Assuming one submits a paper to an academic journal where the editor is positively or negatively biased towards you, what can they do to affect the odds of the paper getting accepted? An ideal answer would include links to academic research attempting to quantify the prevalence/effect of such bias.
Editors don't "affect the odds", they literally decide it. If they want to stop a publication, they can even if all the reviewers say "accept". Similarly, if they want to publish something, they can even if all the reviewers say "reject".
So if the editor is biased against you, best you can do is ask them to recuse and let another editor handle the paper. If that's not possible, you are screwed.
I would guess that an editor with a vendetta against an individual or group could be successful in the short term but would probably cease to be an editor if they generate frequent complaints that are well founded.
However, an editor has a lot of influence over what gets published as they (possibly as part of a group) are the decision makers, not the reviewers. An evil editor could probably cook up rational sounding stuff to "justify" a rejection and it might work a few times. Unlike reviewers, editors are known to authors.
Even uniformly positive referee reports aren't a guarantee of getting published, but if their recommendations are ignored referees will want to know why.
As to "acceptance rates", it is much more unlikely since that assumes long term fairly frequent intervention. Most authors don't publish enough in a single journal to have this come in to play.
But, if you think something is fishy complain about it. Go above the editor if needed. But have some evidence of bias. Bias is bad for scholarship and bad for journals publishing it.
There is also the following effect. If an editor rejects a good paper or accepts junk it will be noticed by the community and the journal administration. In the former case because that good paper probably gets published elsewhere boosting the reputation of that other journal. Again, if it happens rarely (as it does) no one notices, but frequent occurrences will get noticed.