Category: <span>speeding</span>

A problem of photo enforcement is that it encourages optimization of efficiency of collecting fines as opposed to justice. In my experience, these systems have almost invariably led to a culture of enforcement and prosecution based on the bottom line, with protecting the innocent becoming only an afterthought.


Supporters of these systems contend that cameras are cheaper and more efficient than employing officers to do the same job. They figure that a wizard in a box will never be wrong and we can somehow achieve 100% enforcement, with no collateral victims. With this mindset, it follows that any person who contests a ticket is simply a wrongdoer looking for a loophole to escape responsibility. If such a wrongdoer wants to fight his ticket, the logic goes, the odds should be stacked against him. All of that innocent until proven guilty stuff the founding fathers worried about is no longer important when we have a wizard in a box with perfect accuracy. Further, it costs money to run the courts, so if a wrongdoer wants to present his case in court, it seems only fair that he should shoulder the cost to contest.

The problem: there is no wizard. The systems do make mistakes. I’ve personally been the recipient of two such mistaken citations. The first showed another man in another vehicle altogether. The second was issued in violation of French law and clearly shows me driving below the speed limit. Here I will describe both in terms of costs to the defendant.

Citation #1: Scottsdale, Arizona

The first ticket was dismissed eventually, but not before a couple weeks of shenanigans. First, I wasted a couple hours of my vacation talking to the judge and then meeting with the prosecutor. The prosecutor agreed to a dismissal, but also accused me of wasting her time. Unfortunately her office made a mistake on the paperwork so I received a letter the following week from the court informing me of my new court date. I called the prosecutor and eventually this was all fixed, but not without significant stress and time on my part at a time when I was already in the midst of a big move from Ohio to Iowa. Because of all the legal maneuvering, I ended up with 20-something entries on my criminal background check, which will now be visible to potential employers, etc., even though I was not at all involved in the alleged offense (and the prosecutor’s office agrees). I understand that the records are generated automatically when dealing with a court, but I figured I should have some ability to get them expunged given that this was all because of a simple mistake. However, the court in Scottsdale has a policy not to expunge these tickets (I really don’t get the rationale here). So in the end, the City of Scottsdale is libeling me in perpetuity, for objecting to being charged with a crime I did not commit and for which they had zero evidence.

But the city of Scottsdale’s libel didn’t start there. It turns out that some companies have longstanding freedom of information act requests for all photo citations. For this reason, when I found the ticket in my pile of mail, it was surrounded by advertisements for how to beat my ticket. I generally support freedom of information. In fact, I successfully fought the Ames Police Department when they violated such laws. But, this seems like a situation where my personal information should have been redacted. More importantly, while the correct approach to government transparency is beyond the scope of this post, this shows that false citations have a very real impact on defendants’ privacy.

Citation #2: Écully, France

I was found guilty of the second violation, which (allegedly) occurred in France, though hopefully you will read my story because my innocence is really quite apparent. The question of guilt or innocence isn’t really what’s important here. Just note that I had a strong case. This wasn’t some minor point I was arguing. I deserved a proper day in court because I had what many people would agree were reasonable concerns about the accuracy of the ticket. To get this day in court, I had to do the following:

  • Pay an additional EUR 53.24 over the base EUR 45.00 fine (total spent = 218% of the base fine). This could have been much, much more. The judge has the ability to increase the fine to approximately eight-fold, but in practice it seems to be a minimum of double the initial fine. If the judge finds your argument unreasonable, you’ll likely get the high end.
  • Wait 1.5 years for resolution.
  • Write at least five letters (in French) to the authorities. Some went unanswered, including requests for technical details of the radar device that took the photo.

