Andrew at Statistical Modeling, Causal Inference, and Social Science explains the best way to avoid getting hit by a car while riding a bicycle:
Cyclists who wear helmets are more likely to be knocked off their bicycles than those who do not, according to research. Motorists give helmeted cyclists less leeway than bare-headed riders because they assume that they are more proficient. They give a wider berth to those they think do not look like “proper” cyclists, including women, than to kitted-out “lycra-clad warriors”.
Ian Walker, a traffic psychologist, was hit by a bus and a truck while recording 2,500 overtaking manoeuvres. On both occasions he was wearing a helmet.
During his research he measured the exact distance of passing traffic using a computer and sensor fitted to his bicycle. Half the time Dr Walker, of the University of Bath, was bare-headed. For the other half he wore a helmet and has the bruises to prove it.
He even wore a wig on some of his trips to see if drivers gave him more room if they thought he was a woman. They did.
He was unsure whether the protection of a helmet justified the higher risk of having a collision. “We know helmets are useful in low-speed falls, and so are definitely good for children.”
On average, drivers steered an extra 3.3 in away from those without helmets to those wearing the safety hats. Motorists were twice as likely to pass “very close” to the cyclist if he was wearing a helmet.
...I was aware of the "risk compensation" idea, that helmeted riders will ride less safely, thus increasing the risk of accident (although the accident itself may be less likely to cause serious injury), as has been claimed with seat belts, antilock brakes, and airbags for cars. (If it were up to me, I would make car bumpers illegal, since they certainly seem to introduce a "moral hazard" or incentive to drive less carefully.)
But I hadn't thought of the idea that the helmet could be providing a signal to the driver. From the article, it appears that the optimal solution might be a helmet, covered by a wig...
Also amusing, of course, is that his name is Walker.
If you wear a helmet, I don't think you should change your behavior based on this research, including the part about the wig, but that's up to you.