Private (Bounded) Alignment Protocol (PBAP)
A multi-stage negotiation protocol for identifying value alignment between two parties without premature disclosure of private thresholds.
1. Definitions
Parties: Initiator (A) and Responder (B).
Threshold Range: A range [min, max] representing a party's "No Regret" zone.
Flexibility Spread (σ): A percentage (e.g., 20%) defining the maximum allowed expansion of the range.
Target Value (T): The ideal value at the center of the range.
2. Protocol Lifecycle
Phase I: Initialization & Commitment
Initiator A defines a target value TA and selects a flexibility spread (σ).
The system generates an initial range: [TA - σ, TA + σ].
This range is committed to the protocol.
Phase II: Secure Response
Responder B provides their target value TB.
The system generates their range using the same flexibility σ selected by the Initiator to ensure fairness.
Phase III: Overlap Verification (Round 1)
The protocol checks if the two ranges overlap.
Overlap Max = Minimum of both Maximums
If an overlap exists, the deal is COMPLETED. The final agreement value is the center point of the overlapping section.
Phase IV: Feasibility & Directional Disclosure
If the ranges do not overlap, the protocol checks for Bounded Feasibility. This determines if a deal is possible if both parties were to use their maximum flexibility.
Case: B is below A
Feasible if B's maximum possible range reaches A's minimum possible range.
Case: B is above A
Feasible if B's minimum possible range reaches A's maximum possible range.
If feasible, the protocol reveals a Directional Hint(e.g., "Party B is Above") to both parties. If not feasible, the protocol enters DEADLOCK and terminates without revealing any directional data.
3. Security Properties
Internal Comparison
Calculations are performed privately within the system. Ranges are never shared between parties. In a DEADLOCK state, no information (including the direction of the gap) is revealed.
Anti-Fishing Constraint
By locking the flexibility spread (σ) globally for the deal, a Responder cannot use a disproportionately large range to "fish" for the Initiator's budget.
Equitable Surplus Extraction
The use of overlap midpoints removes the first-mover disadvantage. Neither party can "win" the negotiation through aggressive anchoring; the protocol extracts the shared surplus equally.
4. Reference Implementation
The complete, open-source implementation of the BAP engine and this application is available on GitHub.
View Source on GitHub