I found a list of "potential, possible, or probable predatory scholarly open-access publishers" here.
I am just wondering if there is a similar list of reputable open-access journals in the social sciences.
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I would suggest going about this a slightly different way. The reputation of journals derives from views of scholars in a particular discipline. There are many closed access journals that are not very reputable and many open access journals that are reputable. You can figure out the ones that are reputable by looking at three things:
Thus, rather than trying to find a list of reputable journals, think about how you would evaluate any particular journal. If you find correct answers to any of the above questions, there is a good sign it is a reputable journal since the idea of "reputation" is a social construction that reflect precisely the above criteria.
The Directory of Open Access Journals (DOAJ) is an attempt to create such a list for all fields, including the social sciences:
DOAJ is an online directory that indexes and provides access to quality open access, peer-reviewed journals.
They have a search function that lets you drill down to specific fields.
OnlineSchools.org produces a list of various open access journals. While I can't say all are reputable, most look like they point to well established and credible organizations or educational institutions.
I am not aware of a list of "reputable" open access journals in the social sciences. But, as a safe starting point, the most reputable open access journals in the social sciences have an ISI impact factor.
The real problem (and probably the reason for this predatory journal explosion) is that the classic journals have become abusive and predatory themselves. For example Springer/Nature journals will reject your paper without explanation and direct you to one of their fee-paying open access for guaranteed acceptance on resubmission. Worse, the old classic journals do not do peer review often, make decisions based on profitability of your paper and sometimes take months or even over a year to respond. Some do not ever respond. This includes Springer/Nature which did not respond at all to a submission and did not respond to the inquiry about why they did not respond. So, may be these predatory journals are just as predatory as the old corrupted ones. We may have to switch to the new era.