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HN vote weighting: some theory and a suggestion.
A problem which has been brought up in a few threads is that the front page doesn't seem to contain the stories people want it to contain.
I suspect that part of the reason for this is that voting occurs two ways: voting on an article you found on /newest, or voting on an article you found on the front page. The issue is, votes on /newest affect the content of the front page more than do votes on the front page, and this is kind of irretrievable. Most HN'ers don't browse /newest, and the composition of the user-base which browses /newest is different from the composition of the user-base which browses the front page. I don't think that trying to convince users to browse /newest is a good way to fix this. If you need to change the principles of human behavior to use your social doohickey, it just doesn't do hickey.
Let's make some assumptions. Front-page readers are almost entirely motivated by intrigue, and /newest users are motivated at least partially by something else. If we weight more highly the votes of /newest users whose promoted-things are popular with the front-page users, we improve the utility of the site to front-page users. If we further include the karma of the front-page users in the rating-weighting for the /newest users who voted on the article, we (hopefully) improve the utility of the site to front-page users who post constructive comments. In essence, we increase the weighting of users who upvote things which other constructive users later upvote.
This is different from karma-weighted rates because karma-whoring is no longer a useful way to increase one's weighting -- the most usefully predictive users will have their posts upvoted by lots of high-karma citizens, which would be hard to outdo even by karma-whoring sockpuppets.
So... when someone upvotes a post, you increment the article's sorting-score (the score used in sorting, not the true score) proportional to the user's weight, and you increment the weight of previous voters proportional to the user's karma score. You also decrease the weight of the person voting, since otherwise people who vote on everything (and are thus useless from a predictive standpoint) are rated highly. This increases the impact of high-karma users (a good thing) without increasing their power (human beings and power are kind of like fire and gasoline; a bad combination). Since karma distribution is highly uneven, maybe using the square root of karma would be better (less skew).
The problem is that this might encourage people to try to vote "with the crowd" -- since people usually try and get more power, even if it's totally meaningless.