>>1312957There's no conclusive scientific evidence of currently available bicycle helmets reducing the chance of serious head injuries or death.
They protect from perpendicular impact, make non-perpendicular impacts worse, lead to less risk-aversion by cyclists and smaller passing distance by cars. Nobody knows really which effect is stronger, as it depends on too many factors.
Basically, they probably don't make you less safe, may make you more safe, may be useless.
What all studies agree on is that mandating them reduces safety cause the most important factor contributing for cyclist's safety is more cyclists on the road (which makes drivers more accustomed to them) and mandating helmets drastically reduces the number of trips taken by bicycle.