[JohnKSa]

So you are advocating "giving it up" in every case?

This is a strawman. Clearly saying what could have been done is not the same as advocating that course of action in every case.

Second, one has to decide what is important in a situation.

In the situation at hand, a person who decides their purse or wallet is important enough to risk falling down and getting run over, or getting crushed between two cars, or possibly being injured by the thieves should they be armed and choose to inflict harm should hold onto the purse/wallet. A person who thinks differently would likely be well served to let go of the purse/wallet rather than be dragged around by a car and risk staying in close proximity to criminals.

In reality, I suspect that the woman acted, not as the result of careful thought, but instinctively. In this case it worked out well for her. The result could easily have been very different.

To do so in every case subsidizes the behavior by positive reinforcement.

I'll go you one further and state that even doing it in most, or even many, cases subsidizes the behavior. That doesn't really change the facts of the situation, in terms of what is a wise course of action for the persons involved.

The situation is very similar to cutting in line (although with very different consequences). It makes perfect sense for people to want to cut in line (or to take other people's possessions) and if those of us in line (or with possessions) allow those with more antisocial tendencies to have their way, then we reinforce their negative behavior.

Now that we've clearly established the situation, a little analysis is in order. So we've established that it's desirable to prevent people from cutting in line or taking other's possessions. We haven't established that doing so is worth the risk entailed, and while it's simple to say that we should always do the right thing (implying that the right thing is to always stand up against anti-social behavior) it's less simple when we realize that not all anti-social persons are willing to simply back down when confronted. Doing "the right thing" could potential result in the death of the person doing the confronting, or even the deaths of bystanders.

It's one thing to decide that stopping a purse snatcher is so important to you that you're willing to risk your life and financial well-being to make it happen. It's another thing entirely to put the life of others nearby at risk in the interest of doing what you have personally defined as "the right thing".

Finally, this is a complicated topic, and it's a disservice to those who approach it rationally to try to boil it down to a false dichotomy as inane as doing it the "right way" or encouraging the criminals through inaction. Even if we were to focus exclusively on the cost/benefit to society, it's more complicated than that. Saving a purse and standing up to criminals is good, but risking innocent lives to accomplish that goal raises some serious questions about what, exactly, constitutes doing "the right thing."