SkeptiCat,
Your argument about "convincingness" doesn't convince me. It seems more like splitting hairs. Your example relating to people raising their hands when a gun is pointed at them, not because of the gun, but because their desire to live motivates them, seems a bit porous. If the desire to live convinces them to raise their hands, wouldn't they go about with their hands raised during that portion of their lives when they desired to live? Probably (obviously?) not. The presence of the gun is the convincing catalyst that makes the desire to live come to the forefront of attention.
As to convincing criteria, are you saying it is subjective? I'd agree with that. Some people are more easily convinced by a given argument than others who are more skeptical.
I also agree, that the inclusion of facts tends to make for a better argument. I disagree that convincingness is not in an argument. In some cases, adherence to logic is sufficient.