Richard_Kennaway comments on Optimisation Measures: Desiderata, Impossibility, Proposals

[Richard_Kennaway]

Your formula in the proof of Proposition 1 is scaling invariant but not translation invariant:

$rep(p,[u\left]\right)=\frac{u\left(x\right)}{u\left(x_1\right)-u\left(x_2\right)}$

Should it be this?:

$rep(p,[u\left]\right)=\frac{u\left(x\right)-u\left(x_2\right)}{u\left(x_1\right)-u\left(x_2\right)}$

[mattmacdermott]

Thanks, should be fixed now.

It’s not that we needed to add a translation here to end up with the right definition of $OP$ in terms of $u$, but with the way we had written it $\mathrm{rep}$ wasn’t a well-defined function of equivalence classes. We had restated proposition 1 to try to make things cleaner, but turns out it messed things up so we’ve reverted to the previous statement. Hopefully it should all work now.