I do understand, that many would like the rep system to be gone right now, but I think it's mostly because down-repping is heavily abused for quite some time now. In my opinion the problem isn't the down-vote function but its abuse.
From a sociological standpoint it's very effective for a community to have sanctioning capabilities or alternatively a higher instance that takes a close look and sanctions all dysfunctional behavior to a community wide consent. It's pretty obvious that a single community manager simply can't cope with this workload alone, let alone guarantee consent due to subjectiveness, so this leaves the community or no one.
Right now, because of the abuse everybody prefers "no one" and the positive effects of sanctioning are completely disregarded. Positive and negative sanctioning is highly effective in promoting cooperation and motivation. For example the very successful
Tit for tat strategy is just impossible without it.
The GOG community is a good one, but by removing sanctioning capabilities you also remove the basis for social evolution, which is founded on common norms and values. To keep up values, a society needs sanctioning, simple as that. As long as egoistic behavior yields surplus, it opposes altruistic values and without consequences it'll erode the value system.
The problem with the conjunction of down-repping and giveaways is just a collision of different value systems. Sachys' suggestion of separating the groups e.g. by introducing different areas might be a very good idea for a peaceful coexistence.
What has to be stopped is the abuse of down-repping, as single members are forcing their subjective views onto the whole community. The might of sanctioning must be distributed and you have to think about mechanisms that prevent single members of using multiple accounts for aggregating force they normally shouldn't have. You can't prevent it completely, but that's not even necessary for the community to work.
For example, cap down-repping the same way up-repping is capped. Block down-repping until the user reaches a certain rep himself (like it's done with the ability to post links), so a single user can't use a fresh account for down-repping. Improve your detection of multiple accounts. Improve your awareness of down-repping abuse by automatic triggers and a small automatic report of who's involved. It's pretty easy then to review the involved accounts by the community manager. And of capital importance, sanction the accounts which are abusing the rep system (down-rep them, block their ability to use the rep system, ban them, think of combinations and escalation stages, whatever..)
I'm pretty sure, the workload is easy to handle and there aren't many abusers. Stop them and the rep system will do it's job again.
Last but not least, the positive/negative sanctioning system doesn't have to be the rep system. Get rid of it and replace it by something different, but I'm skeptic about what good will come from a complete removal.
(Sorry for the long post guys, I'm not a big fan of them myself.)