The following post was kindly contributed by Eyal Sulganik from IDC (Interdiciplinary Center) Herzliya. Eyal was motivated by our poll on certainty “beyond a reasonable doubt,” which is related to several issues in accounting.
Mathematicians, I believe, are always looking for new areas where their models and concepts can make a difference. Physics, Economics, CS, Biology are just some examples, surely not exhausting a longer list of such areas. Although the origins of accounting emanate from mathematicians (for example: L. Pacioli, and even A. Cayley found interest in it), it is a fact, though not unexplained, that these days (almost) no mathematicians are interested in accounting and there is no field of “mathematical accounting”. In the following few paragraphs I would like to thus draw attention to accounting as a possible field for mathematicians. Surprisingly, a possibly “profitable field”. I believe that accounting can be subject, inter-alia, to use of theories of Formal Systems, Information Theory, Voting theory, Fuzzy Logic, Graph theory and even Catastrophe theory. In brief, accounting (Financial Reporting) deals with the measurement and reporting of economic events . As such, it is a measurement system interlaced with an information system. (Results such as Blackwell theorem on the comparison of information systems are of relevance).
Financial reporting of firms, the lifeline of the Capital Markets, is dictated by “reporting standards”. Those reporting standards are determined by “standard boards” (according to voting rules and procedures, which are very interesting for analysis) and interpreted and evolve over time (as is the case with other languages). The reports are audited by accounting firms. Auditing theory became more sophisticated but even fairly standard tools like Benford Law are not yet routine.
Moreover, a huge debate centers on whether to adopt a rule-based system where “every” possible scenario is prescribed in advance or whether to adopt a principle based system which gives” freedom” to every reporting entity in reflecting the economic substance of an event.
It is well known that a rule-based systems provide greater comparability (between firms), but at the same time, as they are more rigid and make use of “bright lines”, can be more easily forced to reflect form over substance . Indeed, Bright line Accounting rules are not continuous functions and hence small changes in the description or design of an event can lead to enormous differences in the reported values. For example, given that the definition of “CONTROL” was based on a “50% legal test” ,until recently it was the case that if company A was holding 50.01% of the shares of company B (other holders being each much smaller) and sold only 1.02% it could recognize a profit, due to “loss of control”, as though it sold the whole holding and bought back 49.01%. Needless to say that although holding “only” 49.01% , A CONTROLs B (Danny Ben Shahar, Desmond Tsang and Myself are in the process of demonstrating that “accounting theory of control” is inconsistent with Shapley Value).
Principle based systems, on the other hand, must make sure that its principles are common knowledge. For example, if a provision for loss regarding a claim against a firm depends on the chances of loss being “Probable” or “remote” or “reasonably possible” a question arises what the preparers and users of the financial statements think about those terms. Many years ago, me and my colleague Yossi Aharoni found out-through questionnaires- that different types of agents have different probabilistic interpretations to those terms and we explained the mis-communication it can cause. I attach two simple papers (one co-authored with Danny Ben Shahar, the other one in hebrew), that can shed some more light on the above point of view and I dare state a wish that a new field of “mathematical accounting” will be created .