Although I understand and appreciate your approach the particular examples do not represent particularly good ones:
1: Pascal's Wager:
For an atheist the least convenient possible world is one where testable, reproducible scientific evidence strongly suggests the existence of some "super-natural" (clearly no-longer super-natural) being that we might ascribe the moniker of God to. In such a world any "principled atheist" would believe what the verifiable scientific evidence support as probably true. "Atheists" who did not do that would be engaging in the exact same delusional thinking modern-day theists engage in: belief in "beings" despite the utter lack of evidence supporting the existence of such "beings" only in reverse, like flat-earthers.
2: The God-Shaped Hole:
The use of "Omega" here is a fair bit over the absurd line. It very much sounds like you wish to create the following situation for atheists: suppose there exists an oracle that can tell you that there is a "hole" in you and it's "God shaped", but cannot confirm the existence nor non-existence of the "God" that the hole is "shaped" like. Well, then my hole (being an atheist) is penguin shaped ;-).
It is clear that you want to create a world where some form of definitive information about some other "thing" is true while trying to maintain the "true" state of the existence or non-existence of that thing left undecided. Alas, your not allowed that degree of freedom. If definitive statements are made and accepted as true then the thing that the statement references also must exist in some meaningful way.
3: Extreme Altruism
Lots of leeway is left in your example to re-cast the moral dilemma, for example:
a. Charity X is, in fact, using the money you give it to feed people in Africa, but the population that is being helped lives in a fundamentally unsustainable environment. Suppose changes in weather patterns means that getting a meaningful sustained water supply requires considerable cost. In this case the charity itself is engaging in the morally wrong thing by not supporting efforts to relocate the people to a place that can sustain them better. Your analysis (not literally you, the "you" responding to pleas for money) leads you to extreme altruism. Others follow-suit creating an unsustainable dependant society. In the case of extreme charity you accidentally do harm: they're alive, but utterly dependant of the charity of others.
b. Turn the entire situation amoral: why should their lives there be of such an importance to affect me, in any way, here? I.E. why is this a moral consideration at all? In this context person a may choose to contribute to charity X not knowing if "in the large" a "good overall outcome" will result from such a donation, regardless of amount contributed. Another way of looking at it is if I consider increased happiness being an important element of "good morality" (dubious?) then is my personal depletion of resources and the "net" increase in happiness in the receiving population a net increase of happiness overall? And is that the "right" thing? By who's measure?
The above examples are not meant as a broad-stroke justification for a "let-em starve" thing. The issue simply concerns constraining the examples sufficiently to get the outcome you are looking for. To simplify matters this particular example is closely analogous to the trolley situation above: suppose the doctor offered to the patient with the good organs the option of donating all the organs to the patients in need, but as a result the patient would need to survive on uncomfortable synthetic replacements of his organs.
Related to: Is That Your True Rejection?
"If you’re interested in being on the right side of disputes, you will refute your opponents’ arguments. But if you’re interested in producing truth, you will fix your opponents’ arguments for them. To win, you must fight not only the creature you encounter; you must fight the most horrible thing that can be constructed from its corpse."
-- Black Belt Bayesian, via Rationality Quotes 13
Yesterday John Maxwell's post wondered how much the average person would do to save ten people from a ruthless tyrant. I remember asking some of my friends a vaguely related question as part of an investigation of the Trolley Problems:
I don't want to discuss the answer to this problem today. I want to discuss the answer one of my friends gave, because I think it illuminates a very interesting kind of defense mechanism that rationalists need to be watching for. My friend said:
On the one hand, I have to give my friend credit: his answer is biologically accurate, and beyond a doubt the technically correct answer to the question I asked. On the other hand, I don't have to give him very much credit: he completely missed the point and lost a valuable effort to examine the nature of morality.
So I asked him, "In the least convenient possible world, the one where everyone was genetically compatible with everyone else and this objection was invalid, what would you do?"
