This paper studies the balance constraint (debit=credit) in bookkeeping, its causes and its consequences for accounting. Balance in the ledger is shown to: 1) imply balance in journal entries and vice versa; 2) link the value definitions in the earnings statement and balance sheet; 3) have direct implications for valuation puzzles encountered in accounting, like accounting for OCI or stock-based compensation, and the difference between earnings or balance-sheet approaches to valuation. These system-wide effects on accounting highlight a design question: why do we have the balance constraint in bookkeeping? Backward-engineering shows 6 axioms that logically lead to double-entry bookkeeping. The balance constraint follows from the existence of a residual account: owner’s equity. A class of equivalently powerful record keeping systems is shown to exist. These systems use double-entry bookkeeping without the monetary-unit assumption and can be used to record other outputs of the organization, like societal impact. These systems can be implemented in relational databases, a blockchain, or a different technology all together. The discussion covers links with other mathematical descriptions of bookkeeping and potential avenues for future research in the mathematics of bookkeeping.

Axioms for bookkeeping, duality, bookkeeping system design, mathematics, of record keeping.
hdl.handle.net/1765/127710
ERIM Report Series Research in Management
ERIM report series research in management Erasmus Research Institute of Management
Erasmus School of Economics

Renes, S. (2020). When Debit=Credit. The balance constraint in bookkeeping, its causes and consequences for accounting (No. ERS-2020-005-FA). ERIM report series research in management Erasmus Research Institute of Management. Retrieved from http://hdl.handle.net/1765/127710