I don't think his way of explaining it is any easier for a newcomer. It doesn't make sense unless and until you already have a firm grasp of the basis for Occam's razor. And if you know how to justify Occam's razor, you already understand why adding details penalizes the explanation's probability.
Furthermore, his idea can't be summarized as "good explanations are hard to vary". It's more like, "good explanations are hard to vary while preserving their predictions".
I do appreciate that you added a summary.
I don't think he is saying, "good explanations are hard to vary while preserving their predictions".
As described above the statement "Everyone just acts in his own interest" very easily preserves its predictive power in a multitude of situations. Indeed, the problem with it is that the statement preserves its predictive power in too many situations! The explanation is consistent with just about whatever happens, so one cannot design a test that makes one believe that the statement is certainly false. So it is too easy to vary and hence a bad explanation.
I'm sure this talk will be of interest, even if most of the ideas that he talks about will be familiar to readers here.
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In this talk David Deutsch discusses "the most important discovery in human history"; how humanity moved beyond a few hundred thousand years of complete ignorance about the universe. Deutsch attempts to be specific about what led to this change - he concludes that it is the insistence that an explanation be 'hard to vary'.
Whilst a 'hard to vary' explanation is functionally the same as a, more commonly known, Occam's Razor explanation (since fewer parameters necessarily make a fit harder to vary) the slightly different emphasis might be a useful pedagogical tool. A 'hard to vary' explanation will perhaps lead more naturally to questions about strong predictions and falsifiability than Occam's razor. It also seems harder to misunderstand. As we know, Occam's razor suffers because of the difference between actual complexity and linguistic complexity, so an explanation like "it's magic" can appear to be simple. Magic might appear simple, but it will never appear 'hard to vary', so students of rationality would have one less pitfall awaiting them.
Deutsch also touches on what constitutes understanding and knowledge and cautions us not to trust predictions that are purely of an extrapolated empirical nature as there is no true understanding contained there.
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If you haven't already read Deutsch's book "The Fabric of Reality" I'd highly recommend that as well.