In the following sections, I’ll describe the decision to contest a French ticket in terms of decision theory. I did take a graduate course devoted to this topic, but actually I always found it to be really intuitive. Here is a comprehensive graphic, to be described in the following sections.

decision tree - contest a ticket

Alternative #1: Admit guilt and pay immediately

The first possibility, upon receiving a photo ticket, is to simply pay up. In France, for infractions on roads with a speed limit greater than 50 km/h and with a ticketed speed of less than 20 km/h over that limit, the fine is EUR 45, if paid within 15 days. Bear in mind that this 15-day clock is already started by time you receive the ticket. France does not include photos with the original citation. I suspect this is for two reasons:

  • Many people will just assume they broke the law and not consider contesting, but the photo might change their mind.
  • Because the French government is incompetent slower than molasses, it is unlikely that a defendant will receive the original ticket by post and also have time to request and receive the photos by post before the 15-day early payment deadline has passed. Of course it’s not smart to make the decision to contest until you examine the evidence, so this presents a dilemma.

The expected value of choosing this alternative is easy to calculate. There is a 100% chance that you will pay EUR 45.

Alternative #2a: Contest, but only in writing

Granted the decision to proceed to court needn’t be made until a verdict is reached on the written appeal. However, as no new information would generally be available at this later date, there is no value in delaying the decision, meaning that the process can be simplified by assuming you make this decision up front.

The expected value of this alternative can be calculated by multiplying the probability of each outcome by the respective amount paid. Because we do not know the probability of succeeding in court, we cannot solve this in absolute terms. But, we can solve for the success probability above which a rational person will contest. The math shows that a rational person should be willing to contest in writing only if there is greater than a 54% chance of success.

From looking around the internet and from my knowledge of other jurisdictions, I think 54% is very optimistic for a written appeal. It seems that these guys reject almost everything, likely to force defendants to wait another year and proceed to court. Note that I’m not necessarily claiming that the individuals who read the appeals are crooks. In fact, I believe the system is set up by crooks, so that the decision-makers’ options are fairly limited. Also, don’t forget all the normal stuff about how the average person has irrational faith in the wizard who resides in the camera. These people have no real training or incentive to believe you, much less find you innocent.

Alternative #2b: Contest, with willingness to proceed all the way to court

The computation for this final alternative (in fact, there is technically an additional level of appeal, that I won’t cover here) is more involved because the tree has two levels. The best we can do is make the crazy assumption that probability of success on the written appeal equals that in the courtroom. In this case, the math shows that the probability of success must be greater than 32% at each stage for this to be a rational choice (given a willingness/ability to wait 1.5 years).

In reality, the chance of success in the courtroom is likely greater than in writing (and the probabilities are not independent for a given case), but I doubt very much that the win probability in either phase is as high as 32%. Not only can we see my data point, in which I lost even though the camera’s certification was clearly violated, but other anecdotal evidence leads me to believe the chances of success are extremely low in most places in the world (again, irrational belief in wizards, and all that).

The realistic state of freedom in such a system

Of course the calculations above were quite contrived. There is no way to know what your chances are before contesting a ticket using a given argument. This exercise was simply intended to demonstrate the problems with a pay-for-liberté court system.

We can see how they ratchet up the cost at each phase in order to tilt the scales. Given that succeeding in such a trial is extremely rare, unless you actually have a photo of a different car committing the crime, the rational choice is always to just admit guilt and pay. The system is unscrupulous by design, so you would only contest due to strong principles and free cash flow, not because you expect to be vindicated. Poor people don’t really have the liberty of contesting a traffic ticket. I suppose they at least get a free lawyer in extreme circumstances, which undoubtedly helps their chances, but if you barely have enough money to eat would you really want to risk paying twice the original fine?

A fair justice system is only possible if the financial burden is placed on all residents. Deterrents, in the form of financial or other burdens, should be eliminated to the extent possible. Additionally, funding the courts on the backs of losers is a clear conflict of interest. Remember, no safety is gained by collecting fines from innocent drivers.

As a final note, yes I am happy with my choice to fight. The system did lose money on me, which is usually the most you can ask for in modern court systems. I would generally encourage readers to make the same choice.

Arizona court France photocop speeding

I received a photo ticket in France back in 2013. Because the French system is incompetent engineered to deter innocent drivers from contesting tickets, it took more than 1.5 years to finally get my verdict. Of course I was found guilty, which is the typical result when fighting a traffic ticket. (Remember the time Deputy Melchi didn’t know the speed limit?) But in France, they have taken it to new levels of arrogance and disdain for motorists.

