False first appearances
At first sight the kind of case you describe is an example of the 'collective action problem':
[There are cases that have] the following structure: A certain number
of people - perhaps a large number of people - have the ability to
perform an act of a given kind. And if a large enough group of people do
perform the act in question then the results will be bad overall. However -
and this is the crucial point - in the relevant cases it seems that it makes
no difference to the outcome what any given individual does. And this is
true regardless of whether others are doing the act or not. Thus, if enough
people do perform the act the results are bad overall; but for all that, it
remains true of each individual agent that it makes no difference to the
overall results whether or not they perform the action in question. (Shelley Kagan, 'Do I Make a Difference?', Philosophy & Public Affairs, 2011, Vol. 39, No. 2, pp.
The collective action problem is widely regarded as a problem for consequentialism:
The problem, in effect, is this: consequentialism condemns my act
only when my act makes a difference. But in the kind of cases we are
imagining, my act makes no difference, and so cannot be condemned by
consequentialism - even though it remains true that when enough such
acts are performed the results are bad. Thus consequentialism fails to
condemn my act.
In cases of this sort, therefore, consequentialism seems to fail even by
its own lights. For here - unlike the deontological cases that purport to
show that something else matters besides results - the act seems wrong
precisely because of the bad results of everyone's doing acts of the same
sort. Yet consequentialism still cannot condemn the act. Apparently,
then, consequentialism fails to handle a kind of case that even consequentialists admit it ought to be able to handle. (Kagan: 108.)
A second look
However, the case you describe is not one where what the individual does 'makes no difference'. Instead it's one where the individual's action is 'of minimal effect'. An action doesn't have to be of major effect to count morally. An action 'of minimal effect' is still an action that does have results. If the results are harmful, all else equal the action is wrong on consequentialist grounds and may well be open to objection on deontological grounds as well.
The kind of case you raise first received serious and extended attention in Derek Parfit's Reasons and Persons (1984) and the solution to it - or at least the response I've given here - follows his own answer to it.
As analysed above, the example falls within the scope of consequentalism and violates its requirements. It does so irrespective of any principle of uiversalisability. Even if no-one else did your action 'of minimal effect', all else equal it would still be wrong because it produces a bad (if minimal then still real and still bad) consequence. One might appeal to a principle of the moral relevance of minimal effect.