What is the definition of diconomy?

Answer 1

The word you are most likely thinking of is 'dichotomy'

http://dictionary.reference.com/browse/dichotomy

This is a great word with several differnet contexts. Most often when you hear it on the news or someone use it in a speech, they are referring to the more common usage:

"division into two mutually exclusive, opposed, or contradictory groups: a dichotomy between thought and action. "