Not if you aim to enforce a level of discussion higher than mere absence of pathology.
Downvotes are not the way to achieve it. The way to achieve it is by positive personal example and upvoting content which is exemplary. Why are downvotes bad? Because:
We want to allow "mediocre" people (some of which have an unrealized potential to be excellent) that want to learn from excellent people (I hope you agree). Such people can make innocent mistakes. There's no reason to downvote them as long as they're willing to listen and aren't arrogant in their ignorance. Downvoting will only drive them away.
Even smart people occasionally say foolish things. Downvoting sends such a strong negative signal that it discourages even people that get much more upvotes than downvotes. By "discourages" I don't mean "discourages from saying foolish things", I mean discourages from participating in the community in general.
Most content is not voted upon by most of the community, therefore statistical variance is large. Again, since the discouragement of downvotes is not cancelled out by the encouragement of upvotes, you get much more discouragement than you want.
Downvotes transform arguments into sort of arena fights where the people in the crowd are throwing spoiled vegetables on the players they don't like. The emotional aura this creates is very bad for rationality. It's excellent for blue-green politics (downvote THEM!) and death spirals.
Punishment is different enough from deciding who to talk with.
If you don't want to talk to someone, don't upvote her and don't reply to her. The psychological impact of downvoting is equivalent to punishment.
See also Yvain on safe spaces.
This is completely different. "Safe spaces" are about banning content which might offend someone's sensibilities. My suggestion is about "banning" less content.
We want to allow "mediocre" people (some of which have an unrealized potential to be excellent) that want to learn from excellent people (I hope you agree).
To some extend yes, but we don't want eternal September either. There concern about the average IQ that reported in the LW census dropping over time.
Downvoting sends such a strong negative signal that it discourages even people that get much more upvotes than downvotes.
If we would have less downvotes in general then every single downvote would create a much stronger negative signal than it does at the moment.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Thread started before the end of the last thread to ecourage Monday as first day.