Although I think that ultimately humans have a significant degree of free will, it's a lot more limited--by genetics and environment--than is apparent on the surface. Thus the free will defense defends God against being the cause of evil to a much lesser degree than many would think. — Michael Cunningham
The issue with free will is, that free will itself is the compensating good. That it is a good that we are beings of free will, as opposed to some type of slave or puppet. The ability to chose freely leads to some of humans' greatest virtues. It they are not free choices, than they are not virtues. The problem is that if humans are free to chose - it brings in all the possibility of bad choices.
You issue of genetics or environment are to some large degree just observations of some continuum of a series of free will choices. More on this in a sec.
. If an atheist presents a large number of examples of natural evil, shouldn't it be incumbent on the theist to at least make a prima facie case that it's plausible to think there are compensating goods for a substantial portion of those evils? — Michael Cunningham
As above, well if you buy, as I do, that free will is a compensating good for evil acts of free will, that encompasses a great deal of them - For the others 2 points:
The first is are all evil due to natural disasters free of acts of free will? If you build your house on a cliff overlooking the ocean, is it an act of God or an act of free will if a storm knocks it into the ocean?
And this nature of causality can lead back to very small items that can have great impacts - the butterfly effect - my favorite example is suppose Winston Churchill's mother decided to sleep on a different side the night Churchill was conceived, maybe a different sperm would have fertilizes the egg, and an entire different human could have been born, and maybe Hitler would have won the war, and ....
The point is that we tend to look at individual acts, and use our limited cognitive abilities, and within our prejudices look for answers. So here are some questions along those lines.
The earthquake in Haiti kills thousands, some quite horrifically. How could God allow that to happen. Well if 10 years before that Bill Gates decided he didn't need all those billions of dollars he has and decided he wanted to return that side Hispaniola to its natural state and gave every body there $100,000 to move somewhere else. I understand that is crazy - but you get the point.
There are millions upon millions of human choices that if decided differently could have permeated into millions upon millions of different scenarios that could have changed the impacts or effects on much of the evil attributed to God. Awful storms kill thousands of people - the are awful storms on top of Mt. Everest almost every day - Is it the awful storm that kills or some chain of acts of free will that put the people in the way of the storm ?
Secondly - it is really not the main issue, or even needed by the theist - the main issue is cognitive difference between humans and God. And human hubris. In your point above you are just moving the issue of cognitive distance from - if there was a compensating good - would we be aware of it and recognize it, to, there is some right number of compensating goods that allow us to make a valid inference - and if there was such a right number we would be aware of it and recognize it as such. You are asking the same question in a different form.
Finally - again - the theist in these arguments has nothing to prove. The argument from evil is from the Atheist to the Theist - saying your theistic belief is not reasonable. The theist presents his case of compensating goods, based on cognitive distance as a reasonable explanation of how evil can exist, and God can be perfectly moral. And is not convinced his theistic belief is out side reason.