Greg Egan's short story "Axiomatic" is close to the first scenario. Complete synopsis in rot13:
N zna, n pbzzvggrq cnpvsvfg, unf n tveysevraq jub vf fubg nf n olfgnaqre va n onax eboorel. Gur eboore vf pnhtug naq pbaivpgrq ohg trgf n fubeg fragrapr. Gur zna jnagf gb xvyy uvz, lrg vf nyfb bccbfrq gb xvyyvat uvz. Fb va beqre gb or noyr gb xvyy uvz ur ohlf na vyyvpvg qeht gb ercebtenz uvf trareny ivrjcbvag gb bar bs "Crbcyr ner whfg zrng. Gurl qba'g znggre." Gura ur tbrf gb pbasebag gur eboore, abj bhg bs wnvy, ohg orsber fubbgvat uvz, ur nfxf jul ur xvyyrq uvf tveysevraq, naq trgf gur bss-unaq nafjre, "url, fur jnf whfg va gur jnl, zna". Gur eboore unq gur fnzr nggvghqr gung ur unf whfg chepunfrq. Ur wblbhfyl rzcgvrf uvf tha ng uvz, abg va eriratr sbe uvf tveysevraq, ohg orpnhfr [crbcyr ner zrng, gurl qba'g znggre].
Gur qeht bayl unf n grzcbenel rssrpg, ohg gur fgbel raqf jvgu gur cebgntbavfg vagraqvat gb trg n irefvba gung jvyy znxr vg creznarag.
So, what do you do with Gandhi after his viewpoint has changed and he's done the deed? What does Gandhi do with Gandhi? I think this is a case where hardening the problem by elevating the stakes obscures the issue rather than focussing it. Just about any means can be made to look justified by making the ends important enough.
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I would say that is when there is empirical evidence supporting the claim but, try as you might, you can't find any that falsifies it.
I think having a flawed (human) agent using this technique is too susceptible to the agent convincing themselves that they tried hard enough, and so we've just pushed the problem one step back: How do you know when you've tried hard enough.