To debate or not to debate?

Before you can answer that question, you must first determine what kind of debate has been initiated and what kind of debate you are willing to engage in. Then you can make a rational decision.

There are basically two kinds of debates, having distinct objectives: resolution or victory. And these two distinct types are orthogonal (i.e., perpendicular). Orthogonality, and its opposite parallelism, are geometric concepts; nevertheless, they can provide graphical insight for understanding some non-mathematical situations.

In the issue under discussion, if we represent these two types of debate by a pair of normalized vectors (i.e., two directed lines of unit length each) then resolution would be perpendicular to victory, because these goals are completely at odds with one another, in the sense that neither participant can derive any value from a debate in which they have different objectives. The mathematical expression for such a condition is: the cross product of orthogonal unit vectors is another unit vector orthogonal to both original vectors — graphically demonstrating that the originals are completely at cross purposes, and their dot product is zero — demonstrating that the measure of their efficiency is nil.

On the other hand, if both participants have the same objectives (either both victory or both resolution), the analogous mathematical situation is a pair of parallel unit vectors. Here we have a cross product of zero (the participants' objectives are not at cross purposes but, rather, in complete harmony), and the dot product is magnitude one (the debate will be 100% efficient, since each participant will derive the maximum value for their efforts, either resolution for both, or the thrill of confrontational competition for both).

It is my sense that the vast majority of debates are confrontational, and such a debate online is known as a flame war. Both participants seek to be victorious in the eyes of their audience, those witnessing the flamers hurling taunts and insults at each other. It's win-win because everyone derives value for their efforts. Those few debates in which both participants are prepared to accept their opponent's view if his argument is sufficiently convincing, are win-win too, which is intuitively obvious. It is also intuitively obvious that when the potential debaters have different objectives it is a lose-lose proposition. Hence, the general answer that makes sense to me is: decline to participate in an orthogonal debate, but go for it if you and your opponent have parallel objectives.