Merit Decay Curves: Why Power Must Fade

How reputation systems prevent permanent hierarchies through mathematical decay

Why Power Must Fade

Every system of influence faces the same fundamental tension: contributions deserve recognition, but permanent power corrupts. The Roman Republic understood this, limiting dictators to six-month terms. Academic institutions understand it too—yesterday’s groundbreaking research becomes today’s baseline assumption. Even social networks implicitly encode this principle in their algorithms.

The question isn’t whether influence should decay, but how fast and under what conditions.

In the Unscarcity framework, Mission Credits—the currency of the 5% Frontier economy—must decay to prevent the emergence of permanent aristocracies. But the decay rate matters enormously. Too fast, and contributors feel their work is devalued; too slow, and you recreate the wealth dynasties you sought to escape.

This article examines how existing systems handle reputation decay, extracts mathematical principles from real-world implementations, and proposes optimal half-lives for different contribution types.

The Fundamental Problem

Without decay, reputation systems inevitably develop three pathologies:

1. Incumbent Lock-In
Early contributors accumulate advantages that compound over time. In Stack Overflow, users who joined in 2008-2009 hold reputation levels that new users cannot realistically achieve, even with equivalent contributions. As one analysis noted: “People who, a long time ago, asked simple, common questions which, at this point would be booted for not being up to ‘community standard,’ get their at most 200 rep per day years after it has been posted.”

2. Relevance Drift
Contributions valuable in one context become irrelevant as circumstances change. Academic citations demonstrate this clearly: the “half-life” of scientific papers—the time for citation rates to drop by half—averages 6-7 years across disciplines. A groundbreaking 2010 paper on social media algorithms may be nearly worthless for understanding 2025 platforms.

3. Effort Stagnation
When past achievements guarantee future influence, the incentive for continued contribution diminishes. Wikipedia’s editor retention crisis illustrates this: the community’s growth of “lone wolf” established editors with accumulated influence coincided with dramatic drops in newcomer retention.

The solution is mathematical: design decay curves that honor past contributions while ensuring present relevance determines present influence.

Existing Decay Models

Real-world systems have developed various approaches to reputation and influence decay. Understanding these implementations reveals both proven principles and cautionary tales.

Model 1: No Decay (Stack Overflow)

Stack Overflow represents the most prominent “no decay” reputation system. Reputation points, once earned, persist indefinitely (except through specific negative events like downvotes on answers or removed content).

How It Works:

• Users earn reputation through upvotes (+10 for answers, +5 for questions)
• Reputation decreases only through downvotes (-2 for answer downvotes) or content removal
• Privileges unlock at fixed reputation thresholds (e.g., 15 to upvote, 2,000 to edit)

Results:
The system has created significant inequality. The top 0.1% of users hold disproportionate influence, and many high-reputation users effectively retired from active contribution while retaining their status. As noted in analyses of the platform: “StackOverflow is full of outdated questions about older technologies like Java 6 (released in 2006) or Oracle 8 (1997), but these questions and answers are still scored the same, no matter how irrelevant they’ve become.”

Lesson: Static reputation systems create entrenched hierarchies where historical contribution trumps current relevance.

Model 2: Content Decay (Reddit’s “Hot” Algorithm)

Reddit doesn’t decay user karma (your total score), but it aggressively decays the visibility of individual posts through its ranking algorithm.

How It Works:
The “hot score” formula incorporates time decay directly:

Hot Score = log₁₀(|upvotes - downvotes|) + (sign × age_in_seconds / 45000)

This creates a 10× decay every 12.5 hours—a post must gain 10 times as many votes to maintain its ranking over that period.

Results:
Content cycles rapidly, with most front-page posts disappearing within 24 hours regardless of total votes. However, user karma persists indefinitely, creating a hybrid system where content visibility decays but accumulated reputation does not.

Lesson: Post-level decay maintains content freshness but doesn’t address user-level power concentration.

Model 3: Power-Law Decay (Hacker News)

Hacker News uses a polynomial (power-law) decay function rather than exponential decay:

How It Works:

Score = (Points - 1) / (Age_hours + 2)^1.8

The gravity factor (1.8) determines how aggressively posts decay. Higher gravity = faster decay.

Results:
Even the most popular posts fall off the front page within 20-24 hours. The system maintains consistent content turnover without requiring manual intervention.

Key Insight: The gravity parameter (1.8) was tuned empirically to match desired content cycling rates. This suggests that optimal decay rates are discoverable through experimentation.

Lesson: Power-law decay provides smoother transitions than exponential decay for content ranking.

Model 4: Citation Half-Life (Academic Publications)

Academic citations provide the most studied example of natural reputation decay.

How It Works:
Citations aren’t artificially decayed—they represent organic references to prior work. The “cited half-life” measures how long it takes for citation rates to a journal to drop to half their peak.

