# Conditionalising increases expected information?

I saw a talk that mentioned this theorem. I am now trying to find details of the theorem, but I'm not having any luck. I hope that if I can describe roughly what the theorem said, someone can recognise it and point me to some literature.

So the theorem basically said something like the expected self-information of conditionalising on the value of some random variable is always higher than the prior's self-information.

Does that ring any bells?

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This may be a somewhat garbled version of the data-processing inequality. Do you have a link to slides from the presentation, or some other detail, by chance? It is a standard fact that conditioning on an extra variable reduces entropy, for example. – cardinal Jul 16 '12 at 13:52