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.

Here is one other excerpt from the research:

The studies described here show that donors pay attention not only to relevant information (children who can be helped), but also incorporate feelings from normatively irrelevant information (e.g., children who cannot be helped) when that information is brought to their attention. Irrelevant negative feelings associated with those not able to be helped appeared to blend with the good feelings for those who can be helped, leading to dampened warm glow. This effect is not a form of inefficacy attributable to “drop-in-the-bucket” (Bartels and Burnett, 2011) cognitions because it occurs even when a substantial proportion of children, though not all, can be helped (e.g., see Table ​Table11; Figure ​Figure22). The fact that one cannot help other children should not influence the decision to help a child who can be helped.

We demonstrated that fast pseudoinefficacy is an affective phenomenon—positive feelings about the child one can help are dampened by negative feelings associated with children who cannot be helped. In Studies 1–4, we found that affect ratings and feelings of warm glow (associated with the child one can help) were lower when children who could not be helped were made salient. In Study 5a,b, we demonstrated that the children not helped induced negative affect that reduced the positive warm glow for the child that could be helped. We also found that the pseudoinefficacy effect is not merely due to the presence of other stimuli. Warm-glow ratings of a single child who could be helped were not reduced when that child was accompanied by non-affective, non-children stimuli. In further support of an affect-based explanation, Study 5b showed that when other, unrelated, pictures that induced negative emotion accompanied the single child, warm-glow ratings were as low as in the pseudoinefficacy conditions where children not being helped were present.

What can we do to counter the effects of pseudoinefficacy? The researchers offer some suggestions:

But countering, or at least minimizing, pseudoinefficacy might not be easy. Kahneman (2011) summarizes a vast amount of research demonstrating that the human mind processes information in two ways: fast and slow (see also Kahneman and Frederick, 2002; Kahneman, 2003). Fast thinking, akin to what Haidt (2001) calls moral intuition when it comes to saving lives, is like perception. Moral feelings arise quickly and seem veridical, without reflection (Haidt, 2001), much like visual perceptions. But just as the human eye, as accurate as it is, can be deceived by certain patterns creating “visual illusions,” certain forms of contextual information, such as children who cannot be helped, may create “moral illusions.” And just as visual illusions may persist even when we know them to be false, the illusion of pseudoinefficacy may be similarly hard to dispel. In light of our findings, we can delete or minimize reference to the larger need the donation request addresses. One charity put the statistic, “3 million in need” above the picture of a starving child, likely demotivating many donors.

Since pseudoinefficacy appears to be an affective phenomena, perhaps a more promising strategy is the one used by Schwarz and Clore (1983) to block the intrusion of irrelevant feelings. Schwarz and Clore (1983) found that merely reminding respondents about the true source of their feelings (the weather) eliminated the affect-congruent influence on judgments (global well-being). Following, Schwarz et al. (2007), perhaps reminding participants that the source of the bad feelings they experience really is the children they cannot help, and not the child they can help, would eliminate pseudoinefficacy.