I'm working on a high-fantasy alternate world setting, I explained it a bit here. But think of a deconstruction of tolkienesque fantasy. It's a society populated by humanoids, some based in traditional fantasy (elves, dwarf, and dragonkin), and most of the others created by me. There used to be free access to magic, but after a magical industrial revolution, the dangers of large scale magic within cities became apparent. Magic is now restricted to specific workplaces, armed forces (like the bounty hunter's guild), and very low scale magic (think of lighting a candle with your fingers, but never of throwing a fireball). Free use occurs outside of cities (because it's no man's land).
The setting used to be peaceful; everyone did their job and worked towards their communities. There was crime back then, but mostly on personal scale and nothing very serious (think of someone borrowing an axe but not returning it, or passion caused violence). However, there has been a growing amount of crimes, greed, violence and individualism, both in seriousness and in graveness. This sudden rise in the crimes started during the magical revolution, because settlements grew from a few families to more populated towns and eventually self sustained cities. (Assume this happened over the course of hundreds of years, and thus people didn't really noticed it until it was to obvious).
As the cities grew, so did the complexity of their politics. Normal folk were forced to take arms and there were a few wars, but after the first real bloodshed, most societies signed a truce and cut ties unless it was really necessary. This peace also carried consequences, as most of commercial trade between cities was cut, some needs stopped being fulfilled like before (the elves suddenly had a quality drop in their metalwork and the dwarfs were struggling with agriculture and nature related magic, for a simple example). Most of the upper classes in cities were fine, but the poorer folk were not and thus organised crime was born.
Now, here is the issue. All this cities were traditionally monarchies, with very few of them having any real army or some other armed forces besides the king's guards, and the crime rates were rampant. I'm going to reduce the issue for the particular city where the plot starts, we shall call it "City A" because I suck at naming things.
In our City A, the king was faced with violence, an ever growing criminal underworld, people committing crimes out of desperation and others out of pure spite, and his personal guard, while impressive, wasn't able to do much to help. He considers: "Maybe there is a way to get normal folk to take arms again, but this time to protect the city". At first he tried to inspire normal folk through moral and ethical arguments, but it became obvious that only money was enough motivation for anyone to risk his life. Thus, The Bounty Hunter's Guild was founded, with the King as the one offering the rewards.
How would work the legal system for City A, specifically in the criminal aspect? I'm not interested in particular laws (as they come from the morals set by each religion and particular god). Just how does a society with bounty hunters as their principal enforcers handle criminals?
Take into account that city a has the laws close to ours, there exists a magical bureau in charge of magical control and magic misuse. After someone commits a magical crime, this magic bureau investigates and informs the bounty hunter's guild. The king has the resources enough to set several investigation teams, including access to powerful telepaths (but there also exist countermeasures for this). Their magic and technology will mostly be equal or greater than the mafia's. Their principal flaw comes in the lack of organization and experience in fighting crime. I'm asking about their legal system would be different from ours. Would such system work? What are the principal flaws? How would the king control the bounty hunters? Eventually I planned for the bounty hunters become the principal political force, while having the king as their money and resource provider, but ultimately controlling him and his politics due his lack of other armed force. Is this viable or would the criminal underground tear them down before they reach that point?