Syncracy is not a word and for quite sometime it had no mentions in Google. In 2002 only two pages in Google's search result even contained it. Then for some reason people tried to create a definition. There are now definitions such as:

A system of governance which adopts two or more systems such as communism and capitalism.

This is just one such definition. You are not likely to find two definitions that agree with each other. Another definition is:

Syncracy is a social psych term that describes families who make decisions by consensus. Wikis themselves seems a very syncratic mechanism, don't you think? I meant government by mutually Constructive Interference. Now don't go asking me to define constructive interference.

Syncratic

As you notice the two definitions do not agree with each other. One of the causes of this is that some people have tried to adapt the definition of the word syncratic. Even then, syncratic is not a word used in English.

Idiosyncrasy

The most like source of the words Syncracy and Syncratic is the words idiosyncrasy and idiosyncratic. The word idiosyncrasy is defined as:

Idiosyncrasy
noun, plural idiosyncrasies.

1. a characteristic, habit, mannerism, or the like that is peculiar to an individual.
2. the physical constitution peculiar to an individual.
3. a peculiarity of the physical or the mental constitution, especially susceptibility toward drugs, food, etc.

The word idiosyncrasy originated in c.1600, from French idiosyncrasie, from Greek idiosynkrasia "a peculiar temperament," from idios "one's own" + synkrasis "temperament, mixture of personal characteristics," from syn "together" + krasis "mixture". Originally in English a medical term meaning "physical constitution of an individual." Mental sense first attested 1660s.

The real definition

If Syncratic was to be coined as a term, it would be defined as:

Syncratic
adjective

1. created in a style similar to Syncrat.com