The Solar Lottery, said feudalism is characterized not by dueling aristocrats but by the re-institution of serfs. As our own post-millennial economy continues to collapse and so many millions have been out of work for so long, those of us with jobs are terrified of losing them, however crappy they are, and so cling to them fearfully, and those of us without them grow ever more desperate, we're just steps away from the masses swearing oaths of personal fealty to big shots who promise magnanimously to protect them. I'm pretty sure the Koch Brothers and Donald Trump already have scribbler serfs drafting oaths for the masses, yo.
But the feudalism is just part of what's going on in this one; the socio-economic system of the human-colonized Solar system has devolved into a sort of government by game show/lottery, in which everyone who has managed to hold onto his "power card" has a chance every irregular interval of becoming the Quizmaster and the effective ruler of all nine planets (yes, that's counting Pluto; this book is from the late 1950s).
So of course as our story starts a new Quizmaster is chosen, but he might be a ringer: he's the head of a crackpot society who not only believe that there is a tenth planet out there but that they should colonize it, following their prophet out there. So nobody's happy that absolute power has fallen to him, least of all the former Quizmaster. But the moment has been prepared for: to keep truly unworthy rulers from ruining everything, a Challenge system exists whereby one assassin at a time is specially chosen to try to kill the new Quizmaster -- if the assassin can get past the corps of telepaths and other bodyguard types protecting the new Quizmaster that is.
But just as the new Quizmaster has a strange new agenda, the old one has been working against the day with the bottle spun around to replacing him. His plan is a doozy. Only a disgruntled newb in the ranks could foul things up. But of course there is one. Of course there is.
Meanwhile, an expedition launched to find and settle the tenth planet, Flame Disc, encounters weirdness as its crew tries to escape the insanity of the Solar Lottery. I would have like to have seen more of this subplot, which almost threatened to become a first contact story (and I would so love to see what PKD would do with that hoary old sci-fi chestnut!), but it was underserved, PKD more interested in the assassination and conflicting oaths going on back on good old Mother Earth. The result is still a good read, but not his best. Which is as it should be.