Empirical Findings:

• Mean weighted cited half-life across all journals: 6.5 years
• Health Sciences journals: 25-36 months (shorter due to rapid advancement)
• Humanities/Physics/Mathematics: 49-60 months (longer due to foundational nature)
• More than 70% of references are to papers published within 10 years
• Papers older than 20 years are cited infrequently

The Pattern:
Citation decay follows an exponential curve surprisingly well. One analysis found that “every nine years, the likelihood of a paper being cited halves.”

Lesson: Natural decay rates vary by domain, with rapidly-evolving fields showing faster decay. System designers should match decay rates to the pace of change in their domain.

Model 5: Social Capital Decay (Theoretical Framework)

Social capital theory, developed by Bourdieu (1986), Coleman (1988), and Putnam (1995), explicitly addresses the maintenance and decay of social influence.

How It Works:
According to Robison, Schmid, and Siles (2002), social capital “is subject to decay from use, the passage of time, and lack of maintenance.”

Three decay mechanisms operate:

1. Time decay: Relationships weaken without active maintenance
2. Use decay: Drawing on social capital without replenishment depletes it
3. Relevance decay: As contexts change, old connections become less valuable

Key Insight:
Social capital requires active maintenance to persist. Unlike financial capital, it cannot simply be stored. This suggests reputation systems should require ongoing contribution to maintain influence, not just accumulation to acquire it.

Lesson: Reputation should require maintenance, not just acquisition.

Model 6: Time-Window Methods (Yahoo! Spam Detection)

The Yahoo! Spammer IP reputation system uses a fixed time window for calculating reputation:

How It Works:

• Only contributions within a fixed time window count toward reputation
• New contributions push old ones out of the window
• Reputation is recalculated from the remaining data

Results:
This creates a “moving average” effect where reputation reflects recent behavior. Spammers cannot benefit from past good behavior, and reformed IPs can rebuild reputation.

Lesson: Time windows provide a simple mechanism for ensuring current behavior determines current reputation, though they create abrupt cliffs rather than smooth curves.

Optimal Half-Lives

Based on the research above, we can derive optimal decay rates for different contribution types within the Mission Credit system.

The Mathematics of Decay

Exponential decay follows the formula:

V(t) = V₀ × e^(-λt)

Where:

• V(t) = value at time t
• V₀ = initial value
• λ = decay constant
• t = time elapsed

The relationship between half-life (t½) and decay constant:

t½ = ln(2) / λ ≈ 0.693 / λ

For practical application, we can express this as:

V(t) = V₀ × (1/2)^(t/t½)

Proposed Half-Lives by Contribution Type

Based on empirical data from existing systems and the nature of different contributions:

Worked Example: Scientific Discovery

A researcher makes a breakthrough contribution to fusion energy, earning 1,000 Mission Credits.

With a 6-year half-life:

• Year 0: 1,000 credits
• Year 6: 500 credits
• Year 12: 250 credits
• Year 18: 125 credits
• Year 24: 62.5 credits

After 24 years, the original contribution still provides influence, but at 6.25% of its original level—enough to acknowledge the historical contribution without creating permanent privilege.

The “Refresh” Mechanism

Rather than pure decay, the system should allow contributions to be “refreshed” through continued relevance:

1. Citation Refresh: If others build on your work, your credits decay more slowly
2. Maintenance Refresh: Continued engagement in your contribution domain slows decay
3. Application Refresh: Real-world implementation of theoretical work renews credits

This creates a hybrid system where decay is the default, but ongoing contribution maintains influence.

Decay Curve Visualization

Credits (% of original)
100% |*
     | *
 80% |  *
     |   *
 60% |    *  Crisis (6mo)
     |     * Technical (2yr)
 40% |      *  Scientific (6yr)
     |       *  Artistic (12yr)
 20% |        *
     |         *
  0% |__________*_____________
     0   2   4   6   8  10  12  14  16  18  20
                Years

Implementation Details

Translating theoretical decay curves into practical implementation requires addressing several technical challenges.

Computational Approach

Option 1: Real-Time Calculation
Calculate decay at query time using the formula:

def current_credits(original_credits, timestamp, half_life_years):
    years_elapsed = (now() - timestamp) / SECONDS_PER_YEAR
    return original_credits * (0.5 ** (years_elapsed / half_life_years))

Pros: Always accurate, no batch processing needed
Cons: Computationally expensive at scale

Option 2: Periodic Batch Update
Update all credit values daily/weekly:

def batch_decay_update(all_credits, decay_period_days):
    for credit in all_credits:
        decay_factor = 0.5 ** (decay_period_days / (credit.half_life * 365))
        credit.value *= decay_factor

Pros: Simpler queries, predictable performance
Cons: Slight inaccuracies between updates

Recommended: Hybrid approach—batch updates for display, real-time calculation for critical decisions.

