I have created a graphic here that explains the relationship between traffic tickets and accidents at red light camera intersections for Chicago. The explanation of the graphic is as follows:
If the purpose of red light cameras is to ticket risky behavior that leads to accidents, then you would expect intersections that give out lots of tickets to have lots of accidents. After all, more people are breaking the law, so you would expect that as law breaking increases, so would accidents.
A scatter plot is often used to investigate relationships between two variables. In the first figure (the inset left box), you can see a scatter plot of the number of tickets versus accidents. Its quite clear there is no relationship between tickets and accidents. Whether an intersection gives out lots of tickets or few tickets has no relationship to the number of accidents.
You can see the relationship in second figure between tickets and accidents for red light camera intersections in Chicago. The data is sorted by the number of tickets given at an intersection. Please click on the links to see the full graphic on Tableau's website. This makes it clear that there is no obvious relationship between tickets and accidents. The third figure provides the same data in a map view.
The caveats here are that we are measuring whether the overall number of tickets affects accidents. I only have the aggregated ticket data for four years for these intersections, so I can't analyze trends in the ticket data. A more nuanced study could look at tickets and accidents over time to see if there was a relationship. This analysis also does not address whether the presence of a red light camera drops accident rates, that issue is addressed elsewhere.
Data: Accident data from IDOT for 2009-2012, Aggregated ticket data between 2009-2012. A few of the red light cameras were actually put into place in 2009 and 2010. For these, there would be a short time period where accidents occurred but no tickets could be given out. Accident counts were determined by looking at total accidents that occurred within a 100 feet of the red light camera.
Credits: Rajiv Shah & Aaron Moore (GIS work) & Barnet Fagel (for acquiring the ticket data from the city)