Putative Supremacy of Outcomes of Range Voting

I have not seen a reason to think it possible that a single-winner system that produces different outcomes than Range can resist money more effectively than Range does.

Moreover, I think that for elections with 2k or more voters, Approval will produce the same outcomes as finer-grained Range.

How do you arrive at this? My problem with Score/Range is that it rewards people for following polls, and giving your guess at the the front runners a 5 (or whatever the max is) and a zero.

It also encourages parties to eliminate candidates that could split the vote.

Approval is highly dependent on whether or not voters have a good idea who the front runners are. Imagine our vote for a domain name for the forums had Approval voting. People would be trying to guess how other people are going to vote so they can approve or disapprove wisely. (whether or not there are more than 2k voters)