Reject a paper based on relevant but pointless research direction Disclaimer: this is a hypothetical question, not (immediately) related to any concrete past, present or future reviewed paper.
My context is the no-fly zone between Computer Science and Applied Mathematics. In my opinion, there are some research directions within this field that are pointless. Roughly speaking, papers can be either theoretical or applicative. The former provide insight on formal concepts, model interesting physical phenomena, analyze significant properties of an algorithm, and so on. The latter build algorithms to solve real-world applications, or at least provide preliminary results on contrived problems that promise future performance enhancements. In summary, I am very tolerant as to which is my field of research, and I find interesting results almost everywhere.
However, I observe that there appear more and more papers that suffer from the syndrome of the &quot;parameter change&quot;: a model—typically an algorithm—is built that can solve toy problems, but no large-scale application is proved or foreseen; there are no fundamental theoretical problems in either Mathematics or Computer Science (or Physics, Biology, or other fields) involved; then, a second paper changes a minor parameter or adds a light generalization, but still no real applicability is shown; then a third paper. Note that I am not talking about marginal papers, I estimate that half the papers of a top journal (ISI indexed, impact factor, serious publisher...) fall within this description.
Now, my particular problem: I am assigned a paper for review. I am a bit prejudiced by the title and the abstract, but nonetheless I bite the bullet and go through pages and pages of equations, crowned by some computer simulations that allegedly prove the superiority of the algorithm (marginal superiority in an uninteresting toy problem). I am unable to point out any particular error, which is hardly surprising, since what is proved is rather obvious, usually some disguised version of the Stone-Weierstrass theorem or the Lyapunov Stability criterion.
What do you think should be my stance? Some possibilities:

Next time, think better and decline the review because you are prejudiced and unable to produce a fair review.

Well, the paper is correct, isn't it? Judge exclusively by the content.

The editor has asked for your opinion and you think that the paper should not be published. Say so: &quot;It is correct but this line of research is pointless. Yes, I know that there are hundreds of papers within this line, but those are not my business and I am currently reviewing this paper&quot;.


What about consequences of the somewhat quixotic answer 3? It looks like my opinion is minority and probably not shared with editors themselves. Could I be berated or blacklisted by the editor?
Generally, as a reviewer, you are being asked for your opinion of the paper's correctness and its significance (importance, level of interest, etc).  Evidently in this case you think the results are not significant or interesting enough to publish in this journal, so you should say so in your review.  If possible, you should explain why you think so: the authors don't give any compelling applications, the results are only a marginal improvement on what's known, etc.

This isn't reason to decline the review.  Thinking the paper is uninteresting isn't "prejudice".

If the editors don't agree with your assessment, they are free to disregard it and publish the paper anyway.  But you do have a responsibility to give your honest opinion.

In fact, I would suggest that you evaluate the paper's interest before you start to carefully check its correctness.  If you believe it's not significant enough to publish, even if correct, then you can so inform the editors and save yourself the time. 

There are some exceptions, where the editors may only be interested in whether you believe the paper is correct.  Perhaps they are already convinced it is sufficiently important (from their own opinions or other reviewers), or perhaps "importance" isn't a criterion for publication in this journal (e.g. PLOS One).  If that's the case, then the review invitation should make this clear; otherwise, do consider the paper's importance as part of your review.