We are a party of 5 (not including our DM) and we have been playing a campaign for about 2 months. The DM has mentioned the idea of adding some new players (potentially 3). He mentioned that he knew some mutual friends that wanted to start so he just brought it up in group text without asking.

I have a problem with it since I like the number of our current party. Should I offer putting it to a group vote or is it the DM’s right to add new players?

Adding new players should be a group decision

When you form a gaming group and begin playing a game, the DM often gets some sort of authority given to them by the game. However, the DM does not (and should not) run the gaming group — the group does. They have just as much (but no more) say in group-affecting decisions as every other member of the group.

Just because someone is the DM doesn't automatically give them the right to add (or remove) players without consulting the group just as it doesn't give them the right to arbitrarily change the location and time of game night, the type and presence of food at the table, or any other out of the game details.

Now you could give the DM this authority, but that would have to be something the group cedes to the DM, not something automatically given to them without discussion. If you haven't had that discussion explicitly, then they can't and shouldn't be making this (or any) decision for the group.

You should talk to the DM about this as soon as you can, not just for the sake of your current group size, but because a DM that thinks they can add players at will without asking may have a completely different view of their role at the table than you and the rest of the group.

Experience

I've been in the position of DM and player both as a person suggesting someone new to the table and as someone who was concerned about another proposal to add a player. So, I speak with experience when I say that discussing this as a group is the way to go (and that not talking with the group is asking for trouble).

We've had some times where discussion with the group brought up and nipped some serious issues in the bud. For example, one time the DM wanted to invite a player that not only was (unbeknownst to them) extremely insulting to several other members of the table, but would also have introduced logistical issues that would have negatively affected everyone. In the end, we talked it out as a group and decided not to add the person. I firmly believe that had the DM added this person without consulting us not only would it have been a huge breach of our trust, but it would have killed our group.

We've also had much more positive experiences where everyone talked over and decided to let another person in.

Large groups are not easy

Completely aside from the issue of who gets to decide who plays at the table, the number of players can drastically affect how the game goes. Larger groups amplify many of the problems that small groups already experience and can bring some completely new ones to the table as well. If the players and DM aren't experienced this can (but doesn't necessarily have to) be a recipe for unfun to happen.

I've played with more and I've played with less. There's no perfect number for every table, but you have a right and foundation on which you can base your concerns about adding people and you should definitely bring them up to your DM.

Up to the group

This isn't something where DM fiat applies, because it concerns the makeup of your group, not the game world or the rules. Some groups have the DM run all the organisational stuff on their own, including finding players and things like that, but having the situation be like that is still a social agreement between the group not something inherent to the position of DM.

You should talk to the rest of the group about you being uncomfortable with more players being added.

In general, a game consists of one DM deciding to run a game, and one or more players showing up to play. In general, DMs are a lot harder to find than players are, and being the DM takes more work. If a player shows up or a player leaves, the game can continue. If the DM leaves, the game almost always collapses unless someone else steps up.

That doesn't mean that your opinion doesn't or shouldn't matter. You can and should make your concerns known. Among other things, parties of more than 5 players start to have serious bloat issues (sometimes even before that) that your DM might not be taking into account. Also, if your group has agreed on rules about who can join and when, or how major decisions are made (it sounds like they haven't), then those might apply. Finally, and most importantly, a good DM will at least listen to their players and pay attention to their concerns. Games work much better if everyone is getting along, and the DM is the one with the greatest influence on party harmony - and thus has a larger slice of the responsibility in that area.

At the same time, if your gaming space is like the gaming spaces I play in, the DM really is the one with the soft power. The worst you can do if you are unsatisfied is leave, and the very nature of the question suggests that he has at least three other players who'd love to take your place. Trying to put it to a vote is effectively running a power play with power you don't have. Suppose you do "put it to a vote", and then the DM says "I'm going to do it anyway." What are you going to do? What do you have to back this up?

Basically, your best bet (and one that might still fail) is to talk with him and try to convince him. I'm not saying you shouldn't try to bring in the the other members of the party. If the other players agree with you, that will likely make for a more compelling argument. At the same time, trying to wield power you don't actually have is at least as likely to backfire as anything else. I wouldn't suggest it.

It's best to work it out as a group, with the DM having the same say as the players. If it can't be worked out as a group, there's a hierarchy of "who matters" in the answer.

Host > DM > Players

In the end the Host has the final say because, well, its the host's place. The DM has second priority because they are running the game. Adding players can mess up a lot for a DM, especially if they already feel the group is too large to handle. Players have the lowest priority because they just show up to play without putting in much out of session work.

Some of the comments have suggested the DM have more power than the host to add players. Whereas I do see the point that DMing an extra player is hard, it's really not the DM's place to tell the host "You can't do what you want to in your own house." The DM could always say something like, "I can't DM for any more people, would you be able to DM?" There's also the option of finding another place to host it. This solution is far from optimal.

And again, it's best if the group as a whole can make the decision to add someone in.