I observe this kind of thinking especially in politics, for instance when someone brings up that "It is fine to take a few dollars from a lot of people if it helps the country". I think the reason we see things like this is that we can better imagine the value of one thing with awesome qualities than million things of a small quality because we are more used to compare the quality, not the amount, in our daily lives. Is there a name for a similar cognitive bias/fallacy?
Yes. This is a special case of the identifiable victim effect: the cognitive bias implicated in the quote, "A single death is a tragedy; a million deaths is a statistic."
The identifiable victim effect might be paraphrased as the tendency to view harm of many as unimportant. A direct corollary is the tendency to view small harm of many as unimportant. Going off AliceD's example, we might expect taking \$1 from a million to sound preferable even to taking just \$100k from 1 person.
A potential objection might be, "sure, but in this case, 'one person' isn't really an identifiable victim. It's really about the small amount of harm since both victims are just 'statistics'." Fair point, but even if you wanted to classify this as a bias distinct from the identifiable victim effect, they both result from the same cognitive heuristic: experiential thinking.
Experiential thinking, in this context, is evaluating a scenario by imagining yourself in it and judging what that experience would be like. For example, when I imagine losing \$10, it is far preferable to losing \$100k, but the fact that it is taken from a million people has little emotional relevance. You can't imagine experiencing the loss of $10 as more than one person at a time. Similarly, an identifiable victim makes my experiential thinking more vivid because I have a concrete situation in which to imagine myself. I can imagine what it's like being mugged at 11pm in an alley near 130th Street, but "1,000 muggings in the past month" is not something I can relate to experientially.
This comes under the heading of the theory of organized interests.The idea is that there are a few parties that stand to make large gains from a situation, and therefore have an incentive to organize and capture these gains. Meanwhile, there is a large number of people that stand to receive small losses. Because these losses are individually "small," the latter group of people do not have an incentive to organize to defend their interests against the first group.
The doctrine of Pareto efficiency suggests that the action should be undertaken if the aggregate gains outweigh the aggregate losses (because the winners can compensate the losers and still come out ahead; otherwise not.
I don't know if a "cognitive bias/fallacy exist", however you could find some answers to your question looking at the defense mechanisms that each one of us use.
First of all, they rise from conflicts and their nature depends on the quality of conflicts (Anna Freud, 1936). In this case we would talk about:
Denial: A primitive defense mechanism which triggers an exclusion of an unpleasant and unbearable part of the reality from the conscious field. This exclusion occur by fantasy and by behaviour.
An aspect of reality has been refused and unknown, splitting from the coscience (White and Gilliland, 1975).
To sum up, denial allows these individuals to hide from a reality that is too hard to cope with.
I wish to have been helpful.