This says that the way that growing the input by a factor of $~$x$~$ changes the input is exactly the opposite from the way that shrinking the input by a factor of $~$x$~$ changes the input\. In terms of the "communication cost" interpretation, if doubling \(or tripling, or $~$n$~$\-times\-ing\) the possibility space increases costs by $~$c$~$, then halving \(or thirding, or $~$n$~$\-parts\-ing\) the space decreases costs by $~$c.$~$
output?