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.

For example, psychologists conducted an experiment where they gave people a picture and a description of a little girl in Africa who was in desperate need of food aid and asked for a donation. A second group was given the picture of the girl but also given statistical information about the millions of others in Africa who were also at risk of starvation. The group of people who were given the statistics donated less than the group who only learned about the little girl. The researchers concluded that people didn’t donate as much when informed of the statistics because they felt any donation they made wouldn’t make an appreciable contribution to solving the overall problem. This is a false feeling of inefficacy because helping even one person matters.

What we learned from studies like this 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.

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

Robert Kennedy on “ripples of hope”

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.