utopianturtle.top
phd student in cs at princeton researching ethics of algorithmic decision making
she/her 🌈
https://www.poetryfoundation.org/poetry-news/63112/the-ford-faberge-by-marianne-moore
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2. w is a big wrong: consider a set W' = W-{w} \cup {w*}. By inductive hypothesis, it could not be that W', which is of size n+1, fixed any wrongs. But since big wrongs are always wrong, committing w could not fix W' and again n+2 wrongs do not make n+1 rights.
Qed
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1. w is a little wrong: there are at least 2 little wrongs in W (since w was maximally wrong). Combining them into one macro-wrong m, let W' = W - {w, w'} \cup {w*}. |W'|=n so by i.h., m does not fix it. But as W' and m = W and w* then w* could not fix W either, so n+2 wrongs don't fix n+1 wrongs.
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suppose that n+1 wrongs does not ever fix n wrongs. consider any set of n+1 wrongs W and any additional n+2th wrong w*. Order W by wrongness and pick max w\in W. It is well known there is a threshold of wrongness at which a wrong graduates from a "little" to a "big" wrong. So consider two cases: