Residue reasoning is arriving at the truth or best possible course of action by eliminating all other possibilities. Provide your opponent with a list of potential paths and provide reasons for why each one is invalid, untrue or unadvisable until you remain with just one, the one you wish to put forward remains. You can also use established criteria to rank each example according to suitability.
For example:
Jeff lists each type of car he and Tammy could buy. Having convinced her of the criteria by which they will choose, he goes on to list each type of vehicle and rank them according to how well they fulfill the criteria. He dismisses each type that does not fit with their needs and ends up with a hybrid SUV as the most appropriate.
Dramatic flair and charisma lend themselves well to this type of reasoning. Add a bit of panache to your argument through physical acts like counting the possibilities out on your fingers and pulling them back in one by one until your preferred choice is the only one remaining with a finger up. Or you can list them out on a black/whiteboard or PowerPoint presentation if those platforms are available to you and appropriate (please, please do not be the person who prepares a PowerPoint presentation for debates with your loved ones) and make a big deal about crossing each undesirable option out.
Take care to make sure you use take into account all the possible options when using this type of reasoning. Your credibility can take a knock if your opponent finds one or more cases you have failed to address. You can still use residue reasoning when you do not have all the options or a clear superior option cannot be identified – it can be useful in reducing the sheer number of alternatives, and the remainders can then be assessed according to other forms of reasoning.
