Compassion is the one thing every great religion has in common:

ALL the major religions place great importance on compassion. Whether it’s the parable of the good Samaritan in Christianity, Judaism’s “13 attributes of compassion” or the Buddha’s statement that “loving kindness and compassion is all of our practice,” empathy with the suffering of others is seen as a special virtue that has the power to change the world. This idea is often articulated by the Dalai Lama, who argues that individual experiences of compassion radiate outward and increase harmony for all.

It affirms that "the experience of compassion toward a single individual does shape our actions toward others":

What these results suggest is that the compassion we feel for others is not solely a function of what befalls them: if our minds draw an association between a victim and ourselves — even a relatively trivial one — the compassion we feel for his or her suffering is amplified greatly.

What does this mean for cultivating compassion in society? It means that effortful adherence to religious or philosophical dictums (often requiring meditation, prayer or moral education), though clearly valuable and capable of producing results, is not the only way to go. There is nothing special about tapping in synchrony; any such commonality will do. Increased compassion for one’s neighbor, for instance, can come from something as easy as encouraging yourself to think of him as (say) a fan of the same local restaurant instead of as a member of a different ethnicity.

Simply learning to mentally recategorize one another in terms of commonalities would generate greater empathy among all of us — and foster social harmony in a fairly effortless way.

Look for what's in common.

Stanford is studying monks to see how compassion affects the brain.

Yes, CCARE is doing some amazing neuroscience research over at Stanford. I find that research fascinating -- how to train our minds to become more compassionate. What if everyone on earth became 20% more compassionate? 50%? The results would be amazing. That's the kind of vision Meng Tan has for the world. Incidentally, he was also a founding patron of CCARE along with the Dalai Lama. Here's an interesting interview with Meng Tan and James Doty, Director of CCARE.

I'm missing something: how do we quantify compassion?

That's a really good question. There is no hard and fast answer yet. However, researchers are developing a way to measure levels of compassion with MRI scans. From the article on Stanford's study of monks' brains (that you posted previously):

By looking at expert meditators, neuroscientists hope to get a better picture of what compassion looks like in the brain. Does a monk's brain behave differently than another person's brain when the two are both extending compassion? Is selflessness innate, or can it be learned?

Looking to the future, neuroscientists wonder whether compassion can be neurologically isolated, if one day it could be harnessed to help people overcome depression, to settle children with hyperactivity, or even to rewire a psychopath.

"Right now we're trying to first develop the measurement of compassion, so then one day we can develop the science around it," Knutson said.

Last year, there was a whole conference focused on scientific research into the origins, measures and interventions for compassion.

http://greatergood.berkeley.edu/article/item/three_insights_from_the_cutting_edge_of_compassion_research

I remember it very much being a work in progress -- and that greater good conference is a step in the right direction.