Like many teachers trying to support sustained and respectful academic discourse, I instituted the "rules." While most are fairly common—don't interrupt, keep to your time limit, listen to the other person completely before forming your own counter-argument—the two that work best for me are the mulligan rule and the five Rs.
Although I don't play sports, I know that a mulligan is a "do-over." It is an opportunity to let a mistake pass unnoticed or without consequence—something needed when working with students. Many students are afraid to share their real opinion because it might not be PC or it might "come out wrong." When this happens, students' well-intentioned comments might be jumped on, condemned, or exploited. This practice shuts down, rather than encourages, discourse.
The mulligan rule is simple: at any point while making a statement, the speaker can call a mulligan on herself. She simply stops and says "mulligan." She then takes a deep breath and starts her statement over, or opts out of her statement altogether. Nothing she said before that point can be used against her.
This allowance has worked wonderfully with both my former 7th graders and my current college students. Speakers are more willing to engage in controversial discussions because they are allowed to take an immediate second shot at their statement. Audience members listen more carefully to the entire statement because they realize a mulligan might be used at any moment. Discussions are academic arguments (state and support) rather than fights (name-calling and interruptions).
The second practice I instituted was a spin on the talking stick. Many teachers use an object to signify the speaker—only the one holding the object is allowed to speak. If someone wants to say something, he must request and wait for the object. This works well to reduce the number of voices at one time. However, I've also seen many students mentally check out of participation figuring they just won't request the object.
I use a Koosh ball to introduce the five Rs of academic discourse: respond, repeat, restate, rebut, and reinforce. After the speaker has made his "response" to a question and no mulligan is called, I toss the Koosh ball to another student and say "repeat." That student has to repeat what he heard the speaker say. The Koosh ball then returns to the speaker with the command "restate." He then has a chance to agree with the repeater or to clarify his original statement after hearing his words repeated back to him. The Koosh ball comes back to me and I toss it to another student and say "rebut." This student has to agree or disagree with the original speaker's response and give a reason why (support). Because anyone could be called on to repeat or rebut the speaker's argument, everyone needs to listen. Students are encouraged to take notes on each part of the process. A fourth person can then be called upon to "reinforce." This speaker has the option to reinforce the original response or the rebuttal—for or against—with new supporting evidence. Often, I will reclaim the Koosh ball and challenge a student to identify the support given as ethos (credibility/trust), pathos (emotions/values), or logos (logic/reason). I then ask further questions to determine if students feel the reasons are effective or if another Aristotelian method would be more successful.