I'll just say that indeed you do fit the stereotype.

Just for information: Are you deliberately trying to be unpleasant?

You think that your saving ratio is constant as a function of the derivative of your income

First of all, a terminological question: when you say "the derivative of your income" do you actually mean "your income within a short period"? -- i.e., the derivative w.r.t. time of "total income so far" or something of the kind? It sounds as if you do, and I'll assume that's what you mean in what follows.

So, anyway, I'm not quite sure whether you're trying to describe my opinions about (1) the population at large and/or (2) me in particular. My opinion about #1 is that most people spend almost all that their income; maybe their savings:income ratio is approximately constant, or maybe it's nearer the truth to say that their savings in absolute terms are constant, or maybe something else. But the relevant point (I think) is that most people are, roughly, in the habit of spending until they start running out of money. My opinion about #2 (for which I have pretty good evidence) is that, at least within the range of income I've experienced to date, my spending is approximately constant in absolute terms and doesn't go up much with increasing income or increasing wealth. In particular, I have strong evidence that (1) many people basically execute the algorithm "while I have money: spend some" and (2) I don't.

(I should maybe add that I don't think this indicates any particular virtue or brilliance on my part, though of course it's possible that my undoubted virtue and brilliance are factors. It's more that most of the things I like to do are fairly cheap, and that I'm strongly motivated to reduce the risk of Bad Things in the future like running out of money.)

I think that there are breakdown threshold at large value of the derivative

Always possible (for people in general, for people-like-me, for me-in-particular). Though, at the risk of repeating myself, I think the failure of sudden influxes of money to make people richer in the long term is probably more a matter of executing that "spend until you run out" algorithm. Do you know whether any of the research on this stuff resolves that question?

I, using the outside view, [...]; you, using the inside view, [...]

I try to use both, and so far as I can tell I'm using both here. I'm not just looking at my model of the insides of my mind and saying "I can see I wouldn't do anything so stupid" (I certainly don't trust my introspection that much); so far as I can tell, I would make the same predictions about anyone else with a financial history resembling mine.

Now, for sure, I could be badly wrong. I might be fooling myself when I say I'm judging my likely behaviour in this hypothetical situation on the basis of my (somewhat visible externally) track record, rather than my introspective confidence in my mental processes. I might be wrong about how much evidence that track record is. I might be wrong in my model of why so many people end up in money trouble even if they suddenly acquire a pile of money; maybe it's a matter of those "breakpoints" rather than of a habit of spending until one runs out. Etc. So I'm certainly not saying I know that me-10-years-ago would have been helped rather than harmed by a sudden windfall. Only that, so far as I can tell, I most likely would have been.

even if the prior is skewed towards incompetence, that is not much of an effect.

I suggest that people who play the lottery a lot are probably, on balance, exceptionally incompetent, and that those people are probably overrepresented among windfall recipients.

I had a quick look for more information about the effects of suddenly getting money.

This article on Yahoo!!!!! Finance describes a study showing that lottery winners are more likely to end up bankrupt if they win more. That seems to fit with my theory that big lottery wins are correlated with buying a lot of lottery tickets, hence with incompetence. It quotes another study saying that people spend more money on lottery tickets if they're invited to do it in small increments (which is maybe very weak evidence against the "breakpoint" theory, which has the size-of-delta -> tendency-to-spend relationship going the other way -- except that the quantities involved here are tiny). And it speculates (without citing any sort of evidence) that what's going on with bankrupt lottery winners is that they keep spending until they run out, which is also my model.

This paper (PDF) finds that people in Germany are more likely to become entrepreneurs if they have made "windfall gains" (inheritance, donations, lottery winnings, payments from things like life insurance), suggesting that at least some people do more productive things with windfalls than just spend them all.

This paper [EDITED to add: ungated version]looks at an unusual lottery in 1832, and according to ]this blog post finds that on balance winners did better, with those who were already better off improving and those who were worse off being largely unaffected.

[EDITED to add more information about the 1832 lottery now that I can actually read the paper:] Some extracts from the paper: "Participation was nearly universal" (so, maybe, no selection-for-incompetence effect); "The prize in this lottery was a claim on a parcel of land" (so, different from lotteries with monetary prizes); "lottery losers look similar to lottery winners in a series of placebo checks" (so, again, maybe no selection for incompetence); "the poorest third of lottery winners were essentially as poor as the poorest third of lottery winners" (so the wins didn't help the poorest, but don't seem to have harmed them either).

Make of all that what you will.