The Satisficing Welfare Theorem: How Behavioral Firms Produce System-Welfare Gaps by Design

Behavioral firms destroy system welfare as a structural property of their decision procedure

The Satisficing Welfare Theorem proves that when two satisficers with adaptive aspirations interact, expected system welfare goes negative beyond a finite threshold T*, and the deficit grows with the aspiration-adaptation rate λ.

• System welfare is procedurally invisible: absent from the aspiration vector, search trigger, and stopping rule.
• The Hollow Win outcome (0,1,1) — both parties gain while the system degrades — is the generic attractor.
• The theorem is the procedural conjugate of the Missing System Theorem (Postnieks 2026a).

Simon and Cyert built a positive theory that omitted system welfare by design

The behavioral firm sets aspirations for revenue, market share, and cost — but never for system welfare. This omission is architectural, not accidental.

• Simon (1955): satisficing replaces maximization under bounded rationality.
• Cyert & March (1963): firms are coalitions with negotiated goals, problemistic search, and standard operating procedures.
• Aspiration adaptation rule: α = (1-λ)α + λ[β·o_firm,t + (1-β)·ō ] — no S term.

System welfare cannot enter the firm's decision procedure through any channel

S is absent from search triggers, SOPs, coalition bargaining, and the aspiration-update rule itself. The firm cannot learn about system welfare through its own procedure.

• Problemistic search is triggered by private-dimension gaps; S has no aspiration level, so no search is triggered.
• SOPs encode prior satisficing solutions on private dimensions only.
• S-bearers (communities, ecosystems, future cohorts) have no seat in the coalition.
• Even catastrophic S deterioration is invisible to the adaptive aspiration mechanism.

Expected system welfare goes negative beyond a finite threshold T*, and the deficit scales with λ

Under five assumptions (reachability, density advantage, locality, private-return ordering, no-overshoot regularity), the theorem proves three results.

• (i) ∃ T*(η) such that E[w_t] < 0 for all t > T*(η) with probability ≥ 1-η.
• (ii) T*(η) is weakly decreasing in λ; post-threshold E[w_t] is weakly increasing in λ.
• (iii) Hollow Win (0,1,1) is the generic long-run basin.

The ratchet: private outcomes reinforce the welfare-destroying trajectory

Five steps show how satisficing locks firms into the negative-welfare region.

• Step 1: First-contact probability favors X^† (welfare-destroying) due to density advantage ε.
• Step 2: Aspiration ratchet — private outcomes in B update aspirations toward B, ignoring negative W.
• Step 3: Basin contraction — adjacent X* actions fall below adapted aspirations.
• Step 4: Welfare-deficit persistence — escape requires external rule change, shock, or global search.
• Step 5: Higher λ accelerates lock-in, increasing the welfare deficit.

The density advantage holds generically: negative externalities are cheaper

Assumption 2 (density advantage) is the key empirical condition. It holds whenever producing negative externalities is cheaper than avoiding them — which is virtually every industry.

• Polluting is cheaper than abating; exploiting weak enforcement is cheaper than paying living wages.
• Regulatory compliance costs add to X* actions but not to X^† actions.
• Peer-reference competition compresses margins, pushing firms deeper into X^†.
• Exception: industries where welfare-preserving actions are privately cheaper (e.g., solar vs. coal for new builds).

Simulation across 45 parameter cells confirms the theorem's predictions

100,000 draws per cell across λ ∈ 0.1, 0.25, 0.5, 0.75, 1.0 , β ∈ 0.3, 0.5, 0.7 , and three slack levels, tested with normal, lognormal, and triangular distributions.

• Expected system welfare negative for all t > T* across all 45 cells.
• T* decreases monotonically with λ; E[w_t] increases monotonically with λ.
• Hollow Win (0,1,1) is the modal outcome in every cell.
• Distribution robustness confirmed: results hold across all three distribution families.

Three industries show λ-driven welfare destruction at different cadences

Calibrated λ values: fast fashion (λ ≈ 4/year), pharmacy benefit management (λ ≈ 1/year), platform monopoly (λ ≈ 12/year).

• Fast fashion: annual welfare cost $385.4B (textile waste, water pollution, garment worker exploitation).
• Pharmacy benefit management: annual welfare cost $381.0B (inflated copays, independent pharmacy closures, non-adherence).
• Platform monopoly: annual welfare cost $999.4B (adolescent mental health, democratic discourse, local journalism).
• Higher λ corresponds to faster decision cadence and larger β_W (welfare coefficient).

The firm passes procedural-rationality review while the system degrades

Simon's (1976) procedural rationality standard checks whether the decision procedure is defensible — and the behavioral firm's procedure is defensible at every step. The welfare gap is undetectable because the procedure does not measure S.

• Aspirations were set? Yes. Search was conducted? Yes. Acceptable option found? Yes. SOPs followed? Yes.
• The procedure never fails on a dimension it does not measure.
• Procedural rationality is necessary but not sufficient for welfare protection.
• Decision Accounting's Field 17 (SYSTEM WELFARE) is the minimum correction.

Adding S to the aspiration vector is the minimum procedural fix

The structural fix (adding S to the payoff space, e.g., a carbon tax) is necessary but not sufficient. The procedural fix — adding S to the aspiration-update rule — is also required.

• Decision Accounting (Postnieks 2026f) includes 17 fields; Field 17 asks: 'What effect does this decision have on the broader system?'
• Without Field 17, the DA record passes all 15 other fields while the system degrades.
• Field 17 extends Simon's architecture rather than replacing it.
• Regulators must check for the absence of S in the aspiration vector — not merely the soundness of the procedure.

The SWT closes the welfare gap Simon and Cyert left open

The theorem formalizes what happens to system welfare when the firm's decision procedure does not contain it as an argument. The answer: expected system welfare goes negative and stays negative, and the deficit scales with λ.

• First formal welfare theorem derived from the Cyert-Simon behavioral-firm program.
• Identifies λ as the measurable, observable driver of system-welfare destruction.
• Establishes procedural conjugacy between MST (structural exclusion) and SWT (procedural invisibility).
• Shows that procedural-rationality review is insufficient without checking for S in the aspiration vector.