If using winter tires and driving at the same careful speed as using all season tires...then yes there would be less accidents. There would be more margin of safety. That does not happen though does it...users just drive up to a higher comfort level speed and the larger margin is gone and the same number of accidents occur albeit at a higher speed and possibly worse injuries. It would be interesting to see some propper stats on before and after mandating in Quebec. 10% are involved in 38% is not very meaningful. How many of the 10% actually caused anything. Since 90% have winter tires then it is highly likely that accidents involving two cars or more, in the 38%, would include other cars with winter tires who's drivers may have been at fault. We don't know...but it may be the case that the 90% of winter tired cars were involved in 100% of the accidents involving two or more cars.
This is not to say that winter tires do not have merrit when considering better grip and traction...if you need it where you live. At the expense of the well being of the planet.
You are making an assumption here that all drivers behave in a way as to cause accidents. One can't simply assume that people will drive like idiots across the board. Sure there are quite a few who do, although recent highway drives have shown to me that their number might be dropping.
The rest of your post doesn't make any sense. Of course winter tire shod vehicles are involved in accidents in Quebec, including those that involve the all-season users. The point of those stats is that all-season tire users are involved in a number of accidents that is disproportionate with their percentage of the total driving population. Part of your argument seems to stem from the assumption that most of that 38% are somehow blameless victims rather than active participants in the accident. If that is what you are claiming then I would rethink your statement. Are you implying that winter tire drivers are somehow ganging up on their all-season brethren?

As an experiment, let us assume that the level of idiocy and bad luck will be the same in both the winter tire group
AND the all-season group. (Although I would question even this because the voluntary use of winter tires automatically indicates a smarter person from the get-go but I digress). Then the accident rates of the winter tire group could be no worse than the all-season group and possibly better simply because of the extra grip afforded by winter tires. Right away it can be seen that the numbers should show 90% involvement by the winter tire group and 10% by the all-season group. Since this outcome is
NOT the case and in fact the all-season group are involved at a rate almost 4 times their population, we are led to the conclusion that there is something about all-seasons which are inherently less safe in winter conditions.
Ovr, Johngenx, care to throw your opinions in here? I can't explain the above situation any better, nor am I completely sure exactly what Rupert is trying to say or imply.
As a final note, consider the recent experience of our own wing, aka James Bergeron, when he had a tester with all-seasons. He remarked that the difference was startling. Wing, care to comment?