The laws of Loshon HaRa apply whether it is the spoken word, written word, or even gestures. While I'm inclined to think it is permitted (and have done so on select occasions) how would you understand the halachic status of a down vote with respect to hilchos loshon hara?
The real answer is that a down-vote could mean "I don't think this is the kind of question mi.yodeya should focus on", without necessarily implying anything bad about the person who asked it.
Being able to respectfully disagree with an opinion -- while maintaining respect for the person who holds it -- is a hallmark of healthy Jewish learning. R' Moshe Feinstein was asked by someone in Bnei Brak who wanted to give a halacha shiur that would quote the late Chazon Ish, but occasionally disagree. R' Moshe wrote that any respectful quoting of the Chazon Ish's views is a respectful thing, even if you then describe why you disagree. And that the Chazon Ish never expected or demanded that everyone agree with him all the time.
But even if a down-vote was construed as deleterious to the asker (which it shouldn't be), let's review the Chofetz Chaim's criteria for Loshon Hara for a creative purpose:
- If Shmerel asks a question, and I believe that people will be harmed if they treat this question as important, or by extension, if mi.yodeya will lose its ability to help people because it's filled with highly-ranked unhelpful questions, then I should do something about it.
- The downvote system is the best way to to do something about it.
- It's as neutral-tone as you can get
- It doesn't damage Shmerel disproportionately (if at all)
- There is no way (that I can think of) that accomplishes the same goal with less harm to Shmerel.
- The only remaining conditions are ascertaining it's true, and intending for good purposes.
- I think we're all assuming that when we see "Shmerel's question", we've ascertained satisficingly that Shmerel indeed asked this question.
- How do I ascertain that the question is unhelpful, and that my motives are good? Well, that's where I think the system trusts our judgement.
If someone writes something incorrect, it would be proper to downvote him so that other people do not learn to act incorrectly. StackExchange relies on downvoting (not flagging, as some people assume) to mark incorrect information.
Downvoting a wrong answer would be permitted as it has a clear constructive purpose. The Chofetz Chaim and other poskim all permit speaking Lashon Hara for a constructive purpose (subject to several conditions). Helping people learn the correct Halacha and not stray after an incorrect idea is a toelet, a very important one indeed.
According to R. Menahem HaMeiri the definition of l'shon hara, is speech that is meant to be defamatory or hurtful. Thus, statements of a negative nature (such as a downvote) that are given for a positive reason (in this case helping other willing participants on the site find the truth), and not to hurt others, are permissible since by definition they are not l'shon hara. These are his words in is Hibbur HaTeshuva (Meshiv Nefesh I:4):
עקר לשון הרע הוא המתמיד לספר בגנות האחרים ויתן דפי בענינים או שילעג להם למעוט הצלחתם...ומעין זה מי שילעיג על חבריו למעוט השגתם בידיעה...לכונת לעג וליצנות...וכלל הדברים כל אשר יתן מום באדם...ללא כונת ענין נבחר הוא ענין לשון הרע...שאין לספר במומי בני האדם על דרך לעג וליצנות, אם לא יעשה כן...לאיזו כונה
The archetypal l'shon hara is one who frequently relates embarrassing things about others, and adds falsehood to what he says, or he defames them on their lack of success...And similarly one who defames his fellows on their lack of intellect for the purpose of defamation and mockery...The rule is that anyone who ascribes a fault to others...without some specific intent is l'shon hara...For one should not relate the faults of others in context of defamation and mockery, unless he is speaking for some purpose. (Translation my own).
This also appears to be the opinion of this is also the opinion of R. Elhanan Wasserman, who generalises this to all interpersonal mitsvot. He writes in Kovets Ha’arot (Yevamot: 70):
ולולי דבריהם היה נראה, דכל האיסורין שבין אדם לחבירו אינן איסורין אלא דרך קילקול והשחתה שלא לצורך... וכן בלאו דלא תלך רכיל, מותר לספר לה"ר על בעלי מחלוקת כדי להשקיט המריבה. וכן בלאו דאונאת דברים... ומוכח מכ"ז, דכל האיסורין האלו הותרו לצורך תועלת
If not for their words, it would appear that all interpersonal prohibitions, are only forbidden in the context of degrading and tarnishing others for no purpose...And so too with the prohibition of gossiping, it is permitted to tell l'shon hara on disputants to quell the dispute...And similarly with the prohibition of onaat d'varim [verbal abuse]...And it is evident from all this that all of these prohibition are permitted to achieve an end. (Trans. my own).
Importantly, they do not attach conditions to to'elet, as the Haffets Hayyim famously does.
Similarly, R. Asher Weiss Shlit"a writes in Minhat Asher to Leviticus (p. 268) that to'elet renders speech permissible and not l'shon hara, by definition.
באיסורי תורה צריך לדון בדיני דחיה האם תועלת זו ראויה לדחות איסור ...אבל בהלכות לשה"ר לאו מדין דחיה אתינן עלה, אלא יסוד האיסור תלוי במדה רעה וכל שכונתו לטובה...ולא לרעתו אין בזה עבירה כלל, ודו"ק בכ"ז כי לענ"ד ברור הוא
With Torah prohibitions one must evaluate with the laws of dehiya [prioritisation], whether this to'elet [purpose] is sufficient to supersede a prohibition. But with the laws of l'shon hara, we are not utilising the law of supercession. Rather, the very definition of the prohibition depends on negative character traits, and anything in which his intent is for good...and not for someone else's harm, has no prohibition whatsoever, and consider all of this, for in my humble opinion, it is clear.
He shows that this is the opinion of Rashi (Moed Katan 16a s.v. amar lei la'avuha) and sharply disputes (p. 267) the Hafets Hayyim's attempt at escaping the implication of Rashi:
אך בחפץ חיים...כתב...ודבריו קשים לכאו' דמלבד שאין הדברים מתיישבים בלשון רש"י
However in Haffets Hayyim...he wrote...and his words appear difficult, for besides for the fact that his words don't fit with Rashi's wording...
Importantly, he clarifies (p. 267) that there are limits to the limitation of l'shon hara to cases of malicious intent:
דשאני המספר לשה"ר דרך קלות ראש דהרי פושע גמור ובזה ודאי עובר בחטא כיון שהדברים מצד עצמם הם לשה"ר גמור ובדרך שחוק וקלות ראש מנבל הוא את פיו בכה"ג פושע הוא אף שלא התכוין להרע לחבירו
For it is different if a person speaks l'shon hara with frivolity, since the matters are intrinsically l'shon hara and in the context of frivolity and levity, he pollutes his mouth. In such a case, he is a willful sinner even though he didn't intent to harm his fellow.
That is: "I was just having a good time", isn't a legitimate excuse to speak disparagingly about someone. However, by all indications, voting on an answer to help users get accurate information, would be fine.