Permissivism can take multiple forms. For instance, it might permit both fanatical and antifanatical preferences. Or it might permit (or even, its name notwithstanding, require) incomplete preferences that are neither fanatical nor anti-fanatical. But apart from noting its existence, we will say no more about the permissivist alternative for now, returning to it only in the concluding section.
The takeaway, I think, is that those who find fanaticism counterintuitive should favor not anti-fanaticism but permissivism. More specifically, they should favor a version of permissivism that permits incomplete preferences that are neither fanatical nor anti-fanatical.
The paper says: