1. Pete is starving to death on a distant continent, and I can keep him alive by giving $10/month to charity. There are other people on Pete’s continent who are starving to death, too, and $10/month could save them just as well. Suppose that anything less than $10 will be useless to these people, so that if I give $5.00, then I help no one; if I give $10.00, I help only Pete; if I give $15.00, I still help only Pete; if I give $20.00, I help Pete and one other person; etc.
A claim: "If Pete were the only one in need, I might have an obligation to help him; but when the number of people starving on Pete’s continent becomes sufficiently large, I have no obligation to help anyone at all." This is a weird-sounding claim, but I think that many people believe it; anyway, I think many people behave as though they believe this claim and others similar to it. Here I will present an argument which might get at some of the reasons people may have for believing such claims.
Say that the "needy group" is the group of people who, like Pete, are starving and can be saved by a donation of $10/month. Let’s begin with the assumption that if Pete is the only member of the needy group, then I have an obligation to help him, i.e. to give $10/month to charity. We want to know: What happens to my obligation when the number of people in the needy group increases? To see what happens to it, suppose now that there are two people in the needy group — call them Pete and Sue — and suppose that we know nothing about Pete and Sue except that they are members of the needy group. In that case, Pete and Sue are similar to one another in all (known) morally relevant respects, which means that I must have the same obligation (if any) to Pete as I have to Sue. Thus, I may have an obligation to help Pete and Sue (i.e. to give $20/month to charity); or I may have an obligation to help neither Pete nor Sue (i.e. to give 0/month); but I cannot possibly have an obligation to Pete without having the same obligation to Sue. Something similar will be true when we suppose that there are three members of the needy group: I will be obligated to give either $30/month to help all three, or will have no obligation to help anyone. And in general, the following disjunction will be true: Either I am obligated to give X*$10 or I am obligated to give 0, with "X" representing the number of members of the needy group.
For X=1, we have supposed, the left disjunct is true: I am obligated to give $10/month. As X grows, two things happen: The number of people in the needy group grows, and the number in the left disjunct grows. It might be thought that, as the number of people in the needy group grows, my obligation to lend a hand becomes stronger and more pressing. But as the number in the left disjunct grows, any potential obligation I might have becomes increasingly unreasonable. When X=1,000,000, for instance, I am (given the above disjunction) either required to give $10,000,000 per month or I am required to give nothing. But I do not have $10,000,000 per month to give; thus, I must not be obligated to give anything at all. So: When the needy group is sufficiently large, I have no obligation to help Pete, nor do I have any obligation to help anyone else in the needy group.
Where has this argument gone wrong?
2. Suppose you are designing an advertisement for a charity. You know the ad will feature a photo of a starving boy, and you know that the photo will be displayed alongside text like this:
By donating only $____ per month, you can save the life of a boy just like this one.
Your assignment is to fill in the blank. Your only goal is to maximize the amount of donations which will be given in response to the ad; you don’t care whether the way in which the blank is filled yields a true or false sentence. How should you fill in the blank?
It seems to me that if you fill the blank with a very large number, the ad will be discouraging to people. If people think, for instance, that in order to save the boy’s life, they need to donate $500 per month, they will feel that they must choose between the boy’s life and (say) being able to make rent. Given such a choice, most people will choose rent. On the other hand, if you fill the blank with a very small number, then people are unlikely to donate very much money. If people think, for instance, that they can save the boy’s life by donating only 50 cents per month, then their consciences will be satisfied even if they donate only that much. This game will have some things in common with Blackjack.
E.G. 
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