The Probability Broach by L. Neil Smith (American, 1981)

Summary:
Edward Win Bear is a Lieutenant that arrives at a crime scene where a man called Meiss had been shot down. He finds his ID and a weird coin in his pocket. Meiss was part of the Colorado Propertarian Party. Win went to the Propertarian’s place and interrogated Jenny, who had no idea Meiss had died. She told Win that he used to carry a gun provided by the government but didn’t like it because Propertarians didn’t like to get anything from or give anything to the government. They believed that all human rights were property rights, beginning with absolute ownership of your own life. Later he met his boss Roger Macdonald, who told him he would have to be off the case and that he could not know the reason. The next day a car killed Mac, and Win didn’t say anything about being off the case, so he continued investigating. Win got attacked at his apartment, everything was filled with traps. He went to Meiss’s work. He met Bealls, who told him more about Meiss and took him to his lab. Suddenly, there was an attack and an explosion. Win woke up in a strange place. He thought he might have traveled in time. He got to a booth that told him that there were no records of Denver. Then he found out that there was a man that was called exactly the same and was a detective too. There was another attack and he got severely injured. When he woke up, he talked to his healer Clarissa who told him more about where he was, and then he talked with Ed about the differences in each world’s history. In this world, science was more advanced, there was no government, and everybody was free to live their own lives. They could even talk to simians. Win met Lucy and then he discovered she was 135 years old. With Ed’s help, he finds out that Meiss was killed by the SecPol that wanted to take control of the NAC. They had to fight against the Hamiltonian people. Clarissa and Ed got kidnapped, but Win and Lucy rescued them. Win defeated the Hamiltonians with an explosion. In the end, he marries Lucy, and Win realizes that societies can still change.

Another summary:
The story begins with the homicide of physicist Vaughn Meiss, who was also a member of an anarchist party, the Colorado Propertarian Party. The investigation of this case is being led by Lieutenant Edward William "Win" Bear from the Denver Police Department. Winnie is looking for evidence at Meiss' laboratory when he suddenly gets attacked by an intruder. Win, of course, puts on a fight. After an explosion, Win gets unconscious. Soon, Win wakes up. He thinks he has amnesia and tries to ask for help, but he discovers that he is in another dimension, and Denver does not exist. He suspects that Meiss knew about this dimension. Win is now in the North American Confederacy, specifically in Laporte. Since Win is injured, he gets helped by Clarissa, Lucy, and Ed Bear, who turns out to be Winnie's counterpart. They take Win to Ed's place and there he gets attacked again. So, they decide to investigate, and Win learns a lot about this world. He finds out that at some point, history diverged, and this dimension ended up being a Confederacy.

Another summary:
The story begins in an alternate, ecofascist version of Denver in 1984 with Homicide Lieutenant Edward W. Bear (also know as Win) investigating a series of mysterious murders, which include a member of the local chapter of the Propertarian Party and Win’s own boss at the Denver Police Department. After following a lead, Win finds himself investigating the university lab where the propertarian worked, but is ambushed and ends up being propelled into a Libertarian (Gallatinian) alternate universe, where he is also being hunted down. Here he meets his alternate version (also called Ed), a medic called Clarissa, a 136-years-old war veteran called Lucy, and an intelligent simian captain called Forsyth. Together with his new companions, he discovers the Hamiltonian’s (a pro-government faction) plot to turn this anarcho-capitalist world into one more akin to their ideas by means of bringing nuclear weapons over from Win’s world. Win and his friends fight against the Hamiltonians lead by J. J. Madison, and after a series of confrontations, kidnappings, and a convoluted “Congress” session, they finally succeed in foiling the faction’s plans. In the end, Win decides to stay in his newfound home and help prepare an intervention to try and change his original world for the better. 

World view: Describes in a variety of aspects and with some consistency an imaginary state or society which is regarded as better, in some respects at least, than the one in which its author lives.
Future projections: Presents a future-historical goal to be achieved by the efforts of human beings.
Ideology:  It’s either the polarization of an ideology or an absurdist exaggeration of unfortunate or odd circumstances
Characters, plot and writing style: The story features a rebellion against the adverse circumstances (revolutionaries may exploit newer technologies for these ends).
Classification: Dystopia