Prime-based crediting (actuarial entitlement, not deposit-linked)

[franrolotti]

Prime-based crediting (actuarial entitlement, not deposit-linked)

Idea

An alternative to deposit-based crediting is to grant every active member a uniform “prime entitlement” per epoch. This entitlement is calculated using actuarial principles: the probability of illness, the expected payout, and the number of active members.

This mirrors how insurance works in the real world: everyone pays in, and coverage is defined by a risk-based prime rather than by the exact amount you contribute individually. The difference is that in traditional insurance companies set primes conservatively (higher than expected claims) in order to keep surpluses as profit. In a Breadfund, primes could be set fairly, and any accumulated surplus can be redistributed among members or used to enhance coverage in the future.

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User story

A Breadfund of 20 freelancers pools funds to cover illness.

• Deposit-based approach: each freelancer contributes their dues, and their withdrawable balance increases. This is simple and transparent.

• Prime-based approach: the system instead calculates:

  Prime_epoch = P_ill * AveragePayout
  

  where:

  • P_ill = probability a member becomes ill in this epoch
  • AveragePayout = expected payout per illness

  Every member who is up to date on contributions receives this same entitlement for the epoch. Deposits keep the pool liquid, while coverage is distributed equally.

To manage liquidity smoothly, the Breadfund could use a carency period (e.g., a few epoch without coverage to gather an initial liquidity).

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Formulas

1. Expected claims this epoch:

   E_claims = N_members * P_ill
   

2. Expected payout total:

   E_total = E_claims * AveragePayout
   

3. Prime entitlement per member:

   Prime_epoch = P_ill * AveragePayout
   

   (the same for all active members).

4. Liquidity-aware adjustment (optional):

   EffectivePrime = Prime_epoch * R_epoch
   

   where R_epoch < 1 if surplus is high, > 1 if liquidity is tight.

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Benefits

• Aligns Breadfunds with mutual-aid and insurance logic: dues → coverage, not just personal savings.
• Fairer primes: no profit margin like in commercial insurance; surplus can be redistributed or used to improve benefits.
• Members can understand coverage in simple terms: “this month your entitlement is X.”

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⚠️ Risk: uncertainty in illness probability

The system relies on estimates of P_ill.

• If underestimated: claims may exceed liquidity.
• If overestimated: surplus accumulates faster than expected. Doesn't matter as users are informed that this will come back to them when sufficient liquidity and information about the probability of being ill is gathered.

Mitigations:

• Update P_ill dynamically from observed claims.
• Use carency periods to accumulate an initial liquidity calculated on the prime users want to pay.
• Define clear surplus redistribution rules to maintain trust.