They intend to vote it; however, something in their minds repeatedly tells them "it is likely a worthless post because many users have downvoted it. Don't waste your time for reading this post, and downvote it".
This is telling: most of the requests on this topic assume that people voting down are just following the herd. But what about those posts that have hundreds of upvotes? You never hear people complaining about those.
Requests to hide the score almost always focus on the fact that it will hide downvotes, and how that is supposedly a benefit to everyone. What these requests seem to forget is that even downvoted posts get upvotes. And even upvoted posts get downvotes. So voting on SE is not as simple as users just following the rest of the herd. A lot more people are reading a post before voting than people seem to think.
I want to conclude that many users, even experienced ones, are highly affected by vote results on posts, so they may not cast their votes based on content of posts.
Are they really? To make such a statement, you will need data. Luckily, an experiment was done! The results, although not conclusive, are discussed in this post. The most important conclusion seems to be that "there did not appear to be a clear win for hiding post scores in any scenario tested."
I can tell you two ways in which vote results affect me:
- If I am looking for an answer to a specific question, a question with good votes and an accepted answer gets my attention before one with lower or negative votes. Because I know the chances of this question having a useful answer are just a bit higher.
- If I'm just browsing any site, I look at the recently posted questions. And while some scores jump out and pique my curiosity, I don't think they influence my behavior: I usually just open everything.
In the end, when it comes to voting, all that counts is that in order for me to make the right decision on what to do with a post, I need to read the entire post. A post that is highly upvoted or downvoted in a short time may spark my curiosity, but I still need to read the entire post to satisfy that curiosity and determine whether I will downvote, vote to close, edit, comment, upvote existing comments, or write an answer.
Putting the post score at 0 for an undetermined amount of time would change nothing to how I, and probably countless others, vote. It would, like the preliminary results of the experiment on SO state, only create problems for me as a user and as a moderator. For example, it makes it less clear that deletion is an option for certain low quality posts. So, instead of taking the 'correct' action of deleting a low quality post, I might make the mistake of adding yet another downvote, yet more frustration.
So no, don't hide the score.