The Demarchists (pejoratively referred to by outsiders as zombies) were a faction of humanity who had a political system of democratic anarchy, or "Demarchy". The Demarchy functioned by means of a neural implant that constantly sought the user's opinion on aspects of Demarchist life. This constant prompting eventually faded away into the user's neural background, much like the ticking of a clock might fade away into background noise. The Yellowstone Demarchy, which was the main Demarchy in human space for nearly two centuries, used such a technique.
The voting process was run by "Polling Cores" in Demarchist cities and space stations. Each core was tasked with collecting and processing votes, and also determining whether or not the elected decision was the best one in previous elections -- voters who continually made "good" decisions were rewarded by having their vote count for more than one standard vote. Other known Demarchies included the Haven and Europan Demarchies -- the latter appears to have risen and fallen multiple times -- as well as Fand, Grand Teton and many other colonies in human-occupied space.
Until the time of the Melding Plague there were several powerful families within the Yellowstone Demarchy, one of the most influential being House Sylveste, which controlled Sylveste Institute for Shrouder Studies; it also controlled the Sylveste Institute for Artificial Mentation before it was destroyed by Panoply during The Clockmaker incident. It later organized the archaeological expedition to Resurgam to research ancient Amarantin society. They were immensely wealthy, being the closest thing to royalty in the Yellowstone system. Notable members of House Sylveste include Dan Sylveste, who led the Resurgam expedition, and Calvin Sylveste, who was known for the Eighty.
The pre-plague Demarchists -- particularly the Yellowstone Demarchy -- used to have expertise in nanotechnology, life-extension, and biological alterations, among other things. They also utilised a sophisticated information network known as abstraction. Abstraction was used to simulate environments and co-ordinate servitors and other robots. The height of Demarchist society, the Belle Époque, was only brought low by the Melding Plague, which pushed Chasm City, the main city of the Yellowstone Demarchy, into a dark age lasting forty years.
Later, after the Conjoiners stepped in to help revive Chasm City, the Demarchists, unhappy with their new role as second fiddle, declared war on the Conjoiners; a war which first went well as the Conjoiners, thanks to their hive-mind nature, became predictable on the battlefield. The return of the war-hero Nevil Clavain ended that, and by 2615 only the most partisan of Demarchists would even deny an eventual Conjoiner victory.
In any case, human civilisation around Yellowstone was eventually destroyed by the Inhibitors in 2698.
Demarchist weaponry consists of, among other things, antimatter munitions (or "pinhead" bombs, called such for the tiny amount of antimatter necessary), and massive rail guns that accelerate foam-phase metallic hydrogen to a massive speed using a series of timed detonations along a barrel. They also utilised various ionisation-particle weapons and compact "fold-out" beam weapons.
In the afterword of Galactic North, Alastair Reynolds comments that the Demarchists are not his own invention. He credits the Joan D. Vinge book The Outcasts of Heaven Belt as the inspiration for the Demarchist Society.