When people disagree about a decision, they are either disagreeing about 1) the information they have, 2) what they value, or both.
As a child, I noticed a lot of the disagreements children had, were over what was "better". Decisions like which board game to play, which movie to watch, or what food to eat came down to who could convince most of the group of what was "better". The problem was that there usually wasn't a clear winner for anything. How do you decide if Pokemon is better than Dragon Ball Z? I eventually realised that "better" actually just meant "I feel like doing this", and the reasons which followed didn't matter much at all. It seemed like a terrible way to come to group decisions, but I decided I could just avoid disagreements until I was older. Surely adults had a better way of doing this, right?
Disagreements are either about 1) the information each party has, 2) what the parties value, or both. When people disagree about something, they haven't yet found the core of their disagreement and often debate points separate from it. People should never agree to disagree. The key to resolving a disagreement is to understand if there is either a gap in values or information.
People who value different things in a decision are more likely to have different goals, which means they're more likely to disagree.
Imagine you're deciding where to eat dinner with a friend. You think the Thai place down the road is really good and suggest you eat there, meanwhile, your friend has recently discovered a new Italian place they think is better. "My place has a larger menu," you say. "Sure, but mine is better value for money," says your friend. You go back and forth, debating travel time, atmosphere, and novelty amongst other things but still ending in a stalemate.
This is a disagreement of values. You might value variety in a menu, short travel times, and a more casual vibe over the things which your friend values - good value, an upscale atmosphere, and a more novel experience. You might even just feel like Thai tonight.
It's very hard to change what someone values, and almost impossible in a short period of time. This means value-based disagreements are best resolved by finding an option that satisfies what all parties value. It's hard to do this when all parties are optimising for many variables, but if you can reduce it to the one or two most important things, then it's often possible. For example, if upon reflection, your friend mostly cares about trying out somewhere new, and you mostly care about having Thai, you can find a Thai place you haven't been to before.
Sometimes, even if all parties choose the one or two things they value most, there is no "single best option" that clearly satisfies everyone's goals. In these cases 1) the decision can be abandoned, or 2) one or more of the parties can be removed from the decision. For example, the goals of a salesperson and customer are clearly opposed. The salesperson wants to maximise the sale price whilst the customer wants to minimise it. If the most the customer will buy for is $100 and the least the salesperson will sell for is $150 the group decision is abandoned.
Parties who have similar values should have similar goals. If they still disagree, they are disagreeing about the information they have. Things such as what the options are, how risky options are, and how beneficial each option might be.
Imagine that both you and your friend feel like eating Thai tonight and want to try somewhere new. Your goals are aligned, so you find some options online and try to choose one from them. "This place looks good, it has a rating of 4.2 on Google," you say. "I don't trust anywhere less than 4.5 on Google anymore," says your friend. "4.2 on Zomato would be okay, but they're not listed on Zomato".
You're now trying to evaluate the quality of a restaurant given your past experiences and its current Google rating. It seems your friend has had negative experiences with restaurants that have ratings between 4.2 and 4.5 on Google. This has changed his perception of the risk relative to you. Maybe he just got unlucky and he's being overly risk-averse, or perhaps you've just been lucky. So how do you decide?
Information-based disagreements are resolved by finding a source of information that all parties trust. The core issue in the above example is low trust in the Google rating system, which leads to manually adjusting for risk based on past experience in a way that both parties can't agree on. If Zomato had a rating of 4.2 you would both trust it and be able to (finally) go eat. Or perhaps you can ask a friend who has been there, and whose opinion you both trust.
You probably spend a lot of time disagreeing with people and then persuading them to align with you on decisions. I would guess you do this at least ten times a day - convincing your toddler to eat his dinner, persuading a colleague to commit to a deadline, or negotiating a better deal on your rent often start as disagreements. Given how much time we spend on resolving disagreements and how frustrating not resolving them can be, it pays to have a framework. Next time you see a disagreement look for its root - are you not aligned on information or values?