The 20th Anniversary edition of Wraith: the Oblivion has two different ways that the XP cost for learning arcanoi might be reduced, and these seem to conflict when it comes to their mechanics.
The first, Guild instruction, is described on p. 147-148:
Guild instruction in common arts is available to any wraith with Status in the appropriate Guild. [...] For any common art, Guild instruction takes one consecutive day per dot of the art’s rating, and the art’s experience point cost is reduced to current rating x2 experience (or a flat 5 experience for a new Arcanos).
For guild instruction in initiate arts,
the same experience-point cost reduction applies.
The second is based on having relevant backgrounds, and is described in the section on mastering arcanoi on p. 303:
Having a Mentor versed in the relevant Arcanos is useful, however, as is a membership in the appropriate Guild [emph. added]. If conditions permit, the player may roll the relevant Background rating when trying to learn a new Arcanos (difficulty 6). Each success reduces the experience-point cost of the Arcanos by one, to a minimum of one.
A wraith may continue working with teachers to attempt to reduce the cost of subsequent levels of an Arcanos, [...]
If the level of the desired Arcanos exceeds the relevant background rating:
Regardless of the source of the expertise, the relevant Background-rating roll to reduce the cost of higher-level Arcanos purchases is made against difficulty 8. This roll cannot reduce the cost below half the regular amount (rounded up), and Willpower cannot be spent on this roll.
The use of the "Mentor" background is clearly no conflict.
As I understand things, guild membership is represented by the "Status" background, which is where the rules conflict. A Guild Status would seem to qualify a character for both discounts, yet the rules do no specify which discount would apply, or whether both would (though stacking them seems wrong).
Are the rules contradictory, is there a resolution in the rulebook, or am I misunderstanding the rules?
Speaking practically, Guild Instruction will generally give a better discount, so would probably be used over the Background discount. The only scenario in which the BG discount might be better is for learning low-level Arcanoi when a character has high Status, but even then the difference is so small that it's scarcely worth considering a BG discount.
For example, with a Status of 3, I calculate a 78.4% chance that the BG discount is at least as good as the Guild Instruction discount for a level 2 art, but only 35.2% of being better (rolling 2 or 3 successes for a discount of 2, compared to the 1 XP discount for Guild Instruction). A Status of 4 gives you an 87.04% chance of a discount of at least 1, and a 52.48% chance of a discount of at least 2, beating Guild Instruction for a level 2 art and matching for a level 3 art. For higher level arts, a BG roll is less likely to give a better discount to the point that it's not worth it.
Consequently, I'd expect the BG discount to only be used if a character didn't have Status in the Guild. However, I'm looking for a resolution within the rules themselves, which this analysis is not.