Compassion and Altruism with "Strangers"

You can't force connection.   One of the most primitive bits of neural architecture we have developed in our brains deals with Theory of Mind (TOM), and because of it's highly useful nature it is not an aspect of our psychology that can be denied.  In short, we know that other people can hold different beliefs or false beliefs in their minds.  Not everyone is thinking the same thing.  This allows us to then put ourselves in another's shoes, to empathize with them when the occasion permits or demands. But this is not automatic.  In fact, we are able to do so more easily with those whom we consider to be members of our in-group.  Our in-group members are those people who we consider to be extensions of our Self, normally our family (kin), but this can also extend to close others such as friends or important business compatriots. 
For those in our out-group, there are two approaches empathy and compassion can take.  One, we can route compassion through a "common humanity" lens.  In this view, very few people (very "bad" people) are actually in one's out-group.  Then compassion can occur.  The other view one can take is more dramatic.  This is extreme version of TOM, where the other person is just another person, deserving of compassion, whether or not that outcome has anything to do with yourself.  I have always wondered which resonates the most with people, but also realize that this cannot be a universally determined question.  Different cultures see this nothing of self/other as more or less concrete.

What do you think would be the best way to help someone feel a connection to a "stranger" so that they might choose to engage in an altruistic behavior towards them?