Which is the most valid definition of a republican form of government?

A Republican Form of Government is a type of government in which the administration of the affairs is controlled by all the citizens, who choose some elected leaders to run the government by accorded laws. In fact "republic" derived from the Latin "res publica" which means "public things", and it refers to a form of government in which the citizens deal their affairs for their own benefit and purpose, rather than for the benefit of a ruler.

A government system were representatives are chosen to vote on political laws and issues, for the majority of their region or group