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When you guarantee another empire's independence or have a non-aggression or defensive treaty with them, you build up trust with them over time, which in turn is applied as a bonus to their opinion of you.

Does trust also give any sort of bonus to acceptance for other things such as vassal/protectorate offers or alliance invitations?

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Trust is one of the factors that can improve an empire's willingness to become an ally, as it maps 1:1 to increased opinion (which affects offer acceptance). The biggest factors tend to be the relative size/population of your empires and distance from each other. Other factors include whether or not you have common rivals, whether or not you are on good terms with empires they are also on good terms on, and how much your trade deals with them have been in their favor.

For alliances and federation invitations, opinion is explicitly called out as something that influences acceptance:

Federation acceptance tooltip

Regarding vassals/protectorates, the effect is indirect - trust affects opinion, and opinion is a factor in the empire's attitude toward you. Attitude is part of the factors that affect acceptance of vassalization or protectorate status:

Vassalization acceptance tooltip

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  • The factors you listed all affect opinion, but I don't believe they all affect acceptance. I would really prefer to see a screenshot showing trust in the list of factors for acceptance (when you mouse over the check mark or X on a proposal button) or a screenshot showing trust not in the list in a relationship with high (>50) trust. Jan 24 '17 at 18:24
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    @ObliviousSage I don't have a screenshot on hand, but opinion is definitely a factor in acceptance, and trust is a factor in opinion, so even if trust isn't directly listed in the displayed calculation, it's still a factor. Also, to Shaun, in recent games I've played I've found distance to be a huge factor, perhaps the biggest. Settling a colony near a potential protectorate has resulted in them immediately requesting protection more than once.
    – DCShannon
    Jan 24 '17 at 18:28
  • @DCShannon: Good point on distance. Tweaked my answer. Also l, I clarified that trust modifies opinion, which is a factor in acceptance.
    – Shaun
    Jan 24 '17 at 18:30
  • @DCShannon I know trust is a factor in opinion. What I would like proof of is whether trust or opinion is a factor in acceptance. A screenshot showing opinion affecting acceptance would be fine. Jan 24 '17 at 19:01
  • @ObliviousSage In some cases (like alliances), "opinion" is in the tooltip. For vassalization, it doesn't show up in the tooltip, but "attitude" does, and attitude is influenced by an empires opinion toward you (which is influenced by trust). See my edits for details.
    – Shaun
    Jan 25 '17 at 7:26

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