Trying to think about the crucial difference between the Train and the Hospital scenarios (as described in this post at Show-Me) got me thinking about the following pair of scenarios:
......In the first scenario you are a busy person who sometimes gives to charity (whenever you feel guilty), so you have set up an account so that some money is automatically donated to a good charity every month (without you having to think about it)—in effect, you are improving the lives of ten poor people (e.g. educating their children, and providing health cover). One day you see an advert by a much more efficient (but no less reliable) charity, who can help five times as many poor people with the same amount of money; fifty people could be saved, instead of only ten, you think. So you call your bank and alter your details accordingly.
......The second scenario is similar, except that the original charity paid their workers slightly less and instead spent the money on sending you information about the ten people you were helping (e.g. photos of them, and some letters from some of them). You were usually too busy to bother reading all that (more advertising, you thought), but as you picked up the phone to call your bank (as above) you happened to glance at one of the photos (some family looking hopeful). Before your money could help anyone else, it would have to be taken away from them, you think; so you leave things as they are (and get on with your busy life).
......But why should a mere photo make such a difference?