A Graph-Theoretical Approach to the Axiomatisation of National

Accounting

Professor Itsuo SakumaSchool of Economics

Senshu UniversityJapan

Key Words

• Polyani Process

• Graph Theory

• Axiomatisation

Polanyi Process

• A Polyani Process has two elements– (1)Nature Humans

– (2)Humans Humans

• A Polyani Process can be seen as a general description of the national accounts

Origin of Graph Theory

Königsberg Bridge Problem

A

B

C

D

B

A D

C

Leonhard Euler’s solution

Applications of Graph Theory

• Used in engineering, transport networks, chip design …..

• Flow charts often used in statistics but not usually in the framework of graph theory

• Marco Polo, Michael Ward and Robert Hill

Graph theory language

• Digraph– flow

• Tree– edge

• Out degrees and in degrees

Three groups of axioms

• A group– 15 axioms define the economic units, flows,

places, economic objects in a Polyani Process

• B group– 4 axioms formulate the accounting system

• C group– 5 axioms extend the Polyani Process so that it

will include financial and non-tangible assets

Examples of Group A axioms

• Economic objects

• Economic units

• Places of appearance/disappearance

• Places of non-appearance/non-disappearance

Examples of Group B axioms

• Transfers

• Balancing items

• Accounting system

Examples of Group C axioms

• Flows of non-real economic objects

• Places of appearance/disappearance for financial economic objects

• Places of non-appearance/non-disappearance for financial economic objects

Conclusions

• ”Axiomatic approaches to national accounting are useful in that national accountants are invited to rethink what they are doing”

• The graph theory approach is a useful way to teach national accounts to students who have no background in accounting.

Comments

• Why bring in the concept of a Polyani Process?

• Show us a graphical presentation of the national accounts using graph theory.

• A well-written but challenging paper.