Q. Mark and Luke both tell the story of Jesus restoring a blind man’s sight on the road outside Jericho. Matthew tells the same story, but he says that two men had their sight restored. Why is there a difference?

You’re asking about the phenomenon that gospels scholars sometimes refer to as “Matthean doubling.” This isn’t the only place where Matthew seems to turn one character into two.
First, in the story you’re asking about, there definitely seems to have been just one person involved. Mark even tells us what his name was—Bartimaeus. The details of the story are the same in all three gospels. In Mark and Luke, this man calls out, “Jesus, Son of David, have mercy on me!” The crowd tells him to be quiet, but he shouts all the louder. Jesus hears him and calls him over and asks what he wants. He asks to have his sight restored, and Jesus heals him. In Matthew’s version, two men call out, “Lord, Son of David, have mercy on us!” The crowd tells them to be quiet, but they shout louder. Jesus calls them over and asks what they want. They ask to have their sight restored, and Jesus heals them. The only difference is the two men in Matthew versus the one in Mark and Luke. All three writers specify the same setting, on the road outside Jericho, and the same time, as Jesus was heading to Jerusalem at the end of his life. So Matthew doesn’t seem to be relating a separate incident. He’s doubling a character in the same incident.
Similarly, Mark and Luke tell how Jesus healed a demon-possessed man in the area on the other side of the Sea of Galilee. They tell how no one could restrain him, how he came screaming out at Jesus and the disciples, and how the demons inside of him begged Jesus not to torture them. They asked to be sent into a nearby herd of pigs instead, and Jesus agreed. (If you’re wondering why he agreed, consider this post.) The demons left the man and went into the pigs, which all rushed down a hillside into the lake and drowned. Matthew tells exactly the same story, with all the same details, except he says that there were two men involved, not one.
A further instance occurs in the story of Palm Sunday. As Mark and Luke tell it, Jesus is approaching Jerusalem, and he sends two of his disciples to a nearby village to get a colt (a young donkey) for him to ride into the city. He tells them that if anyone challenges them, they are to say that “the Lord needs it.” They bring the colt back, throw their cloaks over its back, and Jesus rides it into Jerusalem, where he is cheered by the crowds. Matthew tells the same story, with the same details, except he says that Jesus told the disciples to get two animals, a donkey and her colt. He says that if anyone challenges them, they are to say that “the Lord needs them.” Matthew then reports that the disciples “brought the donkey and the colt and put their cloaks on them, and he sat on them.” We can at least recognize that Matthew means that Jesus sat on the cloaks, not on the two animals at once. But this is still one further instance of “doubling.”
So what’s going on here? The best explanation I’ve heard, and I find it convincing, is that two is the number of witness in Jewish culture, and Matthew is writing primarily for a Jewish audience. He is the only gospel writer who records how Jesus reinforced for his disciples the rule in the law of Moses, “Let every matter may be established by the testimony of two or three witnesses.”
These three episodes are all well-known stories that circulated widely during the generation between the time when Jesus lived and when the gospels were written down. The times and locations and even some of the names involved are all documented. So Matthew isn’t trying to fool anybody. If he were, he would make up stories that don’t appear anywhere else, so that no one could check up on him. Instead, he’s beginning with the premise that his readers will know the stories only too well, and so they will be struck by the difference in detail. They will wonder what it means, and if they read carefully, they will find the answer right in his own gospel: The testimony of two witnesses establishes a matter.
So Matthew “doubles” characters as a way of saying that these particular episodes bear witness to who Jesus is. Interestingly, in each of them, there is explicit witness to Jesus’ identity. The blind man calls out to him as the “Son of David.” The demons say, “We know who you are, the Son of God.” The crowds who greet Jesus on his way into Jerusalem call him the king who comes in the name of the Lord. So it does indeed seem to be Matthew’s purpose to portray these episodes as bearing witness to who Jesus is.
In our own time and culture, we might still think this isn’t quite proper. What right does Matthew have to change the details in a story from Jesus’ life? But if we can appreciate that he is making use of symbolism even as he otherwise tells the story of Jesus realistically, we can understand his purpose and accept his method.