Why does "group by" need to match select fields?

[Omar Eljumaily <omar2(at)omnicode(dot)com>]

Sorry if this isn't exactly postgresql specific.  I periodically run 
into this problem, and I'm running into it now.  I'm wondering if 
there's something about "group by" that I don't understand.  As an 
example what I'd want to do is return the "id" value for the check to 
each payee that has the highest amount.  It seems like there's no 
problem with ambiguity in logic, but postgresql + other sql servers balk 
at it.  The group by fields need to explicitly match the select fields 
with the exception of the aggregate function(s?).

create table checks
{
   id serial,
   payee text,
   amount double
};

select max(amount), payee, id from checks group by payee;

Why won't the above work?  Is there another way to get the id for the 
record with the highest amount for each payee?

Thanks.