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These might be some typos:
From the following, the second should be :
What can we say about ? Well, if we fix a , then it will appear in of the terms (i.e. all choices of the and variables, and all possible choices of the other variables in the other variables in ).
as in
(i.e. all choices of the and variables, and all possible choices of the other variables in the other variables in ).
In the following, the second term should instead be multiplied over .
Define as selecting variables from , and
I believe the following should be "from positive to negative" rather than "from negative to positive".
How about a fixed ? Well, if goes below , that will kill off of the . So if all other are positive, sending from negative to positive will multiply the expected value by .
And here, it seems "(ignoring the )" might be "(ignoring the )".
In some ways we cannot afford to be sloppy: assume that should be in but isn't; so the true utility is , but a -maximiser might sacrifice to increase ; thus (ignoring the ) maximising may set to .
Thanks to Rupert McCallum for help in identifying some of these typos.
I think these might be some typos you could correct:
, or both measures are undefined.
The should be .
For such an -stable set, and , thus .
There is a missing parenthesis and the should be :