If there's a dispute, you by definition cannot reach consensus without some or all of the participants compromising their position.
Nope.
Consider my example above, of a player feeling that it is unfair that only the
one person gets to rework their character, not everyone. Their position is, in simple terms, "Either everyone should get this benefit, or no one should get this benefit." Meanwhile, my initial position is simply, "The cleric gets this benefit."
No one needs to compromise or give up things they value to make these positions align. It is as simple as, "Oh, that's okay, we can give everyone a chance to do the same thing. The reasons will be different though, so if anyone else wants to rework their character, even in a small way, we just need to sit down and work out the how and why." Likewise, if the player individually wants something (like, say, spending group money on a personal benefit), there's no
compromise required in saying that they'll pay it forward or take a lesser share of future treasure or the like. That's just the players agreeing between themselves how treasure will be distributed, something everyone agrees needs to happen (assuming everyone is actually playing in good faith, of course.)
The only situations that actually meet your description are the ones where two+ groups want, on at least one axis, mutually exclusive things, and thus only one side or the other can get what they want.
My players haven't given me a situation yet where that is true. The closest they've come was when they approached a powerful NPC ally (a disguised gold dragon) and asked if he would be willing to come to their aid, should they get caught in a desperate situation. My immediate response was dismay, as I worried I would be robbing their victories of meaning if I said yes, but crapping on their agency if I said no, both terrible options. However, on reflection, I understood what their true desire was: a safety net, an emergency get-out-of-jail-free card
just in case things went absolutely to $#!+. That isn't a compromise in my eyes; it navigates the Scylla and Charybdis of this problem well. So of course I worked out a solution and confirmed it was sufficient for their needs. TL;DR: NPC made them earrings, one lets them chat with each other freely so long as they're more or less on the same continen (crazy useful!) and the other can be sacrificed to summon the NPC to the party should desperate times call for it, but only once, and only briefly--an escape, a rescue, perhaps a few moments to turn a nasty fight around, but no more. All of my interests were satisfied (I did not feel I was wronging the party, neither robbing their victories nor ignoring their agency), and all of my players' interests were satisfied (they got a powerful NPC's help for an emergency, if needed.)
My experience with consensus-run groups (both in and out of RPGing) is that either a) true consensus tends to generate results where nobody walks away happy, or (more often) b) consensus is used as bad-faith cover by the most persuasive person and-or best lobbyist in order to ultimately get their way.
I don't think either has occurred in my game. I actively engage with my players both in and out of game, both individually and collectively, to make sure their needs are being met. As noted above, I have encouraged an environment where, if someone has an issue, they can bring it to me and I will anonymously discuss it with the group, that way the quiet folks can speak up without having to scrape up their courage first (as someone with at least mild social anxiety, that's something I very much understand.) When there are instigator players, I work with them to make sure their interests are aligning with the group's; as I said, something of a facilitator role, rather than referee or autocrat.
Everyone at the table wants everyone else to have a great time. That means everyone understands that just getting amazing/fun/desirable things for themselves is not enough, or worse, actively detrimental. The party shares gear; the Bard once spent quite a bit of his personal money on a magic ring of flight, only to later acquire a different ability to fly on his own; the ring has since been shared with the party on the regular, such that I want to say the Battlemaster has actually worn it more than the Bard has. This wasn't a request; it was actively volunteered by the Bard, because doing so was helpful to the group and its goals.
That's all you need: a genuine commitment to helping everyone have fun, not just yourself. Finding ways to build a great experience for others, not just yourself. Obviously, still have fun and do awesome things. My job as GM is to help make that happen. Agenda: "portray a fantastic world," "fill the characters' lives with adventure"; Principles: "embrace the fantastic," "be a fan of the characters." My players, likewise, have their own job to do, namely doing adventurous things and being fantastic while doing them. And one of the best parts of most fantasy adventures is struggling alongside your True Companions as you journey forth.