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Psychohistorian comments on "Sex Is Always Well Worth Its Two-Fold Cost" - Less Wrong
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Your proposition appears to be, "evolution::culture can stably involve more than two parents, therefore evolution::genetic can stably involve more than two parents."
To put it mildly, this conclusion does not follow. "Parent" and "offspring" mean completely different things (if they are even cogent concepts) in evolution::culture than they do in evolution::genetic. The article is quite clearly refering to evolution::genetic, so the fact that evolution has multiple definitions is not relevant.
I may have cited multiple definitions of evolution - but it was not to point out the differences between them. It was to pile on evidence from a range of sources.
I don't agree with your statements about the role of parent and offspring in cultural evolution. Nor - as far as I am aware - does anyone else in the field. Parent and offspring share heritable Shannon mutual information. The parent is the source of the information, and the offspring copies from it.