Will the AI accept Start Independence Faction?

Yes: it is accepted automatically.

Interaction · Vassal actions

Start Independence Faction

No costAccepted automatically

Found an Independence Faction against the recipient

What you need

You

To send it

can_create_faction = { target = scope:recipient type = independence_faction }

To see it in the menu

Is landed
Highest held Title is more than Barony Rank
Is not a Governor
Is not a faction member
Is a direct vassal of the target

The character you target

None of these
- Any targeting faction:
  - faction_type = independence_faction

Start Independence Faction is a vassal character interaction in Crusader Kings III. Accepted automatically. Patch 1.20.1.2, from game/common/character_interactions/00_vassal_interactions.txt.

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Quick answers (1)

Will the AI accept Start Independence Faction?: Yes: it is accepted automatically.

Will they accept?

The other character has no choice: the game accepts it automatically.

What happens

Effects

create_faction = { type = independence_faction target = scope:recipient }
If
- Your primary title:
  One of these
  Their de jure liege:
  holder ?= scope:my_liege
  or
  If title tier exactly Duchy › Their de jure liege › Their de jure liege:
  holder ?= scope:my_liege
Then
- Stress and fulfillment impact: by trait: Just +40

• the game's own tooltip text · ◦ our reading of the script line · code the script where neither exists

Who can use it and sees it (is_available, is_shown) (15 lines of game script)

is_available = is_landed = yes
highest_held_title_tier > tier_barony
is_governor = no
is_a_faction_member = no
is_shown = scope:actor != scope:recipient
scope:actor = {
	liege = scope:recipient
}
scope:recipient = {
	NOT = {
		any_targeting_faction = {
			faction_type = independence_faction
		}
	}
}

As written in game/common/character_interactions/00_vassal_interactions.txt.

Can be sent when (is_valid…) (6 lines of game script)

scope:actor = {
	can_create_faction = {
		target = scope:recipient
		type = independence_faction
	}
}

As written in game/common/character_interactions/00_vassal_interactions.txt.

Effects (on_send, on_accept, on_decline) (20 lines of game script)

on_accept = scope:actor = {
	send_interface_toast = {
		type = event_toast_effect_neutral
		title = start_independence_faction_interaction_notification
		left_icon = scope:actor
		right_icon = scope:recipient
		create_faction = {
			type = independence_faction
			target = scope:recipient
		}
		if = {
			limit = {
				is_de_jure_vassal_of_liege_trigger = yes
			}
			stress_and_fulfillment_impact = {
				just = medium_stress_impact_gain
			}
		}
	}
}

As written in game/common/character_interactions/00_vassal_interactions.txt.

Category: Vassal actions
In the menu: under More…
ID: start_independence_faction_interaction

Source: game/common/character_interactions/00_vassal_interactions.txt and the English localisation, Crusader Kings III 1.20.1.2. “You” is the character who sends it (scope:actor, or a puppet acting for you); “the character you target” is the recipient.