Sometimes a question that is not representative of a site makes the HNQ list. This can lead to a large bump in traffic on a question the community may not be well equipped to handle. I propose that moderators and gold badge holders in the tag be able to set the "hotness points" to zero (or vote to reduce the points).
The idea is for the HNQ to represent questions that are both "popular" and a good (not just not bad) fit for the site.
This is now implemented (at least for ♦ moderators):
Moderators have the ability to remove questions from the HNQ List.
There are times when the hotness formula selects a question that a site would rather not have featured. Up until now, the only recourse that was available was to close the question (which may be appropriate anyway but isn't ideal when done purely to manage traffic), or to do nothing. We're putting the power in the hands of our moderators to remove questions that don't set a good example for their sites.
I believe your reasons for this are quite commendable. While it might be challenging to implement, it's not a bad idea at all.
A simpler way, perhaps, to deal with this is to simply increase the weight downvotes are given in the HNQ formula. At the moment, the formula merely looks at the total score. This is problematic because of the huge influx of 101 rep users and the asymmetric voting that leads to. It has been put quite excellently:
The asymmetry of hot list effect also comes into play here. Those coming from Hot Questions may recognize the question is crap, and perhaps 50% of them would downvote it under normal circumstances. But having only 101 rep, they can't. The 5% who want to upvote (for reasons that are difficult to fathom) can and do. Result: vote count that does not represent the opinion of either the particular community, nor the network at large.
It would be good to counteract this asymmetry. If not at the root, (which is the votes themselves) then at least at the undesirable results, one of them being the way it causes a snowball effect in the hotness points.
One such counteracting measure could be that downvotes on the question (not on answers) could be given a lot of weight in reducing the hotness points. So downvotes would take away considerably more hotness than upvotes add.
This would actually be allowing users to remove hotness points more effectively. But, of course, a much larger group of users. (Anyone with > 124 reputation.)
Mostly, the questions we would want to take off the HNQ list are the same questions that are worthy of downvotes. (Lack of research, extremely trivial, etc.)
Right now, very trivial questions often hit the HNQ. The questions themselves may "only" get like +25, but the answers often get +60 or more. This is a lot on many of the smaller sites. Due to the triviality of the matter, most of the HNQ visitors can easily recognize that the answers are correct, and thus upvote with a clean conscience. It's not those users' fault, it's fine to vote that way. But the highly upvoted answers do nevertheless contribute to the snowball effect on the hotness of that trivial/poorly researched question. Normally, such trivial content would perhaps not be upvoted so highly nor earn users so much reputation.
Figuring out how much weight to give downvotes could be done by trial and error. Start with one value. If it's not effective enough, then increase it, etc. This way, the sweet spot could be found. Personally, I imagine that quite a heavy weight could be implemented.
This might cause silly, trivial questions to be less likely to stay in the HNQ for a long time. And it would counteract the present effect in which their hotness is a self-fulfilling prophecy.
Would this ruin the HNQ? I don't think so. Rather, I imagine that it would save the HNQ. This way we could have questions featuring more quality and good content advertised network-wide, rather than a lot of the trivial, clickbaity questions we currently often see on the list.
I agree with the suggestion to take downvotes into account in the hotness formula. If that doesn't produce good-enough results, here are some other things I would try, in order:
Adjust formula for downvotes, per that other answer.
Exclude protected questions from HNQ. This, like the downvotes suggestion, puts the control in the hands of the community instead of requiring mod intervention.
If adjusting the formula for downvotes and/or excluding protected questions isn't sufficient, then allow mods to mark a question as "no HNQ". This would be another option on the mod menu. (Like locks, annotations, and protection, it should be a toggle.)
If all of that fails or is rejected, then make "exclude from HNQ" a high-rep privilege like protection. This has more UI impact and carries a user-education burden, which is why I'm putting it last.
I think tying it to tag badges misses the mark; a high tag score doesn't seem to me to make one more qualified to judge hotness than a more-diversified user with 15k rep. On some sites there are no, or very few, gold tag badges, either because of the number of users or the number and variety of tags. Sites shouldn't adjust their tag collections just to defeat the HNQ list.