In short, the French government is violating their own rules for the usage of their radar units. This is causing innocent people to be ticketed, and the judicial system in France is a farce in its slowness and unwillingness to consider the idea that the prosecution might be presenting bullshit evidence.

It all comes down to what’s known as the cosine effect. Explained for laymen, an object appears to be moving faster when it moves away from a radar gun as opposed to moving across the radar beam. If an object is traveling perpendicular to the radar unit, the speed measured will always be 0 km/h. This corresponds to cos(90) = 0, which is multiplied by the actual speed to give us the measured speed. Likewise, cos(0) = 1, which explains the case that the vehicle is traveling perfectly along the radar’s line-of-sight. If you Google “cosine effect speeding ticket,” or something to that effect, you’ll find that 95% of the results state that cosine effect always favors the motorist. But not so fast!

This advice was true in the good old days when a cop manually clocked speeders and issued tickets. If a police car is parked alongside the road (or driving in the oncoming lane), the radar beam is not perfectly aligned with the car’s trajectory. In fact, to align the beam in this way would require the cop to be in the vehicle’s path, which is not really possible. This offset amounts to maybe a couple percent error in favor of the driver. Because every situation is different, there just isn’t a way to automatically correct for this. Therefore traditional speeding tickets can sometimes be a bit low. This generally has a trivial effect because the angle is very slight.

However, photo radar units are often fixed (in concrete) with respect to traffic. Even mobile units require sufficient setup such that we can consider them to be fixed as well for our purposes here. When choosing the device placement, it makes sense to use a rather steep angle to traffic, in order to clock and photograph only a single vehicle. This will lead to a severe cosine effect. If I’m a software engineer (as I sometimes am, in fact) developing a new photo radar system, I know this angle between the radar beam and traffic. This means that I can hard-code a correction percentage. This way even though my raw measurements will be low, the number printed on the ticket will be correct. And this is precisely what has been done. The certificate for the Mesta 210C (French), a very common photo radar device in France, specifically states on page 2 that the unit must be positioned such that the radar beam is at a 25-degree angle to the trajectory of traffic. This is a suitable assumption for most tickets, but there are two exceptions:

  1. Apparently there is a common problem with mobile devices being incorrectly set up by the police. This is likely accidental in most cases, as the average cop probably doesn’t know the trigonometry well enough to understand the effect of an error or if that error will favor the government or the driver. Additionally, the police officer probably doesn’t have much personal incentive to bias the readings.
  2. If a car is changing lanes toward the camera, the angle will be greater than 25 degrees (as pictured below) and thus the recorded speed will be low (in favor of the driver). If a car is changing lanes away from the camera, the angle will be less than 25 degrees and thus the recorded speed will be high (in favor of the government). Note the cynicism required to assume that something that is anti-people is pro-government.
Radar angle diagram

Normally any error due to cosine effect will be relatively slight. But in my case, cosine effect alone is sufficient to prove that my ticket was issued in error. Additionally, the Mesta 210C must have other factors leading to additional error at incorrect angles, as shown in the table at the bottom of page 2 in this study conducted by the government in Metz (French). Note that the error in recorded speed is quite severe for even a one- or two-degree error in radar placement.

In my case, we can do the following calculations to find the error purely due to cosine effect. First we can calculate the angle of the vehicle to the camera line-of-sight. The best way to do this is using a wheel. We can always be certain that wheels have the same circular shape. The distortion of this shape tells us the angle with respect to the camera. The following image shows a rough calculation, using the inverse sine of the width-to-height ratio.

Calculation of actual vehicle angle

The top photograph is from another certification document. Disregard the direction of travel, as the system works the same either way. We can assume that this photo is correct, but note that my calculations show 26 degrees. This is probably because using a pixel ruler to measure a wheel is not extremely precise. My calculations could easily be off by a degree. The bottom photograph is from my citation. My calculations indicate that the car is traveling at a 15-degree angle relative to the camera’s line-of-sight. This difference is so large we can see it with the naked eye. It could also be off by a degree or so in either direction, but it is very safe to say that this angle is nowhere near the 25 degrees mandated by law. Additionally, to change lanes at a 10-degree angle, as depicted in this photo, is very unlikely given the realities of vehicle dynamics.

