How do you make decisions in teams?

Start with assigning single ownership to all the roles/functional areas that you guys do within your company. Discuss why that's important, agree that your current process wastes a lot of time that could be better used getting things done. That person has the final say over that role.

Create a Roles & Responsibilities document. This can be a simple one pager done in an hour. Write out everything you guys do ongoing. And divide them into reasonable functional groupings. And put one or the other name next to them. That person is the owner.

I've seen many companies have a fun little sand hourglass timer that they use in meetings and they get it started when it's obvious a discussion is ratholing, going on and on. When the sand has expired, be done and move on.

Accountability for the decisions made. Periodically look back at how this is working and make appropriate changes if you find one of you isn't really as strong in an area as you thought or doesn't really enjoy doing something as much as you thought.

Best of luck,

If you're at an impasse, decide which person feels more strongly about it.

That is, it's easy to get caught up in the argument and forget that, actually, it doesn't matter to you that much what the decision is. If either way has pros and cons, then maybe neither of you really know which is best anyway.

Therefore, if it matters more to one person, why not let that be the tiebreaker.

If this happens constantly about all sorts of things and both of you claim that you care about it more than the other, maybe you have a deeper problem. It's healthy to have disagreements, but there's a point at which you just don't agree on basic assumptions or philosophy, and that's not going to be fixed with any sort of process.

Discussion is good. Outright arguing all the time is bad.

The thing that works for me is to always find common ground. I always look for where the team agrees before discussing where we disagree. This method allows you to build decisions up from a solid foundation. This requires someone on the team to but their ego aside and take on the role of "what is best for the company" not "what is best for me." This is a challenging role to take but overall, it will make your company much better.

It sounds like your arguments might have a healthy bit of ego mixed in. This is never good when trying to come to a common decision that is in the best interest of the project/company. If these arguments start to get personal or nasty, then Jason is correct that their might be some deeper issues.

Chris' idea about roles is also a good one. Splitting the work load and trusting the other person to make a good decision will also pay off in the end.

I'm assuming that arguing is not a sign of underlying disagreements between you and your co-founder. If that is the case, the "go with one person's decision one time and the other person's decision the next time" is not really such a bad idea. There are few critical decisions that completely affect your performance (especially when it is unclear enough for two people to feel strongly about their decisions), but the results of putting off many simple decisions can pile up. If you are constantly arguing, a coin toss or alternating between decisions would work better than keeping on arguing.