Any time any two users vote on the same comment, the HN system should create a number representing the "affinity" between the two users.
This affinity should increase if the users voted the same way on that particular comment, and decrease if they voted differently.
Then, instead of displaying the number of upvotes or downvotes next to a each comment, what should be displayed should be the number of upvotes and dowvotes weighted by the affinity of each user who made that vote.
Comments should rise or fall using the formula HN uses now, except it should use affinity-weighted upvotes and downvotes.
In effect, in this system the other users are making "recommendations" on the comments they vote on. And their recommendations are weighted by how similarly their previous votes were to the votes you made.
This scheme results in every user seeing comments customized in a way that automatically infers their preferences.
So, if you prefer deep, insightful comments about technology, you'll presumably upvote those comments, and the affinity between you and the other users who upvoted those comments increases, and when they upvote future comments, the comments they upvote will be more likely to show up on your radar as they'll probably be closer to the top of the page and have a higher numerical score.
Conversely, those people who prefer brief, funny comments would similarly have the comments they see be displayed in a way that caters to their preferences.
Instead of trying to please everyone in a one-size-fits-all top-down approach, this is a more distributed approach which "recommends" to each individual user those comments which are likely to be preferred by that particular user.
Of course, this scheme is more computationally intensive than having the current system of simple, unweighted upvotes and downvotes, or even of manually curated/moderated comments. It also requires active upvoting and downvoting of comments by users for it to work well.
But the advantage of this is that the more users upvote and downvote, the more accurate the system gets in "recommending" comments to them. So implementing this system would provide an incentive for active participation.
It's also an automated, algorithmic system which should scale much better than proposals that require manual human intervention, such as implementing moderation/curation of comments.
A similar scheme could also be applied to articles, such that the HN backend would weigh articles based on the affinity between the user viewing the article list and the users who've voted on those articles.
Then each user would be free to use software running on their own machines to implement the comment recommendation scheme as described above.
In fact, HN wouldn't even need to de-anonymize the votes for this to work. All the HN servers would need to do is make available a list of unique user id's of the upvoters and downvoters. How those user id's map on to usernames wouldn't need to be revealed. But the user id's should remain consistent from comment to comment and article to article, so that the affinity number described in the original proposal could be consistently updated.
So, in this new proposal, each HN user would be assigned a unique id, and when they vote their id would be made available via the HN API along with the comment(s) they voted on when a given story's comments are downloaded for viewing.
Software running on a given user's local machine would then use the user id's and information on how those user id's voted to create a measure of affinity as described in the original proposal, and then sort, rate, or recommend comments accordingly.