First, let us define our terms: solo mean alone, and safer means less likely to die.
Most discussions of safety in backcountry activities are based on a naively passive and fundamentally flawed understanding of how accidents happen. Show me 10, or 20, backcountry accidents and 9, or 19, times I’ll show you situations where bad or casual decisions got the whole mess started. Backcountry is by definition a bad place to get hurt, and while there are any number of hypothetical injuries which might only delay ones schedule, even something like a sprained ankle makes the likelihood of further problems greater.
Safety discussions must therefore focus almost exclusively on prevention. To stereotype, less experienced backcountry travelers spend their time researching and buying an 80 dollar pre-packaged first aid kit. More experienced travelers practice being outside so they’ll have the physical and mental abilities to not need first aid. A simple example would be tailoring macro and mezzo route choices to your abilities. A micro example would be not panicking and recovering when you loose your feet on a stream crossing, and knowing how to fall so that the inevitable slip doesn’t result in a stick impaled in your leg. The particulars of this difference are almost unquantifiable, so let us look at some examples.
Griz country: There are no statistics which I’ve seen that suggest hiking with two, or even three, people is safer than hiking solo. Hiking with four or more does seem to be statistically safer. My interpretation of this is that only with four people is the visual and aural footprint of the group so big that situational awareness can be discarded. Solo or with a partner the need to evaluate the situation before and while on the trail is the same; look for sign, determine if you’re in problematic terrain, and if you get too close to a bear act deliberately. Most people would be safer solo because they’d either be more aware in the moment, or not go into high-risk areas in the first place. Indeed, it would be easy to make a case that for most people hiking in Griz country in groups of two is less safe than being alone.
Climbing: Here we must make a distinction and restrict the discussion to true backcountry conditions, which is rather different than taking whippers on a well-cleaned crag a 2 mile hike from the road. 10 miles back, the last 2 miles of which were likely nasty talus, you should think about falling a lot differently. Even if the rock is bullet and your gear good, the consequences of breaking a hold while running out easy terrain are a lot bigger. In other words, your style should be a lot closer to that of a free soloist. This is even more the case when ice or alpine climbing. The rope team and the gear you place is more of a psychological aid than a physical one, as it serves mostly to let you climb comfortably and closer to your abilities on terrain you could theoretically solo 99 times in 100. In this respect a partner is safer. A partner is not safer insofar as being tied in might encourage you to treat the outing like a cragging session and pick a route too close to your limits.
Avalanche terrain: The more I learn about backcountry skiing safety the more I wonder if we think about it all wrong. On many occasions I’ve skied things while wearing a beacon and having partners nearby when I wouldn’t even have been in the same neighborhood without them. Given the many ways avalanches kill and main folks which beacons do nothing to prevent, I wonder how much validity this safety gear has, and if we should all be skiing things as if we were alone, with technology as a mere bonus. The most potent consideration here is of course the extent to which social factors influence decision making and put people in places they wouldn’t otherwise go. For full discussion see this. In my mind the jury is very much out of whether partners make most skiers safer most of the time.
Whitewater: Another ambiguous situation. In theory partners will help you scout things more efficiently, collect your gear if you swim, and haul you out of a strainer if you swim in a bad spot. The first can certainly be true, but is a convenience only, as is the second. You shouldn’t drop your paddle anyway, though eventually you will. The third case is desperate at best, and one no one should ever be in. As I’m to chicken to be much of a whitewater person, I’ll defer to Doug Ammons, the first person to run the Stikine solo: “The Stikine condenses the sport’s full range of experiences and challenges into a single day. It’s a gut-wrenching, threatening place — you have to have the mindset that you want to be in there alone. It’s is every bit the equivalent of soloing a major Himalayan peak.” Read the linked-to interview and decide for yourself.
Mountain biking: Does having someone to ride out and fetch a helicopter to evac you with your broker back make you safer? If it does that’s a kind of safety I can do without. Ride conservative when help is more than a cell phone call and 30 minute wait away. If you don’t having a friend to pull spinal traction will be little comfort.
In summary, there are many cases in the backcountry when being with a partner or group makes you safer. However, they are far fewer than most people think, and when other people do lend added safety it is often for reasons different than those usually considered. Most backcountry travelers have a disturbingly passive understanding of their own safety, and would benefit from a more rigorous consideration of short and long range safety factors.