What's the term for an economic policy that has negligible effect for most, but a significant effect for a few? I remember this came up around tariffs in the US on aluminum. They have a negligible effect on the price of an aluminum can, but aggregated across all the aluminum cans sold, it can have a significant impact for a handful of US aluminum producers.
Utility Trade-offs: Pareto Efficiency vs Equality

While I tend to agree with the notion of Tragedy of the Commons as per the comments, I will provide an additional economic framework to answer your question. Perhaps this is something you already know, but is nonetheless useful for answering your question as per the welfare-economics tag. As to the exact name of the policy, I'm not sure there is a name for the policy, but the underlying economic concept can be characterized as a utility trade-off and that's likely how a policy maker would approach this.

Consider the following social indifference curve, I just made it myself, don't scrutinize it too much:



Assuming the First Theorem of Welfare Economics held before the tariff, then that point would have been on the pareto efficient curve which is the gray line in my graph. This curve is also known as the utility possibilities curve, which shows the highest utility one party can have without reducing another party's utility. 

In your case, since the aluminum producers were worse off, then this is a utility trade-off. And we recall that society may be willing to trade off one group's utility for another's utility, sometimes on the grounds of equality, but for other reasons too.