If I were to post an answer on a (eg) question tagged as 'cryptography' and receive two upvotes, one from joe-bloggs and one from a recognised expert in the field, it would be nice if that second vote carried some extra weight. In some ways this will help with the 'fastest gun in the west' problem, in that the earlier answers can hopefully be overweighted by the opinions of experts voting on later answers.
I'm not quite sure of an easy way to judge 'experts', but I think this weighting system would be quite valuable if it could be implemented somehow.
One option would be to allow users to nominate themselves as experts in up to five particular tags which they can only change infrequently (to stop gaming). Any votes they place (up or down) against questions in one of those tags could then carry a weight of 1.5 (rather than just 1 as it is now). These 'expert' tags should appear in the user profile page for maximum transparency.
The half vote shouldnt be displayed against the answer score, but can instead be tagged in the backend that the answer has received an additional half vote. When it receives a second half vote then the score will jump by 2. This means that only when two experts have agreed does the answer move by an extra point.
Similar Question: Indicate How Trustworthy the UpVotes Are
Note however that this is not an exact duplicate. The previous question discussed (extensively and exclusively) using Rep as a means of weighting votes. This system does not rely on rep.