They should be allowed to, but their decisions should be public. Currently Reddit moderators are able to arbitrarily and secretly remove posts and comments, even when doing so goes directly against the stated goals and published rules of their community.
They should. However, they should not be allowed to misrepresent their rules. I know a few subreddits that claim to be unbiased (to attract subscribers) but engage in highly selective moderation. While it’s ok to do so, such subreddits should be forced to explicitly declare their leanings and moderation policies in the description.
This is probably easier said than done, for at least a couple reasons:
a) How do you determine which subreddits need to disclose that information?
b) How do you put something as abstract as what warrants moderation in a community into a simple description? Codes of Conduct can help with this, but as I'm sure others will inevitably point out, those can be abused by poor moderators as well.
Depending on the context of the community, such things can actually do more harm than good - many users react negatively to any display of authority, no matter how reasonable it is. I don't think community managers should have to subject themselves to the questioning of users who don't have anything better to do, if they don't feel like it adds to their community.
Of course, this does work in some places - Wikipedia is extremely transparent about its moderation actions and policies - but I don't think it should be the default for every single community.
I mean if the mods want to run their subreddit as a dictatorship that's allowed, and having a public log wouldn't stop that. It just means that you can't pretend you're not intervening if you are.
Yes and no. Like, is there a guy who decides who to kick out of the intramural softball league? Probably yes. But people will see that it's happened and talk about it, and if it was unreasonable then at some point they'll have a word with the guy, and maybe oust him or start their own splinter league or what have you. All of which is sort of possible on reddit up to a point, but those mechanisms are much less functional because the only community interaction is the subreddit itself where the moderator can just silently remove any posts they don't like.
It could go either way. If the purpose of the community is to benefit the moderators, they should have more control to censor. If the purpose of the community is to benefit the users, they should have more freedom in what they're allowed to say.
This is a rather 1-dimensional view on community moderation.
The purpose of a community is (generally speaking) to provide a place for people to engage and interact with each other, not to 'benefit' any one particular group of people. Users should have the freedom to discuss what they want, yes - within reason, as long as it doesn't jeopardize the core goal of the community. Moderators need to use their best judgement and knowledge of the community to determine what meets that criteria.