If even two hedonic states can stand in a 'parity' relation resistant to cardinal ordering, then a single-number hedonimeter would systematically misrepresent the structure of hedonic value.
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The structure of hedonic value(in ethics and value theory)
The underlying pattern or framework of how different pleasurable experiences relate to and compare with each other in terms of what makes them valuable.
hedonimeter(Edgeworth 1881; used here as a benchmark for maximal precision in happiness measurement that current methods fall short of.)
A hypothetical device envisaged by Edgeworth to show precisely how happy a person is at any given moment.