Indeed: to reward quality over quantity you'd need to use a function such as x^2, or probably x^2/C for some constant C.
Interestingly, Oxford University used to mark final exams for Mathematics and associated schools (such as Computer Science) in this way. Questions would typically start with parts that were largely "book work" and move on to parts that required more careful thought. In addition, you could answer as many questions as you like. Therefore, to avoid people getting lots of marks by just answering all the book work, the papers were scored by squaring the scores for each question and then summing those squares.
That is: overall_score = sum(q in Questions | score(q)^2)
This practice stopped in ~2003 (now you can still answer as many as you like, but the mark for the paper is the sum of your top 3 marks for individual questions, so it's only really worth answering 3 as well as you can).
Someone who submits only for the karma can already make lots of mediocre submissions and boost their karma far more than under a logarithmic scale.
The only case I could see where your point is valid is if "karma abusers" withhold lower quality submissions in the hopes that they'll submit a really popular one. Do you know if they do this? Or am I misunderstanding the rationale?
The maths is backwards. To take an example, if I submit two stories under a log2-scaled points system which get four upvotes, then if you submit a single story, that story needs to get 16 upvotes for you to match my karma.
Assuming that people are chasing karma (let's leave why to the side for a second, because I don't understand it either), then it's far more efficient to submit lots of low-scoring stories than to even bother thinking about high-scoring ones.
