I find this proposal completely unreasonable: "the questioner should have the right to petition the mods for a reversal of the vote."
For one, think of the amount of workload this would add for the moderators. Moreover, moderator might not be an expert in the area of the question. I think it is optimal if much more moderating is done by community than by moderators (and moderators are only needed for exceptional cases). This is exactly why there are close/reopen votes, delete/undelete votes, review queues, etc. And, to some extent, also downvotes fit under community self-moderating.
From the top of my head I can think of only one situation where you should contact moderators in connection with downvotes on your question - if you suspect serial voting which went undetected.
Of course, nobody prevents you from flagging a post and asking moderators to revert the votes - but I am pretty sure that such flag would be declined.
If you want some feedback on reasons for downvote, you can simply ask in a comment to your question - maybe somebody will mention why they find the post problematic (be it the downvoter or someone else). Other options, although probably less optimal, are asking on meta or in chat.
I will add that if I ignore the part of the question I quoted in the first paragraph, then I consider this to be quite reasonable question for meta. However, I am not sure whether the discussion will add much to the previous discussions about downvoting without a comment (both on this meta and on other meta sites). To list a few:
1It is explicitly mentioned here that for users below 2k reputation points, casting a downvote leads to displaying a tooltip reminding them that leaving some feedback in a comment might be useful. Although the discussion is primarily about the feature requestion, you can find there comments and links to other discussions related also to downvoting without commenting.
(I am perfectly aware that MathOverflow is a separate site which differs in customs and culture from other sites in the Stack Exchange network, at least in some aspects. Still, I found the linked discussions from other metas quite relevant here. One additional reason to link posts from Mathematics site is that the OP seems to be active mostly on MathOverflow and Mathematics.)