Hi Pablo, I noticed that you changed this page to state that MacAskill et al. merge tractability and neglectedness into a single factor called leverage. I think that's a misreading of the text: they actually split the dX/dW term in a different way from OCB's original formulation, so that the first factor is tractability and the second factor is leverage instead of neglectedness. Here's the relevant quote from the paper:
An alternative approach is to identify ‘tractability’ with the overall difficulty of the problem. Let W0 be the total amount of work that would be required to solve the problem (or to achieve some relevant benchmark), and let X0 be the value of X that would count as a full solution. (The simplest way to think about this is that X is ‘the percent solved’, so that X0=100.) We can then write
dXdW=X0W0×dX/dWX0/W0.
The first factor on the right-hand side, X0/W0, measures the overall easiness of solving the problem, while the second, (dX/dW)/(X0/W0), measures how much easier it is to make progress at the current margin.... To avoid confusion, let us call this second factor leverage.
I think that the intent of the bolded text (emphasis mine) is to redefine tractability as "the overall easiness of solving the problem," or X0/W0. The factor (dX/dW)/(X0/W0) is what they're defining as leverage, not dX/dW as a whole.
Thank you for correcting my mistake and explaining your correction. I only skimmed the text and mistakenly assumed that leverage referred to the second of the two factors in (21):dEVtotdW=dEVtotdX×dXdW, which in the ITN framework is decomposed asdXdW=dX%dW×1W. But it is clear from the quote you provide that the authors are instead proposing an alternative decomposition of that factor, dXdW=X0W0×dX/dWX0/W0, and that leverage refers to the second term in this decomposition, i.e. dX/dWX0/W0 rather thandXdW. Apologies for the confusion.
Hi Pablo, I noticed that you changed this page to state that MacAskill et al. merge tractability and neglectedness into a single factor called leverage. I think that's a misreading of the text: they actually split the dX/dW term in a different way from OCB's original formulation, so that the first factor is tractability and the second factor is leverage instead of neglectedness. Here's the relevant quote from the paper:
I think that the intent of the bolded text (emphasis mine) is to redefine tractability as "the overall easiness of solving the problem," or X0/W0. The factor (dX/dW)/(X0/W0) is what they're defining as leverage, not dX/dW as a whole.
Hi,
Thank you for correcting my mistake and explaining your correction. I only skimmed the text and mistakenly assumed that leverage referred to the second of the two factors in (21):dEVtotdW=dEVtotdX×dXdW, which in the ITN framework is decomposed asdXdW=dX%dW×1W. But it is clear from the quote you provide that the authors are instead proposing an alternative decomposition of that factor, dXdW=X0W0×dX/dWX0/W0, and that leverage refers to the second term in this decomposition, i.e. dX/dWX0/W0 rather thandXdW. Apologies for the confusion.