The Greater Good Science Center at U.C. Berkeley reports on the phenomenon of "compassion collapse" (why we feel more compassion for one suffering person than for many), and how we can increase our compassion:
We find that when there are more suffering victims, people think they will feel more compassion. Given this expectation, people may become concerned about the financial and emotional costs of intense compassion. Compassion for many victims can be seen as an expensive proposition—one that will not make much of a difference. People may also become worried about being overwhelmed or burned out by compassion for many sufferers.
For these reasons, people may actively and strategically turn off their compassion. According to our theory, compassion collapse is not due to a limitation on how much compassion we can feel. Instead, it’s the end result of people actively controlling their emotions.