How to handle a possibly biased editor?

Probably not what you want to hear, but... There's the option of submitting it somewhere else?

As far as as I know, your options are:

1. Appeal the decision. Many publishers have an official appeal process; typically this will bring the decision to the attention of the editor-in-chief.
2. Submit the paper elsewhere.
3. Abandon the paper. Not a good option if you think the real problem is the editor rather than the paper.

It is very rarely a good idea to appeal a paper rejection. Here's why:

• Appeals are very rarely successful. There typically needs to be a very objective set of evidence in your favor. But rejection decisions are often based largely on subjective measures.
• Since journal editors tend to be senior researchers, the editor who rejected a paper often has more experience than the author of the paper. Furthermore, the author's opinion is always colored by personal involvement. It is thus more often the case that the author's opinion of a rejection is mistaken. This is a statistical point, and of course you will believe that it does not reflect your particular case.
• An appeal may negatively impact your relation with the editor(s) of the journal, particularly if they feel it is not warranted or if your emotional attachment to the process leads you to be unkind.
• Appeals are often handled very slowly; after all, the editors (who are typically volunteers) don't want to encourage the use of the appeal process.

Thus, even if you are right and the editor is really wrong, you are usually better served by submitting the manuscript to another journal. This is especially true if you believe that the editor is truly acting in a malicious way, since then you have even lower odds of success.

For reference, here is Springer's policy and advice on appeals. See also this question and answers to it.

Bottom line: as @Vincent suggests, you're almost always better off submitting to a different journal.

I have had this situation before (an editor that given 2 positive reviews, continued to get more and more and more reviews until someone gave a negative one, then rejected it). We contacted the editor-in-chief with our concerns about how our review process was being handled, as the editor's conduct against us appeared to go against the policy of the journal.

The editor was removed from the process, the paper was 'unrejected' and we were given a new editor. The paper was published soon afterwards.