Absolutely not. Assessing the quality and correctness of groundbreaking research requires a large amount of both talent and effort; a reddit or HN style voting system would swamp the signal with uninformed noise.
However, maybe something like PageRank might work out well. The more citations your papers get, the more weight your reviews will have. Certainly, there are problems, like people learning how to game the ranking system.
On the other hand, the current system is certainly worse in this regard.
Running pagerank on authors with an unnormalized weighting function of "how many papers does author X have which cite something written by author Y" (so that if author Y publishes the same paper multiple times it doesn't have any effect even if both copies get cited, while author X publishing the same paper several times downweights all of his outgoing links equally) could work, though.