10k undergrads would have few to no highly upvoted publications, and thus little to no voting power, even in aggregate. An even smaller fraction of them would have highly upvoted papers in the specific subfield of the paper they’re voting on, making their aggregated voting power even more worthless.

The only way to game the system would be to somehow convince a ton of highly upvoted people in a given subfield to upvote a paper in that particular subfield (and give up some of their voting power accordingly, since voting would cost you karma). Heck, make it so that you can only vote on a certain number of papers each month (5-10?), to make votes even more valuable.