How do you measure between the horns of a Dilemma ?
A dilemma is a situation in which there are two choices, but neither choice is ideal. Therefore, the expression "horns of a dilemma" indicated that neither "horn" is comfortable; it is often expressed that the subject who must choose is "sitting on the horns of a dilemma"--not a very confortable thought!
As Chris indicated in his response, it's hard to give you a direct answer as the question is vague: what do you mean by "measure" between the horns of a dilemma? Could that mean, how does one determine which choice is the least unpleasant course of action? It depends on the choices. So, I guess the way you measure is by weighing the pros and cons of each option and determine the best course of action. If you can give us more information about your question, we can help you further. Good luck!
This question is a bit vague but we can say something in general about dealing with arguments that pose a dilemma.
Let me pose a classic dilemma we can use for illustration. A contemporary version of the Euthyphro dilemma starts from the assertion that goodness comes from God. One asks whether God commands what is good because it is good or if it is good because He commands it. One can posit that if God commands what is good because it is good then there is something superior to Him which he must consult to know what is good. This would deny certain attributes that are required to be divine and make God a third wheel. On the other hand, if something is good simply because God comands it then goodness is arbitrary. God could have made murder good and charity evil by divine fiat. Well that doesn't seem right either. So, it is argued that there is a dilemma here with two horns. Horn one ruins God's sovereignty and horn two makes goodness arbitrary.
If this is a genuine dilemma then we can accept neither horn without a grave rational cost. There must be something amiss with our beginning assertion. But, if another option besides the two horns can be shown, then we can call this a false dilemma. For instance, God could command what is good because He is good as a necessary feature of His being. In this way we can diffuse the percieved dilemma. this is sometimes called "splitting the horns of the dilemma".
So, that is how you deal with a dilemma in a nutshell. If it is a genuine dilemma then there is an incoherency in what is initialy posited since either horn of the dilemma leads to an impass. If it is a false dilemma, there is a third (or more) option that diffuses the dilemma. So I suppose to "measure" between the horns of a dilemma would be to deny the original assertion that led to a dilemmas or find a way to split the horns of the dilemma.
Hope this helps,