The odds of winning an argument require more than just logic and rationality, as there are a lot of other factors involved.
By understanding and changing the 'frames' a person uses and center them around a shared belief, we can help our cause.
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Frames, with respect to a discussion or argument, are different categories to 'slot' an idea or topic, just like a car can be evaluated by its color, price, or model number.
During the course of an argument, to increase compliance towards your belief, you can change the framing of the existing belief of the listener.
Instead of challenging someone's existing belief, which always leads to resistance, it is much better to connect your own position to their beliefs.
Hope allows you to come up with creative solutions to the disputes at the core of the conflict.
You may see a way out of what seems to be a locked battle of wills. This is what happens in ordinary problem-solving, when thinking outside of the box can help all sides come up with a solution.