Ordinal utility differences (Q6549139)

The author proposes to us a new kind of quaternary relation when investigating ordinal utility differences. To define the quaternary relation the author introduces a standard binary pre-order relation ``preferred or equivalent''. The binary relation is called ordinary representable if there exists a function \(v: X \rightarrow R\) defined on a given set of options \(X\), which assigns to elements \(a,b \in X\) values \(v(a) \geq v(b)\) whenever \(a\) is ``preferred or equivalent'' to \(b\). The new quaternary relation \(R\) among any four elements \(a,b,c,d \in X\), which is introduced in the paper, is interpreted as \(a\) is preferred to \(b\) more intensively than \(c\) to \(d\). Relation \(abRcd\) takes place if and only if three properties of the binary pre-order are fulfilled. Five properties called neutrality, reversal property, concatenation, co-concatenation and separability, which the quaternary relation \(R\) should have. The main result of the paper is the proof that the quaternary relation \(R\) is a pre-order and posses the five properties and two further properties called divisibility and Archimedeanity.