"So how come I see so many cyclists jumping red lights?" or some variant thereof is the constant background hum to any kind of discussion on cycling in the UK.
"A driver came right out and side swiped me"
"Really? Thats terrible, I saw someone jump a red light on his bike!"
"Oh? Good for you, now fuck off you unsympathetic bastard, I thought you were my friend but you bring me this shit in response to some fucking moton trying to kill me?"
Well, thats what you want to say, but you don't, because we're British and we seem to think its fine to rain hate down on us for being cyclists and because we don't want to make a scene. But why do we keep hearing this?
Lets assume for the moment that all road users are just people, lets cross off the mode of travel under their name for the moment and say people are more or less the same. It would follow that roughly the same proportion of people in each group would be likely to break a rule if they thought they could get away with it without hurting anybody. Shall we say 1 in 10?
So a driver gets to a stop line with a red light, there's a 10% likelyhood he'll go through it if he can get away with it. Or, in other words, there's a 90% chance that the driver will stop. And if caught behind the first car, the second driver in a line can't jump the red light - there is therefore a 10% chance that a driver can jump red - a probability of 0.1. Its also likely to be the case that unless they jump red as soon as the lights change from amber, they won't be able to do so because there's just nowhere a car can go across a busy junction, so unless the car driver who will be willing to jump red is at the front of the queue and within a narrow time window (as likely as not therefore 'amber gambling' or accelerating hard as the lights change to red) its just not feasible to jump a red light in a car. It does't matter how many car drivers are there - the chance of a red light being jumped by a car driver is independent of how many drivers there are.
Lets look at cyclists now - every cyclist has the opportunity to jump a red light at every single junction. We can, if we want, usually filter to the front. So if there's one cyclist, the probability of there being a red light jumping bike rider is 0.1. If there are two the maths starts getting more fun...
Both jumping the red light would be 0.1 times 0.1 - or 1 in 100. Both not jumping red would be 0.9 times 0.9, or 0.81 (81 times out of 100 you'd see neither jumping red). So in other words you'd see at least one of them jump a red light 19 times out of 100 - and this can very easily be well after the light has changed to red because a cyclist can not only always get to the front but can jump the light at any time.
So lets say on your daily commute you go through 10 sets of lights and at each set there are 10 cars other than the one you're in. The probability of a driver jumping a red light at one of those lights is easy to calculate - and its as near as dammit 69% chance. But lets also say that because only the first car can jump red, and you can only really say with certainty a car 1 or 2 places in front of you has jumped the light (the vehicle is the same size as the car you're in after all), you'll only see a fifth of them. So 13.8% of your commutes you'll see a red light jumping driver.
Lets now assume that at the same junctions there's the same number of cyclists - that means you've a hundred cyclists with a chance of jumping red - there's a 99.99% chance of seeing a cyclist jumping a red light (in fact by the time you've passed your fourth junction there's a 99% chance there's been a cyclist jumping red).
The simple truth is that we're all just stupid monkeys, and regardless of the mode of travel you'll find people who think they can break the rules and thats all fine. That you see more cyclists than motorists break a particular rule doesn't mean that they're worse offenders - it just reflects what you're in a position to see and the opportunities they have.
Your belief that cyclists are worse than motorists for jumping red lights doesn't mean that cyclists really do break the rules more - it just means you've not done the maths.