We develop a theory of biased extensive measurement which allows us to prove the existence of a ratio-scale without transitivity of indifference and with a property of homothetic invariance weaker than independence. These representations, which cover the cases of interval orders and of semiorders, reveal a unique biasing function smaller or equal to 1 that distorts extensive measurement and explains departures from its standard axioms. We interpret this biasing function as characterizing the qualitative influ…
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