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sj999900

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. 

sj999960

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 :