How about either of these ideas?
Idea 1) Bring back the thumbs down, and as long as users are signed in, they can do a thumbs down, but, no one, not even the one who downvotes, sees any thumbs down totals on ANY post while signed-in. Only those who are NOT signed into the site will see the thumbs down tally in each post.
This satisfies the signed-in user who wants to downvote a comment to get his/her need to disagree met, conveniently.
This satisfies the signed-in user who does not want to see the downvotes and get agitated by them.
This allows the newbies who have not yet become registered members, and also the lurkers who chance by the site, and anyone else who is not signed-in, to see the downvotes, as a way to satisfy those downvote advocates who say that their downvotes help those who do not yet know better in what they read here.
Because signed-in users do not see the tallies, this should placate those users who believe that some users give thumbs-down not based on personal integrity but for lesser reasons such as they see a high-count of negative votes and want to join the smack-down, or just want to feel they belong, or like to game the system, or are just jerks, or see that their buddy gave a downvote so they want to as well, making the downvote into a popularity contest, or have a compulsive need to make themselves known, or any of those less-than-noble reasons that are disliked by those who would not have those reasons and would not want to see them quantified.
Advocates of downvoting say they do it because they disagree with the post. They don't say that they do it because they were influenced by the existing downvote count that they saw in the post. Therefore these advocates should not insist that they need to see these tallies prior to casting their downvote. Right? Good. For those downvoters who still want to see who else downvoted, for those downvoters who give social meaning to their downvote, for those downvoters who essentially are human beings with these legitimate desires, they can sign-off and take a look anytime. In exchange for having been given this convenient wordless way to express their opinion, their possibly contentious opinion, they can sign-off and take a look, knowing that a few extra keystrokes on their part to meet their own extra needs serves a greater good than what we had before. They are big enough to do that much. Keep in mind, all registered users would have to be as big, if they were as curious.
For those remaining downvoters and any upvoters who read the above and believe they would have to sign-in, sign-off, sign-in, sign-off, just to get through a thread, well that is elective behavior and if you really follow the downvoting to that degree then now we are talking about something obsessive perhaps, people who are living a side life inside this downvoting thing, a choice outside of giving feedback.
Idea 2) Bring back the thumbs down but forget Idea 1 and just have a toggle button in your profile to globally suppress the downvote count so that each user can decide if he/she wants to see them or not.