Let me break this down a little.
First, the RP being influenced by the majority only works in an ideal world. This is not that. You're new to holding an RP and I can see that because of that line of thinking. It's democratic, so it must work... Right? Wrong. You're the GM, by virtue of the existence of a single GM that has incredible influence over the RP, every RP with one central GM like this is a dictatorship. And nothing major happens without your say-so.
There's also the structural flaws. Unlike a country, people can come and go as they please with little to hold them down or in anywhere, and sometimes when people go, they go for good. They'll have no reason to stay if they're the 'minority', because they're not being satisfied.
Next, you seem to misunderstand how character development and establishment works.
If you pay close attention to movies, games, and shows, you'll realize that character development and establishment doesn't happen with one actor on an empty stage. They need something to interact with, which has been achieved somewhat with player interaction... Which is also a problem, I'll get to why in a moment. But going back to one actor on an empty stage, for character development and establishment to truly happen, you require events for them to react to, crisis, complications, you name it. How they deal with that, is what develops or establishes a character, depending on the event and the character. The only character in this RP not experience this problem of 'one actor empty stage' is yours, because yours is the only one who is majorly affected by the revelation as an heir to a mafia regime.
You will need to think harder about the social ties of other players in your RP. It may not seem major at all, everyone's friends in the OOC right? Except the problem is... In IC, their characters aren't. Trust me, when you do start to make little lines connecting characters whether you write it out or it's recorded in your head, you'll begin to realize who is on the outside of the player inner circle. The people who are outside that social circle are the ones most likely to leave early, simply because there are less people who are significant to their character.
Next, is player interaction. In society, how easy is it for you to actually walk up to someone and try and make friends with them out of absolutely nowhere? Now see what I'm getting at?
The only relationship some of the player's characters have so far with other characters is because they were all at the shrine and are now involved with the Vongola somehow. That's all. Most of us don't have any real opinion of one another. We just all happen to be gathered under this one banner for god knows what. We need more events to tie us all together.
We also wrote ourselves into that situation believing it was time to move on. I remember distinctly you said we were finally getting 'to the meaty bits', so I had figured it was time to get moving onto that. Except now we're taking a day to do pretty much nothing, you never said anything about it in the IC as a note, and I saw no mention of it in OOC (if there was, apologies, but even then there's nothing to do).
You're new and that shows, but that reason alone shouldn't stop you from trying harder than what you're doing now.
Basically for around half a week we've agreed that we should move on, and there hasn't been a post getting to actually moving on, so... Move on. Let's get to the fun part like you said we would almost a month ago.