Frameworks give the judge a way to compare competing arguments. If one team gives the judge several good arguments about the economy, and the other team presents several equally strong arguments about the environment, a judge has no way to evaluate which arguments are more important unless debaters explicitly compare the importance of the arguments. Without comparison, the judge will have to choose how to compare these arguments on their own. Frameworks can help solve this issue. Unfortunately, many debaters use frameworks incorrectly and therefore don't address this frequent problem effectively.
A common framework that debaters use sounds like this: "if we can prove that accepting the resolution will do more good than harm then we win this debate." For the resolution "Resolved: China should broker an Israeli-Palestinian peace deal," a common framework might be "If we can prove that the benefits of brokering a peace deal outweigh the costs we should win this debate."
The problem with these frameworks is that they are not useful. They do not provide the judge a specific way to compare arguments, or set a specific standard for how the round should be decided. Therefore, when encountering these frameworks it can be fun and effective to combat them during crossfire.
Here are a few questions that can be used to highlight weaknesses in 'cost vs benefit' frameworks:
What happens if one group is paying the costs while a different group is getting the benefits? Should China sacrifice 10 citizens if it means saving 100 people from other countries? Should elderly people be valued less than young people because they don't work and use more resources than younger people in areas like healthcare? How do you define a fair comparison between groups of people?
Would you rather have 100元 now or a year from now? Does that mean that present benefits are more important than future benefits? Does that mean we should prioritize getting as much benefit as we can right now no matter what the costs in the future? What if the benefit now is small but the cost grows larger with time, should we accept it then?
How will you measure the costs and benefits? What about intangible benefits, like beauty or happiness? If we can't measure those things then how do we know if it is worth it to preserve a natural habitat, to save an endangered species, or to sacrifice economic production for a national holiday so people can spend time with their families? How can we compare things if they aren't measured in the same way?
Remember, in crossfire it is important to be polite but firm when asking questions. Use questions to reveal logical flaws in opponents' arguments, and avoid letting an opponent use up all the time without answering. It is not necessary to convince the opponent they are wrong, you are trying to show the judge that they are wrong. Simply mention how something does not make sense or how it seems like a worse standard than your framework, then move on to the next thing. There is always time to bring up the logical flaw in a later speech.