You first need to verify the actual problem at hand. See, voting behaviour is something you should affect as little as possible. Users should always be free to vote however they like, as long as they are not exploiting flaws in the system.
The phenomenon "pile-on voting" can have any number of reasons: It could all be genuine votes, regardless of the score. It could also be a snowballing effect: A post that already has upvotes will gain more exposure and therefore more upvotes. For downvotes, the very same attention applies on a psychological level (rather than a system boost): "Why is that downvoted so heavily? Gotta check it out!". Or, in the case of Stack Exchange, the post might be pushed to review queues or be brought to users' attention through some other way - which increases exposure and therefore more downvotes.
As for solutions, you have very little in terms of community options. You can try educating people - PSAs, guidelines, something to tell users how they are supposed to use their votes (which, again, runs a bit contrary to the idea of being free to vote how they please.) You need to point the community as a whole at these resources.
At the end of the day, this kind of voting behaviour tends not to be actively harmful to the community. It is not at all easy (or, even possible) to define, detect, and identify this kind of vote(r) - which is necessary before you can consider addressing individual users about their "wrong" votes. As such, I cannot honestly recommend taking much action about this beyond attempting to educate the community.
If, however, you have influence on the technical side of things (and you truly deem this voting behaviour to be an actual problem), you might want to rethink the score feature entirely. If you want to show a raw score, that also means people get to see the raw score, and subsequently use it in their voting behaviour.
You can make people value their own votes more. Someone who sees a post that already has lots of votes in a given direction might not want to vote in that direction if their votes have a certain value to them. There are a few ways of doing that: A low amount of votes per time unit, or making the vote have a big impact on some feature on the site.
As I said above, you might also consider not showing the raw score. An option would be fuzzing the score somehow (a "topic heat" meter comes to mind). The implications are, however, that your voting system becomes largely useless because you just removed a core element.