Compelling 2015 research by Paul Slovic and others shows that we are often likely to help a person in need, but we are much less likely to help that person when our attention is simultaneously directed toward other people that we are unable to help. The fact that there are multitudes in need dampens our willingness to help a person we are most assuredly in a position to help. Here is the summary of the research:

In a great many situations where we are asked to aid persons whose lives are endangered, we are not able to help everyone. What are the emotional and motivational consequences of “not helping all”? In a series of experiments, we demonstrate that negative affect arising from children that could not be helped decreases the warm glow of positive feeling associated with aiding the children who can be helped. This demotivation from the children outside of our reach may be a form of “pseudoinefficacy” that is non-rational. We should not be deterred from helping whomever we can because there are others we are not able to help.