Normalised MEC (fish example)
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Notes
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I think I've done this correctly, but I'm not sure. I tried to follow the formula here: https://www.cs.cmu.edu/~epxing/Class/10810-07/lectures/normLec.pdf (slides 9 and 11). I didn't know for sure what should count as the population variance and population mean, so I used the variances and means across all theories and options. It's possible the "standardisation" approaches here are relevant, but I think that's something separate: https://medium.com/@swethalakshmanan14/how-when-and-why-should-you-normalize-standardize-rescale-your-data-3f083def38ff
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Reasons to think I did it correctly: The variances of the normalised functions come out as equal, which is the goal. The pattern of results in the three-option case seems to make sense; playing around with the T1 credence (and by extension with the T2 credence) suggested this basically gives an answer that's less favourable to T1 than the non-normalised answer was, but can still go T1's way if T1 credence is high enough, and especially can mandate the compromise egg curry; this seems to make sense, because normalisation reduces the disproportionate apparent "stakes" for T1.
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Things I'm still confused about: Does it make sense that in the two-option case, post-normalisation, it seems that all that matters is the credences (it basically seems to be My Favourite Theory), based on playing around with the credences? Does it matter that the normalised CW scores are negative in most cases? (I don't think so, as utility functions can be given a positive affine transformation.) Can/should I fix that? Why are the ranges the same (but opposite sign) in the two option case, but different (though similar) in the one option case?
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With three options
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Credence assigned
Non-normalised choice-worthiness
Expected CW of option
Mean of theory's (T's) CW function
Variance of T's CW function
Overall mean
Overall variance
Normalised CW
Expected CW of option
Variance of T's normalised CW functions (just to check I did my calculations right)
Ranges of normalised CW
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Fish curryT10.3205-90-22.05-28.333333332858.333333-10.333333331534.666667-52.75736418-101.5282061534.66666769.61041107
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T20.6795107.6666666676.333333333-124.53196591534.66666777.83247868
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Tofu curryT10.32055516.85304689-132.1052385
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T20.67955-202.3644446
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Egg curryT10.320505.43613.18934104-101.5471547
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T20.67958-155.6649574
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Two options only
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Credence assigned
Non-normalised choice-worthiness
Expected CW of option
Mean of theory's (T's) CW function
Variance of T's CW function
Overall mean
Overall variance
Normalised CW
Expected CW of option
Variance of T's normalised CW functions (just to check I did my calculations right)
Ranges of normalised CW
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Fish curryT10.25-90-15-42.54512.5-17.52341.666667-46.82386793-165.68445572341.666667-68.43488389
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T20.75107.512.5-205.30465172341.66666768.43488389
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Tofu curryT10.255521.61101597-199.9018977
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T20.755-273.7395356
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