So this has come up once or twice in the Ars Magica game I presently run/play in and perhaps I'm missing the obvious here, but when two magics cross paths, how does one determine the ultimate effects.
Examples;
A demon uses his powers to create an unnatural fire that burns across some-ones path. A Magus uses a Creo Aquam effect to try and douse it.
A Magi casts a Mentem spell to make a peasant want to eat an apple, another Magi immediately casts a Mentem spell to make the peasant not want to eat the apple.
Two Magi cast 'Unseen Servant' and want their Unseen Servant to move the same chair, but in opposite directions.
I have had a few inclinations in this regard, the two most obvious being 'Magnitude of the Effect determines who wins' or 'Casting Total determines who wins'.
My 2 cents, and don't take them seriously, I don't know what I am talking about:
Since the fire is unnatural, my view is this: A) If the CrAq is fast cast as a defense, it needs to be at least half the magnitude of the Demon spell. b) if its after the spell is cast in order to combat the aftereffects I'd say half the magnitude if the Demon spell was Immediate, and same magnitude if the spell has a duration.
On Mentem vs Mentem it would depend on two things. First spell duration (x duration beats immediate). Magnitude (higher magnitude should beat lower magnitude). If they are the same spell, I'd say spell total or finesse.
Unseen servant vs Unseen servant. Definitely Finesse vs Finesse
in (1) What is the definition of 'unnatural fire'? Is it just fire the demon summoned? Infernally tainted fire? If the demon is actively feeding it, then he'll probably just resummon it if the fire is put out. Really, I would just convert the fire's damage to whatever base Creo Ignem that would use, and base the magnitude of Creo Aquam needed to put it out with that. If you wanted the fire to feel extra-hard to put out, due to demonic origin, then apply the Realm vs Realm penalty as if the fire had an infernal aura of appropriate strength for the demon who summoned it. [Caveat: I haven't looked at ROP:I in a while.]
(2) greater magnitude of spell strength should prevail. If pretty equal, look at the peasant's personality traits. He may also be superstitious, and these conflicting urges may send him running to the nearest parish.
(3) Assuming the spell is a concentration, it will probably require some finesse rolls. If the spell is momentary/not guided, and cast at the same time, the chair is probably going to vibrate back and forth a bit.
Basically, your inclination of 'higher magnitude wins' feels like the right answer, mostly, though I would clarify it to be the highest base (modified by + strength magnitudes) rather than final. the spell Maybe Eat That Apple, base 3 +3 moon duration should lose to Really Don't Eat That Apple, base 3 +1 strong urge +1 concentration. My inclination is to do my best to have both spells 'succeed' as much as can be reasonable; I wouldn't be surprised for a strong Unseen Porter competition to snap chairs in half.
I wouldn't mind house-ruling it, that in the case that two Hermetic Magi were casting conflicting spells on the same target at the same time, they would automatically enter Certamen.
But that might only work if the conflicting spells were both the same Technique and Form, so Certamen would automatically be in the TeFo combination. If the conflicting spells had different TeFo, I am not certain how to resolve it.
I can't believe noboy mentioned the P-word yet. It's all mine!
That would go with the fast-casting defense rules; the magus would need to figure out the Form (Per + Awareness vs 15 - demon's power magnitude) and beat it with a fast spontaneous effect of any appropiate Te/Fo combination. If the spell gets to half the demon's power level then he can protect one target, and if he can get to the demon's power level then he cancels the effect completely. Easy!
For these two, Penetration is the tie breaker.
Obviously the spell with the best initiative would take full effect until the slower opposing spell arrived. Then, let the spell with the higher penetration win. Though the 2nd case can be really tricky if the two Mentem spells have different baselines and scopes. Let's call these magi Eat-That-Apple of Tremere and Don't-Eat-That-Apple of Tytalus.
Eat-That-Apple of Tremere is obviously a Rego expert, and he uses The Call to Devour Apples, ReMe 20, a version of The Call to Slumber that makes the victim extremely hungry about apples for D: Sun (hence the +2 mags over Call to Slumber). Don't-Eat-That-Apple of Tytalus, on the other hand, is a Creo specialist, and casts on the target Panic of the Trembling Heart (CrMe 15, with base 4 and D: Sun, that creates fear of a specific item; in this case, the apple). So I'd say that if Don't-Eat-That-Apple of Tytalus beats Eat-That-Apple of Tremere pentration (which he surely will, as he because of some weird twilights he had got Minor Magical Focus: Fruits and Potent Magic: Fruits, Puissant Penetration and Special Circumstances: meddling with Eat-that-Apple of Tremere schemes, and also his spell is 5 levels lower, and thus easier to boost penetration), then the target would be craving and, if he finds any, devouring all apples except that one that scares the hell out of him. He would probably be quite confused about his sudden and conflicting feelings about apples, as well, and I'd personaly suggest to grant him one warping point, for spending the day pushed by magic in two conflicting directions.