So now that I’ve shown the angle to be incorrect, we know that the camera was used in violation of French law and that the ticket never should have been issued. However, for completeness, we can calculate the actual error due to the cosine effect. In an optimal situation, the camera is at a 25-degree angle, so if a vehicle is traveling at 90 km/h then the measured speed will be 90 × cos(25) ≈ 82 km/h. The system can correct for this by dividing the measured speed by cos(25) to get the actual speed. In my case, assume that the vehicle was only traveling at a 15-degree angle to the camera. If my car had been traveling 90 km/h then the measured speed would be 90 × cos(15) ≈ 87 km/h. The system doesn’t know the angle though, so it still divides its measurement by cos(25), which produces a result of approximately 96 km/h. Note that this is the minimum error, because the Metz report indicates that this model is susceptible to greater error. It is likely that my car was traveling far below the speed limit when it was clocked.

France is writing tickets and prosecuting for this! This guy had a similar problem, though he is French so he managed to win his case in court (though they still didn’t give his money back). My reading of the relevant documents leads me to believe that it is actually a punishable crime to use a radar device in a manner not conforming to the certification. If a criminal element exists in prosecutors’ offices or among speed camera operators, we should demand charges. If we did so, it would only be fair if we stripped them of all of their due process rights, eliminated the presumption of innocence, and charged them a fine up front before giving them a court date 1.5 years in the future.

court France photocop speeding

A really basic point that I try to emphasize here is the importance of strong principles. Principles are what drive good, rational people, who understand the dangers of living with criminals in their midst, to treat each crime with consistency, ethics, and unwavering fairness to the accused.

(Note: Europeans get really upset if you refer to minor traffic violations as crimes. Their governments have convinced them that these little things are something different, and therefore get fewer protections. In the US, the legal system also commonly makes a distinction, but in the English language we commonly do not. In this post, I use the term crime to mean “some behavior that society has decided to outlaw,” because using consistent definitions is an important basis for solid principles.)

Take speeding for example. Yes, driving too fast is dangerous. Yes, this affects others so it makes sense that regulations exist. Overall, I’m fine with the idea of having motor vehicle laws including speed limits, with various caveats. However, things are not so simple. A given speed limit set by the government may or may not be appropriate given the science. People are sometimes wrongly accused of things. People are wrongly accused of murder and people are wrongly accused of speeding. These things happen, and it is the job of the judicial system (and actually the police, in the first place) to minimize the chances of dealing out punishment to an innocent party. If you get a ticket, the judicial system exists (in its origins anyway) for your benefit.

Many people say, “but the system will break down if we allow every person a fair trial.” This is an extremely common response when talking to French people about photocop tickets, and it is an extremely short-sighted view. First, note that taking money from innocent people does nothing to prevent future violations, so the very problem that the law exists to address is completely unaffected. Second, note that gutting protections for the innocent financially benefits the very group of people gutting these protections. Yes, some people that are accused actually did the crime. Some of those crimes are actually a menace to society and I think we can mostly agree that the culprit should be punished. But if the list of infractions in a jurisdiction is so long that the jurisdiction cannot employ enough people to handle the burden on the court system, then not all of those laws are really necessary. The reason an unprosecutable number of traffic tickets are written is that the current laws are catching massive swaths of the population (and many of these people have reasonable defenses). If such a large percentage of drivers is ticketed for speeding, for example, then the current speed laws and enforcement are clearly not serving the will of the people, regardless of effectiveness.

A government simply should not be able to force a citizen to part with freedom or property without providing ample evidence that a crime occurred and that the accused is, in fact, the culprit. This is what it means to have principles. Most current governments (certainly that of France or most US jurisdictions) are not principled. Some of the actors in these systems naively believe that photo-enforcement, for example, is 100% correct. That’s cute (also wildly wrong), and individuals may think they are acting in a principled manner, but the system itself is really not interested in working for the people.

court France photocop speeding