We have a bias in favor of "specific" victims.
"We are much less interested in helping a victim – we only want to help the victim," Jonah Lehrer says in that blog post. He correctly calls this "deeply irrational." It makes no sense to distinguish between people who are "specific" and those who aren't. Everyone is a specific individual!
Lehrer quotes a new study that asked people questions to try to determine how much they used analytical thought as opposed to hunches. The more analytical people showed less of an emotional bias in favor of specifically identified victims:
Individual differences in analytic (“rational”) processing style moderated the effects of different request types on donations to a Zambian relief fund. Less-analytic processors donated more to a single identified victim than to requests describing statistical victims or a combination of both; more-analytic processors showed no differences.Lehrer also notes:
[T]he floods in Pakistan have received far less attention than warranted, in part because most of the stories focus on the vast scope of the disaster, and not on individual tragedies.There are a couple ways that the "focus on the vast scope" could diminish people's caring. Lehrer means it causes us to view the victims as faceless and indistinct. But that wouldn't seem to fully explain the disparity: we are seeing photos of specific victims in the flood, not just statistics.
Another factor is that, even if we understand that the flood is taking an enormous human toll, the huge scale (it's said to have affected 20% of Pakistan, which has a population of 170 million) makes it seem so unmanageable that we instinctively throw up our hands. Trying to solve the problems seems hopeless. With the trapped miners, there's a discrete mission that needs to be accomplished, and we can imagine instantly feeling joyous once it's over. Despite the suffering and anxiety, the miners can eventually be reunited with their loved ones, and everyone will have a new perspective on life. With Pakistan, the best imaginable success would be to gradually mitigate the enormous damage; saving everyone or nearly everyone is out of the question. It's similar to why movies with happy endings are so popular.