Credit Categories and Tracking

Each credit entry should include:

{
  "credit_id": "uuid",
  "holder_id": "user_uuid",
  "original_value": 1000,
  "current_value": 847.3,
  "contribution_type": "scientific_discovery",
  "half_life_years": 6,
  "issued_date": "2025-03-15",
  "last_decay_calculation": "2025-11-21",
  "refresh_events": [
    {"date": "2025-09-01", "type": "citation", "effect": "decay_rate * 0.9"}
  ]
}

Aggregation Rules

When displaying total influence:

1. Sum all current_value across active credits
2. Apply domain-specific weighting (governance decisions weighted by governance credits)
3. Apply time-of-last-contribution recency bonus (active contributors get slight boost)

Edge Cases

Death or Incapacity:
Credits should continue decaying normally. This prevents “ancestor worship” where deceased contributors accumulate permanent influence.

Disputed Contributions:
Place credits in escrow during dispute resolution. If contribution is invalidated, credits are revoked; if validated, credits resume normal decay from original issuance date.

Collective Contributions:
Split credits among contributors based on peer-assessed contribution ratios. Each portion decays independently.

Transfer Attempts:
Mission Credits are non-transferable by design. Any attempt to transfer resets credits to zero for both parties.

Preventing Gaming

Any reputation system faces gaming attempts. Decay mechanisms introduce new attack surfaces that must be addressed.

Attack Vector 1: Sybil Attacks

The Attack: Create multiple identities to earn credits across many accounts, then aggregate influence.

Defense Mechanisms:

• Identity Validation: Proof-of-Personhood requirements tie accounts to verified humans
• Social Graph Analysis: SybilGuard and similar algorithms detect clusters of fake accounts by their connection patterns
• Economic Costs: Meaningful contributions require time investment, making mass identity farming expensive
• Behavioral Detection: Machine learning models achieve 97-99% accuracy detecting Sybil accounts based on activity patterns

Attack Vector 2: Decay Gaming

The Attack: Time contributions to maximize influence at critical moments, then coast on decaying credits.

Defense Mechanisms:

• Minimum Sustained Contribution: Voting rights require minimum recent contribution, not just accumulated credits
• Decay Acceleration for Inactivity: If no new contributions in 12 months, decay rate doubles
• Fresh Contribution Weighting: Recent contributions weighted more heavily in aggregate calculations

Attack Vector 3: Artificial Refresh

The Attack: Generate fake “citations” or downstream applications to slow decay on existing credits.

Defense Mechanisms:

• Independent Validation: Refresh events must come from accounts without prior connection to the original contributor
• Quality Threshold: Only citations/applications above certain impact threshold qualify for refresh
• Diminishing Returns: Each refresh event has decreasing effect (first refresh: 10% decay slowdown, second: 5%, etc.)

Attack Vector 4: Contribution Inflation

The Attack: Pad contributions with low-value work to maintain active status.

Defense Mechanisms:

• Peer Review Gating: New credits require peer validation before issuance
• Proof-of-Diversity Validation: Multiple diverse validators must confirm contribution value
• Quality-Adjusted Decay: Low-quality contributions decay faster than high-quality ones

Attack Vector 5: Timing Attacks

The Attack: Coordinate with others to time contributions for maximum collective influence during specific decisions.

Defense Mechanisms:

• Rolling Windows: Influence calculations use 30-90 day rolling averages, not point-in-time snapshots
• Anti-Coordination Detection: Statistical analysis identifies coordinated timing patterns
• Random Jitter: Small random delays in credit issuance prevent precise timing

The Meta-Defense: Transparency

All credit calculations, decay rates, and gaming detection should be publicly auditable. Bad actors cannot game a system whose mechanisms they don’t understand—but neither can good actors trust such a system. Transparency enables:

1. Community detection of novel attacks
2. Independent verification of fair treatment
3. Continuous improvement based on observed manipulation attempts

Conclusion: Designed Impermanence

Merit decay isn’t a punishment for past contributors—it’s an acknowledgment that relevance is contextual and temporal. The scientist who discovered penicillin deserves recognition, but shouldn’t govern antibiotic policy 80 years later based on that discovery alone.

The proposed system encodes several principles:

1. Contributions matter, but current contributions matter more
2. Different contribution types warrant different decay rates
3. Ongoing engagement should slow, but not stop, decay
4. The system must resist gaming while remaining transparent

By building decay into the fundamental mathematics of influence, Unscarcity prevents the emergence of permanent hierarchies while still honoring those who contribute to the Frontier.

Power must fade—not because past work has no value, but because the future deserves fresh voices at the table.

References

• Bourdieu, P. (1986). “The Forms of Capital” in Handbook of Theory and Research for the Sociology of Education
• Coleman, J.S. (1988). “Social Capital in the Creation of Human Capital.” American Journal of Sociology
• Clarivate. “Cited Half-Life” - Journal Citation Reports documentation
• Parolo, P.D.B., et al. (2015). “Attention decay in science.” Journal of Informetrics
• Robison, L.J., Schmid, A.A., & Siles, M.E. (2002). “Is Social Capital Really Capital?” Review of Social Economy
• Stack Exchange Meta. “Should reputation decay?” - Community discussion
• Wikipedia. “Exponential decay” - Mathematical foundations
• Wikipedia. “Sybil attack” - Security considerations
• Wikimedia Foundation. “Research:Editor retention” - Wikipedia editor dynamics
• Various. Hacker News ranking algorithm analyses