He mumbled something about counterfactuals and refused to answer. But I learned something very important from him, and that is to always ask this question of myself. Sometimes the least convenient possible world is the only place where I can figure out my true motivations, or which step to take next. I offer three examples:
1: Pascal's Wager. Upon being presented with Pascal's Wager, one of the first things most atheists think of is this:
Perhaps God values intellectual integrity so highly that He is prepared to reward honest atheists, but will punish anyone who practices a religion he does not truly believe simply for personal gain. Or perhaps, as the Discordians claim, "Hell is reserved for people who believe in it, and the hottest levels of Hell are reserved for people who believe in it on the principle that they'll go there if they don't."
This is a good argument against Pascal's Wager, but it isn't the least convenient possible world. The least convenient possible world is the one where Omega, the completely trustworthy superintelligence who is always right, informs you that God definitely doesn't value intellectual integrity that much. In fact (Omega tells you) either God does not exist or the Catholics are right about absolutely everything.
Would you become a Catholic in this world? Or are you willing to admit that maybe your rejection of Pascal's Wager has less to do with a hypothesized pro-atheism God, and more to do with a belief that it's wrong to abandon your intellectual integrity on the off chance that a crazy deity is playing a perverted game of blind poker with your eternal soul?
2: The God-Shaped Hole. Christians claim there is one in every atheist, keeping him from spiritual fulfillment.
Some commenters on Raising the Sanity Waterline don't deny the existence of such a hole, if it is intepreted as a desire for purpose or connection to something greater than one's self. But, some commenters say, science and rationality can fill this hole even better than God can.
What luck! Evolution has by a wild coincidence created us with a big rationality-shaped hole in our brains! Good thing we happen to be rationalists, so we can fill this hole in the best possible way! I don't know - despite my sarcasm this may even be true. But in the least convenient possible world, Omega comes along and tells you that sorry, the hole is exactly God-shaped, and anyone without a religion will lead a less-than-optimally-happy life. Do you head down to the nearest church for a baptism? Or do you admit that even if believing something makes you happier, you still don't want to believe it unless it's true?
3: Extreme Altruism. John Maxwell mentions the utilitarian argument for donating almost everything to charity.
Some commenters object that many forms of charity, especially the classic "give to starving African orphans," are counterproductive, either because they enable dictators or thwart the free market. This is quite true.
But in the least convenient possible world, here comes Omega again and tells you that Charity X has been proven to do exactly what it claims: help the poor without any counterproductive effects. So is your real objection the corruption, or do you just not believe that you're morally obligated to give everything you own to starving Africans?
You may argue that this citing of convenient facts is at worst a venial sin. If you still get to the correct answer, and you do it by a correct method, what does it matter if this method isn't really the one that's convinced you personally?
One easy answer is that it saves you from embarrassment later. If some scientist does a study and finds that people really do have a god-shaped hole that can't be filled by anything else, no one can come up to you and say "Hey, didn't you say the reason you didn't convert to religion was because rationality filled the god-shaped hole better than God did? Well, I have some bad news for you..."
Another easy answer is that your real answer teaches you something about yourself. My friend may have successfully avoiding making a distasteful moral judgment, but he didn't learn anything about morality. My refusal to take the easy way out on the transplant question helped me develop the form of precedent-utilitarianism I use today.
But more than either of these, it matters because it seriously influences where you go next.
Say "I accept the argument that I need to donate almost all my money to poor African countries, but my only objection is that corrupt warlords might get it instead", and the obvious next step is to see if there's a poor African country without corrupt warlords (see: Ghana, Botswana, etc.) and donate almost all your money to them. Another acceptable answer would be to donate to another warlord-free charitable cause like the Singularity Institute.
If you just say "Nope, corrupt dictators might get it," you may go off and spend the money on a new TV. Which is fine, if a new TV is what you really want. But if you're the sort of person who would have been convinced by John Maxwell's argument, but you dismissed it by saying "Nope, corrupt dictators," then you've lost an opportunity to change your mind.
So I recommend: limit yourself to responses of the form "I completely reject the entire basis of your argument" or "I accept the basis of your argument, but it doesn't apply to the real world because of contingent fact X." If you just say "Yeah, well, contigent fact X!" and walk away, you've left yourself too much wiggle room.
In other words: always have a plan for what you would do in the least convenient possible world.