I still fail to see how you demonstrated that. You have failed to take into consideration important variables that I have attempted to address. In particular, you have applied a type of thinking that some people have today to a situation that would necessarily require them to have a different type of thinking. It doesn't make a whole lot of sense to simply transfer it over as such. Granted, we don't have a whole lot of experience with a society where everybody is individually motivated to help, but I think you'll find at the very least that the people who are altruistically inclined to help the homeless or what have you these days don't really decide to swindle everyone.
Also, it does not require everyone to think the same way for this to happen; in fact, very few people have to think this way.
I'm not sure I agree that 1 in 100 is "very few", but point taken.
I don't mind other people giving to beggars, but one thing I have noticed is that beggar-friendly cities tend to attract far more beggars (San Francisco and Vancouver are two that come to mind).
This point is simply irrelevant unless you mean to suggest that the increase is due to people trying to take advantage of the lucrative beggar market rather than working.