This question and my comment there made me think, and it seems to me that to completely avoid any sense of a "pack mentality" that could be applied to when votes are cast to close a question, the current format would have to be changed.
For one, there shouldn't be an indicator that others have already voted to close a question. If a question deserves to be closed on it's own merits, there is no need to know that others have already voted to do so. There is no need for a question to show that it already has 4 votes and just needs one more to be closed, so that another individual can come along and "do the right thing" and add the last vote to put it over the top. If a question deserves to be closed, and there is no "pack mentality" being applied in this situation, then it will earn all the votes it needs to close all on it's own. Right.
Also, when you DO vote to close a question, there should be no indicator as to what reasons were already chosen. Why? Think about it. If a question doesn't earn a preponderance of the SAME reason for being closed, maybe it was closed for the wrong reason. However, if there is an indicator that 3 people already voted a question as being Off Topic and one person votes Not Constructive the next vote is more likely going to be Off Topic just because there are already three votes cast for that. I don't care who you are, there is no denying that seeing the results BEFORE you vote influences the results of a vote.
I'm not saying that these stats should be removed completely, but they don't need to be visible.
There have been elections where Exit Polls that were televised before an election was over were shown to influence not only voter turn out, but the vote swing itself. People want to be on the winning side. They want to appear to be doing the right thing. They look for any indication that they are doing the right thing. When there is a clear cut path and guide set up for them, they are more likely to follow it. History has shown us that there are far fewer trail blazers than there are people who follow those trails.
EDIT I don't know if I just didn't explain myself properly or what, but I am not proposing that people not be allowed to provide reasons with their vote to close. I am not proposing an edit to the number of votes needed to bring the question to a moderators attention to close it, or even to close it automatically. I am simply proposing that the visible tally of current votes already cast to close it be removed, as well as the visible tally next to the reasons for closing.
If as has been said there is no pack mentality at all occurring when people vote to close questions, then what I propose would have no detrimental effect on the current system. If however, there are people are are influenced by the presence of existing votes to close, then there would be a difference in the number of questions closed by voting.
update obviously I'm disappointed by the responses, since I now know that people actively do sift through the questions to see which ones have close votes, so they know to join in the pack and close it. Sad to learn that although questions aren't necessarily closed simply because they deserve to be closed, those who feel the need to know that others have voted to close it won't admit they feel that way at least PARTIALLY because of the presence of those votes. If they weren't influenced, they wouldn't need an indicator. It really is that simple. I'll flag the question for removal.
Yet another edit this question only has downvotes and just keeps accumulating more. I don't agree with the reasons given for the presence of a visible VTC tally, and I haven't been given a convincing argument for why it is necessary to have that visible tally... so why can't I get the question removed? It serves no purpose to keep the question here. I'm obviously in a minority, if not alone in how I feel about this, so it doesn't even serve a useful purpose to keep the question for archival purposes. I get it. The community disagrees with me. Delete the question please.