I’m not sure what the exact mathematical proposal here is, but I shall guess the following rule: If X has voted positively on Y p times out of n votes so far, if X’s next vote is an upvote it will confer a karma score of -log((p+1)/(n+2)), and if it is a downvote, log((n-p+1)/(n+2)). X voting positively on each of Y’s n posts will give a total karma of log(n+1), negatively on everything gives -log(n+1). Logs are base 2. Votes never count for nothing, because X’s votes on Y so far are only a sample from which we cannot conclude that X will vote with certainty either way.
This actually rates newbies’ votes above everyone else’s in importance: X’s first vote on Y is always worth the maximum possible, +/- 1.
The general principle of the proposal is that to the extent that you can predict an opinion, you are less incrementally informed by finding out what it is, which as a matter of information theory is true. How far might one take this? For example, it suggests ignoring anyone’s political views once one has identified them. SJWs and NRXs alike would be the first to be tuned out. If they want to be paid attention to they would have to find ways of saying new things, although (since they Have Views that determine all their views on individual things) this is likely to converge on finding new ways to say old things, i.e. writing clickbait. On the reader’s side, one should primarily read people one knows nothing about, at least until one has “solved” them and can predict all their further output well enough to get diminishing returns. Personal relationships likewise: they can’t last if they’re based on novelty. Once you have solved a potential partner, then you can decide whether you want to continue to spend time with them for what they are, rather than what they may be. This is the purpose of the rituals of dating and courtship.
I’m not expressing an opinion for or against this, just following the idea.
ETA: Some mathematical simulation shows that if half of X’s votes on Y are positive, the total karma resulting from those votes by the above rule depends sensitively on the order in which they are made. For example, 20 positive votes out of forty can easily give a total karma of anywhere from about −11 to +11. If all upvotes precede all downvotes, the total is −33.6; if the reverse, +33.6. Also, after a long string of positive votes, a single negative vote cancels out most of the karma, and vice versa. The rule I proposed seems too sensitive to properties of the vote sequence that one might not wish it to be.
I didn’t think of that, but do you think karma shouldn’t depend on the order in which votes are made? Shouldn’t a person who gets 20 downvotes followed by 20 upvotes have higher karma at the end than a person who had 20 upvotes followed by 20 downvotes? The first indicates improvement; the second indicates getting less interesting over time.
I am confused by how you’re doing the computation, though. If half of X’s votes on Y are positive and half are negative, I would expect to compute X’s total contribution to Y as zero. I wouldn’t keep a running sum of X’s contribution to Y’s karma on each thing Y has said. We can also go back and recompute the contribution to previous comments as X makes more comments. But I’d probably rather have an adaptive algorithm so that the score on individual comments reflects the situation at the moment the rating was made.
Even if we did it that way, though, this sensitivity is not a real problem. Nearly every adaptive algorithm or learning algorithm has that kind of sensitivity. It never matters in practice when there’s enough data. Text compression algorithms don’t have drastically different compression ratios if you swap text input blocks around.
I’m not sure what the exact mathematical proposal here is, but I shall guess the following rule: If X has voted positively on Y p times out of n votes so far, if X’s next vote is an upvote it will confer a karma score of -log((p+1)/(n+2)), and if it is a downvote, log((n-p+1)/(n+2)). X voting positively on each of Y’s n posts will give a total karma of log(n+1), negatively on everything gives -log(n+1). Logs are base 2. Votes never count for nothing, because X’s votes on Y so far are only a sample from which we cannot conclude that X will vote with certainty either way.
This actually rates newbies’ votes above everyone else’s in importance: X’s first vote on Y is always worth the maximum possible, +/- 1.
The general principle of the proposal is that to the extent that you can predict an opinion, you are less incrementally informed by finding out what it is, which as a matter of information theory is true. How far might one take this? For example, it suggests ignoring anyone’s political views once one has identified them. SJWs and NRXs alike would be the first to be tuned out. If they want to be paid attention to they would have to find ways of saying new things, although (since they Have Views that determine all their views on individual things) this is likely to converge on finding new ways to say old things, i.e. writing clickbait. On the reader’s side, one should primarily read people one knows nothing about, at least until one has “solved” them and can predict all their further output well enough to get diminishing returns. Personal relationships likewise: they can’t last if they’re based on novelty. Once you have solved a potential partner, then you can decide whether you want to continue to spend time with them for what they are, rather than what they may be. This is the purpose of the rituals of dating and courtship.
I’m not expressing an opinion for or against this, just following the idea.
ETA: Some mathematical simulation shows that if half of X’s votes on Y are positive, the total karma resulting from those votes by the above rule depends sensitively on the order in which they are made. For example, 20 positive votes out of forty can easily give a total karma of anywhere from about −11 to +11. If all upvotes precede all downvotes, the total is −33.6; if the reverse, +33.6. Also, after a long string of positive votes, a single negative vote cancels out most of the karma, and vice versa. The rule I proposed seems too sensitive to properties of the vote sequence that one might not wish it to be.
I didn’t think of that, but do you think karma shouldn’t depend on the order in which votes are made? Shouldn’t a person who gets 20 downvotes followed by 20 upvotes have higher karma at the end than a person who had 20 upvotes followed by 20 downvotes? The first indicates improvement; the second indicates getting less interesting over time.
I am confused by how you’re doing the computation, though. If half of X’s votes on Y are positive and half are negative, I would expect to compute X’s total contribution to Y as zero. I wouldn’t keep a running sum of X’s contribution to Y’s karma on each thing Y has said. We can also go back and recompute the contribution to previous comments as X makes more comments. But I’d probably rather have an adaptive algorithm so that the score on individual comments reflects the situation at the moment the rating was made.
Even if we did it that way, though, this sensitivity is not a real problem. Nearly every adaptive algorithm or learning algorithm has that kind of sensitivity. It never matters in practice when there’s enough data. Text compression algorithms don’t have drastically different compression ratios if you swap text input blocks around.