The Support Benefit of Horse animal companion on page 216 of the Core Rulebook.
"If your weapon already has the jousting weapon trait, increase the trait’s damage bonus by 2 per die instead."
The question is what is the "increas by 2" really mean, "1+2=3" or "1→2"?
We all know when you are on a mount (not the companion) the base lance damage would be 1d8/1d6+1+Strength.
But I'm not sure on a Horse Companion (with the Support Benefit) the base lance damage should be "1d8/1d6+3+Strength" or "1d8/1d6+2+Strength" ?
If the answer is "1→2", there seems no reason for a cavalry to choose a jousting weapon, since other weapons can gain the benefit with no difference.
The key part of the rule phrasing is “increase the trait's damage bonus by 2 per die instead”. The key word to your question being the word instead. If they intended it to stack, they would have said something like “in addition to”. So the damage is a total of +2 when using a jousting weapon with the support benefit of a horse animal companion.
Also, nothing in the rules is preventing one from using the two-handed damage die while mounted. Being mounted just allows one to use a lance one-handed.
The total damage bonus is +3 per die.
Jousting is normally +1, but the horse support increases it by 2 instead of giving you its own circumstance bonus when you're wielding a jousting weapon.
Strictly speaking, there's no "stacking" because you're increasing the value of Jousting rather than applying the normal bonus.
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When mounted, if you moved at least 10 feet on the action before your attack, add a circumstance bonus to damage for that attack equal to the number of damage dice for the weapon.
So normally, a jousting weapon will add +1 per die as long as you move at least 10 feet before attacking with it.
So if you run on-foot at someone with a +1 Striking Lance, then the weapon would be dealing 2d8+2 damage (plus STR bonus or other bonuses to damage). And you would have to wield the weapon in 2 hands.
If you are instead mounted on a Warg or something like that, then you could wield the weapon in 1 hand because of the jousting trait, but it drops the damage die to d6, so it would deal 2d6+2.
if you moved at least 10 feet on the action before your Strike, add a circumstance bonus to damage for that Strike equal to twice the number of damage dice. If your weapon already has the jousting weapon trait, increase the trait's damage bonus by 2 per die instead.
If using a different weapon, the Horse has a similar benefit to the Jousting trait. It adds +2 per die though. So a scimitar would be adding +2 damage, and a +1 Striking scimitar would be adding +4.
That doesn't make sense with a jousting weapon though. The bonuses wouldn't stack since they are both circumstance bonuses. So jousting and its damage bonus becomes effectively a dead trait.
So the Horse rule says to instead add +2 to the damage boost of the jousting trait. That is what the 'instead' is referring to - adding to the existing bonus instead of providing its own.
This effectively makes the damage boost stack. +1 per die from jousting and +2 from the Horse benefit.
So on a horse with a +1 Striking lance you would be dealing 2d8+6 2-handed or 2d6+6 1-handed.
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The Horse support and Jousting trait are both Circumstance bonuses, so they can't stack. Instead, you need to increase the Circumstance bonus from the Jousting trait to 3 per damage die instead of 1 per damage die.
This would be equivalent to stacking the 2 per die you get from the horse and 1 per die you get from the weapon.
If it just increased the Jousting bonus to 2 per die, it would be no different than using the Horse's support with a regular weapon, and thus there would be no incentive to use a Jousting weapon.
The Support Benefit of Horse animal companion on page 216 of the Core Rulebook.
"If your weapon already has the jousting weapon trait, increase the trait’s damage bonus by 2 per die instead."
The question is what is the "increas by 2" really mean, "1+2=3" or "1→2"?
We all know when you are on a mount (not the companion) the base lance damage would be 1d8/1d6+1+Strength.
But I'm not sure on a Horse Companion (with the Support Benefit) the base lance damage should be "1d8/1d6+3+Strength" or "1d8/1d6+2+Strength" ?
If the answer is "1→2", there seems no reason for a cavalry to choose a jousting weapon, since other weapons can gain the benefit with no difference.
Yeah, the "instead" word is kind of in a strange place, since it can be vague enough to simply be read as a substitution value instead of a substitution effect, which was my initial confusion.
The most common use of the word "instead" refers to substituting something for something else. In this context, it can refer to "increase the trait's damage bonus by 2 per die instead (of 1 per die)" just as easily as any other form of substitution, and either one could be correct. However, the intended context is "increase the trait's damage bonus by 2 per die instead (of the Horse Support Benefit's usual effect)," since this is trying to spell out an exception, and that exception has to do something. Because it's read as a substitution effect instead of a substitution value, it means that you actually would increase the value by 2, to a total of 3, and not increase the value by 2, in place of the existing increase by 1.
Incidentally, both of these readings are equally valid from an English language standpoint, since both are substitutions, one being of value, and the other being of effect, and the sentence structure does not differentiate between the two in any way. The only reason the latter would make more sense than the former is due to the context of "the effect has to do something, Paizo wouldn't try to write an exception to not have it do anything."
They stack.
I got confused initially too. The critical word is "by."
Increase the trait's damage bonus -by- 2 per die instead
If that was replaced with: "Increase the trait's damage bonus -to- 2 per die instead" then it wouldn't stack.