner behavior under various distribution schemes
4. Edge Case Analysis: Study behavior during extended low-activity periods

Tools & Resources

• ETC mainnet transaction history (full archive)
• Economic simulation framework
• Game theory modeling tools
• Statistical analysis software

Assumptions & Constraints

• Distribution must be calculable from block headers only (stateless)
• Miners should receive fees within a reasonable timeframe
• Empty blocks should still provide some reward to prevent mining abandonment
• Parameters must resist manipulation by miners controlling < 50% hashrate

Research Plan

Phase 1: Theoretical Foundations

• Formalize manipulation resistance as a function of L (window size)
• Calculate theoretical minimum L to resist OCA attacks
• Model miner expected value under different curve shapes
• Analyze empty block incentives for each configuration

Phase 2: Historical Analysis

• Extract historical ETC fee data from archive node
• Identify periods of low activity (consecutive low-fee blocks)
• Identify periods of high activity (fee spikes)
• Calculate what miner revenue would have been under different parameters

Phase 3: Simulation

• Implement simulation framework for fee distribution
• Test uniform distribution with L = 10, 50, 100, 200, 500
• Test exponential decay curves with various half-lives
• Test linear decay curves
• Measure variance in miner revenue for each configuration

Phase 4: Game Theory

• Model rational miner behavior for each parameter set
• Analyze attack profitability (spam, empty blocks, OCAs)
• Coordinate with Manipulation Resistance research
• Identify Nash equilibria under different configurations

Phase 5: Recommendation

• Synthesize findings from all phases
• Propose specific values with supporting evidence
• Document edge cases and risk factors
• Prepare specification text for ECIP-1120

Expected Outcomes

1. Recommended Parameters: Specific values for:
   • BACKWARD_FEES_BLOCK_COUNT: The smoothing window size
   • Distribution curve formula (uniform or decay function)
2. Economic Analysis Report: How parameters affect miner revenue stability
3. Manipulation Resistance Proof: Mathematical analysis showing attack resistance
4. Edge Case Documentation: Behavior during extreme conditions

Success Criteria

• Manipulation attacks require > 50% hashrate to be profitable
• Miner revenue variance reduced by > 50% compared to immediate payment
• Empty blocks still provide meaningful reward (preventing death spiral)
• Fee receipt delay is acceptable (< 1 hour at current block times)
• Parameters are simple enough for community understanding

Dependencies

• Manipulation Resistance Analysis - Attack vector validation
• Economic Modeling - Long-term sustainability analysis
• Network Analysis - Block time distribution data
• ETC archive node access for historical fee data

Current Status

Status: TODO

Progress Log

• 2025-11-27: Initial research plan drafted
• Pending: Begin Phase 1 theoretical foundations

Appendix: Pseudocode Reference

// Backward-looking fee distribution (uniform)
function calculateDistributedFees(
  blockchain: Blockchain,
  parentHash: Hash
): bigint {
  let totalFees = 0n;
  let ancestorHash = parentHash;

  for (let i = 0; i < BACKWARD_FEES_BLOCK_COUNT; i++) {
    const ancestor = blockchain.getBlockHeader(ancestorHash);
    if (ancestor === null) break;

    // Each ancestor contributes 1/L of its collected basefee
    const ancestorFee =
      (ancestor.baseFee * ancestor.gasUsed) / BACKWARD_FEES_BLOCK_COUNT;
    totalFees += ancestorFee;

    ancestorHash = ancestor.parentHash;
  }

  return totalFees;
}

References

• Roughgarden, T. Transaction Fee Mechanism Design - Section 8.3.1 on ℓ-smoothing
• EIP-1559 Specification
• ECIP-1017: Monetary Policy
• Besu Reference Implementation