You could try not acknowledging downvotes on a new item until the number of downvotes reaches a threshold. For example the first downvote on an item would have no impact on the score or the placement of the item on the page. If the threshold is 2 then, the item would be affected after 2 downvotes. At that point the normal result for downvoting would occur. This would require two people to independently interpret the quality of an item. Though, I am only considering the case of an item being only downvoted.
Another idea I have is to require a reason for the downvote. Reasons could include: disagreement, uncivil, or offtopic. The score could be affected according to the reason. This could make downvoting more thoughtful and scores could be impacted less for disagreement.
Last idea: Instead of hiding all scores. Only hide the score for items with a score less than or equal to 1. These scores have less relevance and I think people will be less critical of comments if they don't see a negative score attached.
Another idea I have is to require a reason for the downvote. Reasons could include: disagreement, uncivil, or offtopic. The score could be affected according to the reason. This could make downvoting more thoughtful and scores could be impacted less for disagreement.
Last idea: Instead of hiding all scores. Only hide the score for items with a score less than or equal to 1. These scores have less relevance and I think people will be less critical of comments if they don't see a negative score attached.