Updated: Aug 26, 2022
Believe it or not, this website does not represent the end-all for the correct way to run parliamentary debates. This is especially in terms of how to claim abuse on the top-of-case. A lot of teams do not bother running a topicality. In fact, some teams will challenge definitions even though it has relatively little bearing on the debate overall.
What to do:
First of all, resist the urge to go into full-fledged crisis mode or shout at the opp that they are completely and totally wrong! They aren't necessarily. A lot of arguments of abuse contain the essential elements of a topicality, such as the violation and counter-definition. In this case, it's best to respond as you normally would to any T.
Most T-not-Ts look like this, and are not really a cause for concern. Some tournaments even specifically say topicalities are not allowed, so you may end up running something more or less looking like this. This can also be a good strategy for inexperienced judges to make it more understandable.
Counter-value (or WM or VC or definition) debaters:
Some opp teams are taught that they should always run a counter to an aspect of the gov case, most often a counter-value in a value round. Their own value may be better for their case, or it may not. They may attack your own definition, or they may not. Either way, this is a little more puzzling than the first type of T-not-T, since they do not necessarily show that a definition or value is abusive.
The best course of action is to defend your own definition and attack your opponents, as usual, but especially to pick at their motives for introducing a counter-value. Remind the judge of your right to define, as the gov team, and that opp must have a pretty good reason for breaking down the fundamental rules of parli.
Even after establishing that your definition is better, tell the judge that it doesn't even matter, since you win off both anyhow. Do your regular weighing/impact calc, but with each item in question. That way, the judge's decision on the definition does not necessarily determine a win or loss.
Diehard counter-value debaters:
Sometimes, debaters who prepare a counter-value during prep time are just itching to use it. In fact, they want to use it so badly that they don't care that their counter-value is nearly identical to the original value.
Case in point: gov brings up the value of net benefits, then opp contests, saying that a counter-value of quality of life is much better.
What's the difference between the two? Unclear. In these situations, it is easy to short-circuit and spend all your brain energy wondering what compelled your opponents to do such a thing.
But instead of attacking their counter-def, just point out that there is not a huge difference between the two, and continue on with the arguments. While your opponents waste time arguing that quality of life really is better, you will have the upper hand in terms of the actual contentions, which judges prefer.
During your rebuttal speech, explain why you win on both, which is pretty easy, considering they are basically the same thing.
While it can be scary to see debaters with completely different styles and structures, remember to stay calm. Judges, especially inexperienced ones, may have trouble following a definitions debate, so keep it simple. The cleanest team often wins!