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## A method for the efficient settlement of multi-way debts.

Problem
If Amanda owes you ten pounds and you owe Bert five pounds then the direct settlement method means you have to write a cheque for five pounds even though in total you're owed money.

Solution
Amanda pays you five pounds and Bert five. You don't write any cheque at all.
This can be applied to any group of traders.

Algorithm
Each member of a group calculates the total owed or owing to the others.
Members are paired and settle by one transaction between them and one 'to the rest'.
Each pair is now treated as a single entity and the process repeated

The selection of pairs and which is to deal on behalf of both can be optimised.

Analysis
This method is at least twice as good in number and size of transactions as the 'all debtors pay into the pool then all creditors take out' method.

Financial institutions that get paid commission or charge interest while we're waiting to get paid won't be too happy.

The full paper is at
http://vulpeculox.net/ob/DebtSwapping.htm

• #### Paul Lillebo

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Jun 5 2013: In the example you give, it seems that 2 checks are written in both the original situation and in the proposed solution. The only difference is in who writes the checks. No?
• #### Peter Fox

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May 7 2013: This is about the SETTLEMENT of debts not SWAPPING loans.