How my co-founder and I handle disagreements around important decisions
At the underlying level, the both of us know we'd always do what we believe is in the best interests of the company. The incentives are fully aligned. We'd also always do what's right for the long term even if it may mean pain in the short term - this is also established as a given between the both of us.
So it then comes down to what each of us actually believes is right for the long term growth of the company. We may differ in this regard.
In most of the cases, it becomes quickly apparent who feels stronger about their opinion. And if it is clear one person feels way more strongly about it than the other person, then we'd go with the decision of the person who feels more strongly about it.
In cases where both of us feel equally strongly about something, which is rare and happens once every ~18 months, it'll be the CEO's opinion that we'd go with.
The approach I've described above isn't necessarily only useful for co-founder disagreements. It could be applied - with some tweaks - to couples, 2 functional heads that work closely with another, a manager and a subordinate, and so on. For some example if you are 2 functional heads where you both feel strongly about something, then you'd setup a process between yourselves that when you are unable to come to a consensus, you'd ask the CEO to be the tie breaker.