The 'let's automatically enter Certamen!' thing sounds half good half bad to me. It seems elegant, but ignores penetration and also drags down the only real contribution of the poor Tremere to Hermetic Magic. All that bluff about Certamen being the definitive non lethal problem solver among magi... and it was something that already was happening automatically whenever TeFo combinations matched!
So if only to pay some respects to the Founder I'd let things be.
Looking over your examples, I assume that you are interested in those cases, where several magic (or other supernatural) effects work on the same target.
You are not asking about one supernatural effect affecting another (like in ArM5 p.83 Fast Casting or in Vim magics).
Several effects competing on the same target looks to me like an educated troupe decision: in particular, because often only parts of the effects will compete (e. g. ArM5 p.134 ReCo 5 Spasms of the Uncontrolled Hand versus p.135 ReCo 25 Strings of the Unwilling Marionette).
I would suggest to compare the remaining Penetration Totals/Penetrations (ArM5 p.82/p.184) of the competing effects - after taking into account and deducting the target's Magic Resistance, the Aegis the target is in, interaction of the Auras affecting target and casters, and pre-existing effects like e. g. ArM5 p.160 PeVi casting total reductions on the casters: the effect with the highest remaining Penetration Total/Penetration prevails, then the one with the next highest, and so forth.
I appreciate, that this favors simple effects like Spasms of the Uncontrolled Hand over involved ones like Strings of the Unwilling Marionette.
This also allows for the competition of effects of all Realms and of all traditions of magic, without having to compare levels e. g. between Hermetic spells, the charms of HMRE p.79ff Learned Magicians and/or demon powers.
From my perspective, the 'let's automatically enter Certamen!' thing only happens because Tremere invented Certamen as a means for Hermetic Magi to resolve differences non-lethally, power against power. No other wizards have this option.
Penetration wasn't something I had thought about when I offered the house-rule option of Certamen. But I am thinking it may have occurred to Tremere in his quest to get out from under the thumb of Tytalus.
And probably it was some undeveloped method he used against him (surely he needed one, being Tytalus how they are in terms of relations with those under their care) and then he thought that with Bonisagus' help he could turn it into the weapon to seize control of the whole Order.
My concern was turning Certamen into something that could have happened before by accident, when similar magics collide instead of an idea from Tremere. But maybe making that accident a tool you could use at will was an accomplishment big enough.
Penetration to me, while an obvious mechanical answer, seems to have some problems that produce very odd results(mileage may vary of course.)
The most obvious being that an apprentice casting say a Level 5 spell for which he has a penetration of 5 is suddenly overcoming a level 40 spell cast by a much more powerful magus who has a penetration total of 0. It undermines, to some extent, the notion of Magnitude representing the power of a spell. Now in some ways, this is reflected in other aspects of the rules(Spells to hurt demons are better learned at lower levels to bypass magic resistance) but in situations where magic resistance is not applying it seems odd, and in other ways counter to the rules we do have for directly counterspelling.
My central issue is ultimate with effects on identical targets that compete. That is; two magical effects created that produce results that are mutually exclusive. The Demonic Fire/Magically created water example, is directly from in-game, the others are an extrapolation from other contexts. Our in-game decision was to contrast magnitudes of effect followed by casting total and go from there with the most dynamically interesting answer(i.e. The Demonic Fire resists being expunged completely, proving its magical origins, but you've cleared a path you and the grogs can run through, if your quick.)
The competing Mentem effects, or should I say, Mind influencing effects is a future planning sort of issue, since the Mages are dealing with non-Hermetic forces focused in that direction and 'how do we undo this mind whammy' or 'can I use my own mind whammy to conflict with that mind whammy' are definitely going to come up.
From a game abstraction point of view I feel like the dice should matter here to a certain extent; i.e. It feels more dramatic for there to be a chance, through randomness, for a lower effect to potentially overcome a greater one and vice versa.
A supernatural fire is already burning without fuel (though it may also ignite fuel that is nearby), so why would water put it out? In theory you can use a creo ignem spell underwater.
the peasant decides they want to eat an apple, but then changes their mind.
depending on the chair they will either pull it apart or hold it in place. Same as if two matched people were pulling on the chair.
The fact is each spell goes off, so the question is then resolved in terms of what the spells actually do. On number 2 depending on durations the peasant may feel incredibly conflicted about eating the apple.
In that specific case, your troupe would first have to phrase the reason for the mutual exclusion of the effects, wouldn't it?
If for example I conjure two magical towers in the same place, the later just will uproot and destroy the former, unless the former has some protection from magic. There is no mutual exclusion or direct competition of spell effects there: it is just that the spells' results affect each other. And you need to come up with the specific resolution off the cuff: Does the former tower topple or burst? Do its remains affect the latter tower while it appears?
Show specific effects. Then we'll talk about interactions.
Ditto.
They both have the same exact strength, per spell description. Standoff, perhaps modified by stress die. This is a contest of Str vs Str, not magic vs magic.