I have noted that the vote mechanism assign the same score for one vote up/down independently by the user score. In my opinion this is not fairly as high scored users has a deeper understanding of the subject discussed. I think that a better way would be assign a score by this formula
vote up/down = +/- int(log(user score))
what do you think?
The proposal is intuitive and appealing. It appears predicated, though, on the implicit assumption that high-rep people provide better information than low-rep people about the quality of questions and answers. This appears derived from equating reputation with knowledge, capability, or capacity for judgment. That equation is debatable.
(On our site there are users with enough reputation through sheer activity alone to have earned tag badges in subjects where they are not very knowledgeable. I will, with some diffidence, hold myself out as example number one: purely because many questions are tagged with r, I earned a tag badge for r before knowing enough about that software to even offer an R-based answer to any question! On the face of it, then, my votes on R-tagged questions and answers ought to count less, not more, than those of experienced R programmers.)
A deeper concern I have is that differential voting power could create an insular clique of high-rep people who effectively control the scores of questions and answers. I worry that this could narrow the site to reflect only the interests of its most active users.
When proposing significant changes to how this site works, we should always ask ourselves, what higher purpose would the change achieve? In this case, would we attract or retain more users? Probably not. Attract high-quality users? On the contrary, such people might be put off by having relatively little influence despite attaining demonstrably high levels of expertise. Improve the ratings of questions and answers? Perhaps--although that depends on assuming reputation (which measures activity) reflects the capacity to judge quality, as I discussed in the opening paragraph.
An interesting way to pursue the original idea would be to implement an alternative reputation/score measure in parallel with the existing one. At first this could be done invisibly and experimentally (by making the measure visible only to a few experimenters). If at some point evidence arose that the alternative were beneficial, then the alternative scores could be displayed to the world.
It is natural to apply such a weighting and I like the idea, but consider the challenge that the reputation a user has earned is bound to the tags of the answered questions. This can be included into the score model by setting the weight of a user vote to 0 if no reputation has been earned in this tag and normalization per tag otherwise, but what shall be done in case of rare tags ?
What shall be done if a question has multiple tags and the user has not earned (enough) reputation in all of these ?
In summary, such a change, although appealing and certainly more correct, might introduce more problems than it does solve (occam's razor).
Another solution could be to drive more responsible users to this site. If every question get the attention it deserves it is not necessary anymore to apply weighting to improve the meaning of answers with a small number of votes.
very bad, bad, neutral, good, very good
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While it is an interesting suggestion (with which I have some misgivings), I think this is a solution in search of a problem that isn't there. One thing that is worth bearing in mind here is that there is already a species of de facto weighting, from the empirical fact that users with higher reputation use the site more often/consistently and therefore cast more votes. For example, at the time of writing this post, our highest reputation user is listed as having cast 32,216 votes on CV.SE and another 1,433 votes on CV.SE.meta. (Using the simplifying assumption of 10 points per vote, that is 336,490 score contributed by that user.)
Consequently, while an individual vote from a high reputation user is treated as giving the same score as an individual vote from a low reputation user, high reputation users have generally contributed far more score to questions/answers merely from higher numbers of votes cast, which follows from their generally higher level of participation on the site.
