Biased extensive measurement: The homogeneous case

In the homogeneous case of one type of objects, we prove the existence of an additive scale unique up to a positive scaling transformation without transitivity of indifference and with a property of homothetic invariance weaker than monotonicity. The representation, which is a particular case of a semiorder representation, reveals a unique positive factor α?1 that biases extensive structures and explains departures from these standard axioms of extensive measurement (α=1). We interpret α as characterizing the qualitative influence of the underlying measurement process and we show that it induces a proportional indifference threshold.