The Wall Street Journal summarized some recent research on the topic regarding bicycle helmets ...
From 2009 to 2010, free bicycle helmets were issued to 1,557 volunteers in Bordeaux, France. The subjects' average age was 32 years; 58% were women. Previous helmet users were excluded.
Data was collected daily at seven locations, each equipped with two cameras programmed to detect moving objects, isolate cyclists and calculate their speed. Cyclists were photographed from above and behind.
Helmet use was recorded in 99, or 3.8%, of 2,621 movements made by 587 cyclists captured on camera.
There are some important caveats about the unobserved cyclists and whether they are meaningfully different from those observed in the data. Moreover, it can certainly be the case that volunteers are inherently different from the rest of the population. Nonetheless, while this is a simple data point, it does support the notion that pushing for greater helmet use by cyclists is not necessarily welfare improving.Cycling speed of helmeted men averaged 11.9 miles an hour compared with 10.4 miles an hour for unhelmeted men. Helmeted and unhelmeted women cycled at 10.2 and 9.9 miles an hour respectively, suggesting risk compensation is a male behavior, researchers said. That behavior disappeared when helmeted men cycled in areas where speeds were extremely fast and the objective risk of injury increased, the study found.
EDIT: The original article is gated and such that details of the experiment are fuzzy. I can interpret the passage above a few ways that (subjectively) make the selection effects more or less relevant.