William Morris, I think, once described political parties as being like two carriages travelling in the same direction, splattering each other with mud.
Apt, and timeless. In the Byzantine Empire supporters of cahriot racing teams amounted to political parties. No need for pretend great ideological division, simply factionalising among the ins and outs, a way of identifying supporters and leaders together, and of organising patronage. Of course, games were a part of the public sphere, a time when the body politic met in the same physical space as their ruler, and could organise as a mass voice, so the association of sporting alliance with political is not as hairbrained as it might seem to us moderns.
Of course, there would be no fundamental ideological difference, but a network of patronage. Such networks would seek to encourage rewarding loyalty and discouraging defection. Luck and happenstance and a little judgement would dictate who would decide to join the ins or the outs (depending on how likely it was though you'd oust the ins and get rewards ffor being an out).
Take the issue of Blair, of course, that is about ins and outs, and especially as since Blair has held onto such a stable cabinet for so long (it only really started to turn over in the past two years, really). So all the out labour MP's see a chance of getting into ministries by defecting to Brown, or being loyal to him.
Of course, at the heart of this model is the Emporer, the supreme owner of inship and benefactor magistrate extraordinaire. This turmoil is the price and consequence of leadership - mark you wwell, fair reader, that it is all so unnecessary. Who really needs Emporers? Who needs a walk on part in a crowded mob scene?