I’m DMing a 5e game and I really don’t like how tacked-on social encounters feel. I could certainly use some homebrew systems, but tracking them is still fairly arbitrary since 5e just doesn’t have good underlying mechanics for them.
I really like the implementation in Modiphius’ Infinity 2d20 system, where you have separate “wound” trackers for combat, social encounters, and hacking. Combat of all 3 types works basically the same too; there’s no need to learn wildly different rules. I played the Song of Ice & Fire RPG a while ago and remember liking its implementation too, though I don’t remember the rules.
What are some other systems that treat social encounters with the same importance as combat?
Some quick recommendations, let me know if you want to know more about any
Genesys - Uses a separate wound tracker (Strain) for all kinds of mental fatigue. Including its "debate" system for when a single roll isn't enough. Essentially it works like a combat with turns and all. Its narrative dice system is good at keeping things non-binary so it does drive the narrative by itself. There is also talent support for those who want to build for social encounters.
Ironsworn - Essentially PbtA at the core with basic social moves. When more granularity is desired the debate can use the fight framework. Why I mention it specifically is also its really awesome approach to trackers. You don't have to fill the tracker but can roll against it whenever you feel the goal is met.
Burning Wheel (and Torchbearer) - Uses a rock-paper-sissors like system where each side's action is played against the other's. Really cool system.
Exalted 3e - Have the least experience with this but the one that I like the most of the meaty systems. It boils down to manipulation of characters Intimacies. Everyone has them. They are things like Love (person) or Affiliation (group). And you cannot convince anyone without tagging in one or more Intimacies, unless you threaten them. The more socially sly a character is the harder it is to find out about their Intimacies so there is a whole system for that too. So you may start engaging with someone to first discover an intimacy or two that you then can use to manipulate them. Once manipulated to a suitable level you can "cash out". I may have some details wrong, was a while. If interested I'll pull out the book and freshen it up.
I second Genesys especially for social encounters. It doesn’t over complicate but enables doing “damage” in a back and forth between sides through opposing checks depending on the argument approach. Also as a system it greatly lends itself to role playing and descriptive play through the mechanics themselves.