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Lumifer comments on Measuring open-mindedness - Less Wrong Discussion
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First you need to get precise about what you are testing -- in particular, define "significantly better arguments".
I don't know the details of your statistics, but is it possible that the way you are choosing "principal vectors" is entangled with how the resulting clusters rate?
The word “better” may be replaced with “more coherent” or even “more grammatically correct”. Fundamentally, the question is whether the difference in ratings arises from the difference in the comment qualities (other than political orientation) or from the difference in those who rate them.
The system chooses vectors automatically. But I think the above question would still be valid even if people were divided in two groups in some totally arbitrary way.