Order Invariance in Shared-Cap Priority Waterfalls

Executive overview

Several collateral pools may pay overlapping creditors, each pool by its own priority tiers and each creditor up to one aggregate cap. If recoveries are computed by processing the pools one at a time, the answer can depend on which pool goes first, which makes the processing order a hidden modelling input.

This paper gives an exact pairwise test for when the order cannot matter, for any caps and pool values. A creditor eligible in only one of two pools must rank strictly above, in that pool, every shared creditor. For each shared creditor, the two pools must agree on the ranking, including ties, of the shared creditors it weakly outranks in both. The test is sufficient for any common splitting rule satisfying the paper’s axioms, and necessary and sufficient under proportional splitting.

Findings, in order

1. Exact criterion. Under proportional splitting, every creditor’s total recovery is the same for all processing orders, caps and pool values exactly when every pair of pools passes the test. Sufficiency holds for any common splitting rule satisfying the paper’s axioms.
2. Small counterexamples. Every failure contains one of three obstructions on two or three creditors. A polynomial screening test finds one and returns it as a certificate.
3. Strict priorities. With strict priorities and the same eligible creditors in both pools, the test is avoidance of the permutation pattern 132, so compatible second-pool orders are counted by the Catalan numbers.
4. Admissions and reserves. For one open slot and one soft-reserve slot, both accepting all students and using a common master ranking within groups, admitted sets are independent of precedence for every applicant set exactly when no reserve-ineligible student lies between two reserve-eligible students in that ranking.
5. Funding, pool-at-a-time rules and averaging. Equal totals do not imply equal pool-level funding; no pool-at-a-time rule that respects local priority and wastes nothing is order-invariant on every structure; and averaging over processing orders can break priority within a pool.

Novelty