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gjm comments on Akrasia, hyperbolic discounting, and picoeconomics - Less Wrong
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No, that's too general; for instance, hyperbolic discounting is F(a,b) = b-a, but hyperbolic discounting is inconsistent in the relevant sense. For consistency we need F(a,b) F(b,c) = F(a,c), or equivalently F(b,c) = F(a,c) / F(a,b) = G(c)/G(b) where G(t) = F(a,t). (Note that the dependence on a has gone away.) This is equivalent to discounting things at time t by a factor G(t), which is the general form I described.
Depending only on time differences is the same thing as being invariant under time-shifting your whole life.
I started getting into this, but there's not really much point - the important thing is that we agree that if we require that preferences be invariant under time-shifting and not reverse as the choices approach, then only exponential discounting meets these criteria (treating not discounting at all as a special case of exponential discounting)
Right.