Pseudoinefficacy 

Perceived efficacy has an enormous impact on people's willingness to provide aid. Building on a series of psychological studies, the concept of pseudoinefficacy refers to the idea that people are less willing to help one person when they are made aware of the broader scope of people in need that they are not helping.

What we learned from these studies was that people don't feel as good about helping others when they realize there are some people who are not being helped. Many people simply give up and don't even help those they can help.

But this is wrong! Just because we can't fix a problem completely doesn't mean we should wak away and do nothing. Even partial solutions save whole lives.

Each time a man stands up for an ideal, or acts to improve the lot of others, or strikes out against injustice, he sends forth a tiny ripple of hope, and crossing each other from a million different centers of energy and daring, those ripples build a current that can sweep down the mightiest walls of oppression and resistance.
— Robert F. Kennedy

Learn More:

"Pseudoinefficacy: negative feelings from children who cannot be helped reduce warm glow for children who can be helped" by Daniel Västfjäll, Paul Slovic, and Marcus Mayorga. Frontiers in Psychology, 2015.

"I will be a hummingbird" by Wangari Maathai. A kid-friendly, animated parable that illustrates the power to overcome pseudoinefficacy.