I find myself falling into the category of people who are indifferent to large numbers. If I come across a story on the news about a particular person who was murdered I feel devastated, and it is very difficult for me to watch. However, when statistics, and death tolls flash on the screen, I don't find myself cringing near as much.
Stanovich and West labeled two models of thinking System 1, and System 2. The models of thinking affect the reactions that people have to the world. System 1 includes a characteristic called affective bias, this concerns a reliance on affect and emotion to navigate in the world. System 2 monitors the quality of the intuitive impressions formed by System 1. The last important element is attention, attention magnifies emotional response.
Infusing System 1 with powerful affective imagery would help to get people to respond genocides, but that would require the media to do its job and report the incidences as aggressively and vividly as they are. Bringing people who experienced these atrocities into our communities would also help to engage people.