Do the party skills of my companions add up?

Solution 1:

As per the Mount & Blade wikia:

Personal skills

Personal skills are granted only the individual character.

• Power Strike
• Power Throw
• Power Draw
• Weapon Master
• Shield
• Ironflesh
• Athletics
• Riding
• Horse Archery
• Trainer (*)
• Persuasion

(*) Trainer is a notable exception in that it stacks. Trainer grants the experience to all (valid) party members, but as a personal skill it belongs only to the character who learned it. Multiple characters with Trainer therefore accumulate a higher experience gain.

Leader skills

Leader skills are granted to the entire party, but only the party leader's skill value is used.

• Inventory Management
• Prisoner Management
• Leadership

Party skills

Party skills work like leader skills, except that the highest level any party member has is used. In addition to this, there is a bonus awarded if there are multiple characters with the same party skill in one party. (That is, both the player and at least one companion exceed level 2 in the particular skill) In that case the highest level is used and the following bonus applied for the second highest skill level:

0 - 1 = +0
2 - 4 = +1
5 - 7 = +2
8 - 9 = +3
10    = +4

• Looting
• Tracking
• Tactics
• Path-finding
• Spotting
• