I may be missing something here, but what sort of conflict are we talking about?
What sort of conflict might pop up which could not be resolved by the two people cooling it and (virtually) walking away?
What could be at stake in a discussion forum aside from opinion? The only thing someone could lose is the feeling that they have convinced someone else of something...
What would a mediator do, tell someone that their opponent is right, and that they NEED to CHANGE their mind?
Could someone draw a hypothetical situation where there would be a conflict which necessitates a mediator (rather than a time-out)?
The conflict we are talking about is the one described in the first point in the OP: different sets of values cause strong clashes that become difficult to resolve.
Conflict occurs in miscommunication in which one or both parties fails to be willing to compromise or reach a middle ground; see the above. Disregarding my tongue-in-cheek response to your original post, I should note that I actually did attempt to concede to CR in chat in hopes to resolving things only to get more hostile responses for a while before a resolution was made.
People generally have much more trouble conceding something if they feel it is A) clashing with their personal values or B) going against forum rules. Crockett displayed problems with A and I displayed problems with B initially. I could have avoided B at the start by throwing in an additional comment to any of my posts asking CR to take this issue to PMs. However reviewing my posts I failed to do so which contributed to his increasing need to criticize me on A even as I switched to attempting to resolve things with him on chat. (I should note Nae's reaction to your humor is also fairly similar to to his reaction to mine which was used in a similar situation. If this demonstrates anything, it should be that
humor needs to be used carefully when diffusing arguments.)
In this scenario, a mediator does not need either side to change their mind but rather to step in and put a constructive halt to the situation, which OldTrees did to allow discussion to continue on the thread. By this point I had attempted to concede to Crockett on chat solely to end the argument but as stated above by this point he had misunderstood me so much that he was refusing to accept any concessions I made.
A good example of another situation in which a mediator may have been helpful would've been the openEtG arguments a while back. A few users attempted to suggest that people on both sides of the copyright issue of 'copying/remaking' EtG be mediated by a neutral party, but a biased person then went and assumed said neutral party. However his bias prevented the discussion from remaining truly neutral and as such the arguments only became more harsh until everyone was forced into the 'cooldown' period mentioned above.
@ Naesala - I think this is a wise idea. Most chat mods take the role of warning and banning as needed but we rarely see chat mods attempt to mediate harsher discussions beyond continued requests to take things to PMs, which both parties sometimes ignore. Chat mods being open-minded and proactive mediators in situations would help resolve conflicts much more smoothly.
@ Treldon - Since there is no one staff member in the forums who is specifically requested to do this I would say it is the responsibility of all users to look out for their peers and mediate as needed. (See Counterpoint 1)