What's not included in the description of the fasces is the meaning of the bundled sticks. Warring tribesmen lived across from each other, on either side of the Tiber. As their populations grew they were faced with continued warring with each other, or working out an alternate solution; and so formed an alliance, deciding that together, they were stronger than either tribe was separate. (I think this is also the source of Castor and Pollux being weaned by the she-wolf.) As they joined forces they extended their reach out to other tribes, offering them the opportunity to become Romans, by joining with them, rather than fighting them. So the individual sticks represented the individual tribes, and later the individuals, who, bound together, were stronger than the sum of their parts.