Consider two simple, non-exhaustive theories.
Theory 1, Strong Materialism: The only ontological primitive is matter. This is to say that there is nothing but physical things, and everything that happens can be reduced down to the material. Minds and consciousness must then be some emergent phenomenon based on matter. For example, some people who take this view speculate that consciousness may be “what an algorithm implemented on a physical machine (like your brain) feels like from the inside.”
Theory 2, Strong Solipsism: The only ontological primitive is my own mind. This is to say that there is nothing (or at least nothing worth believing in) but mental phenomena. Someone who takes this view might say that they have no good reason to believe that their experiences have a physical antecedent, and everything that exists is just what’s going on for them mentally. People with this view might point out that perceptions of things outside themselves don’t actually indicate those things — just the perceptions themselves.
There are also dualistic theories which assert the existence of both physical and mental primitives, but I don’t want to focus on them here, and they’re not too popular among the LessWrong crowd anyway. There are a series of problems with different forms of dualism involving the prior complexity of believing in multiple ontological primitives as well some curious means by which the physical and mental interact. It's generally agreed that dualistic theories would force us to believe in more unlikely phenomena than either materialism or solipsism and aren’t comparatively plausible.
My impression is that most people who I’ve listened to or read from who have discussed these ideas (including Brian Tomasik and Eliezer Yudkowsky), seem to prefer materialism. There are two good reasons people have for this. First, even though when I perceive something, it does not with certainty imply the existence of that thing (only of that perception), it is perfectly consistent with the existence of that thing. Second, I observe many people other than myself, and their behavior and feelings seem to be a lot like my own. Given both of these observations, the likelihood in Bayes rule for materialism is relatively high, while for solipsism, it’s not.
I think that these two points are strong reasons to suspect that materialism is a good theory and may have an advantage over solipsism. But it seems to me that when many people discuss the question, they mention these two points, miss applying a crucial counterpoint, and go along discussing metaphysics as if solipsism weren’t worth much consideration. I think this is a mistake.
Anyone who supports materialism has to bite a bullet. It implies that somehow, someway consciousness and qualia are phenomena that reduce down to the activity of physical systems. From a Newtonian perspective, atoms are much like billiard balls, bouncing around together, and from a quantum perspective, they are waves/particles interacting through forces and entanglements. But using either interpretation, how puzzling is the view, that the activity of these little material things somehow is responsible for conscious qualia? This is where a lot of critical thinking has led many people to say things like “consciousness must be what an algorithm implemented on a physical machine feels like from the ‘inside.’” And this is a decent hypothesis, but not an explanatory one at all. The emergence of consciousness and qualia is just something that materialists need to accept as a spooky phenomenon. It's not a very satisfying solution to the hard problem of consciousness. This belief in some mysterious ability for the mental to supervene on the physical is almost as ad hoc as the belief that dualists have in immaterial minds!
Suppose that you update on the evidence that you experience conscious qualia and your various perceptions about the world. How do the two theories compare? Both of them assume only a single primitive, be it the material or the mental (a huge advantage of either of these theories over dualism). But conditioning on the existence of consciousness, materialism must assume the existence of a strange phenomenon whereby physical things somehow cause qualia, and solipsism doesn’t do a good job of accounting for much of the structure in observations and your perception of other people much like yourself. In this sense, materialism has a relatively low prior and solipsism has a relatively low likelihood — qualitatively, at least.
Comparing these two posteriors quantitatively is hard, but it’s not a lopsided debate like I think many people assume. There’s definitely a huge advantage that solipsism has over materialism. So I recommend taking it seriously.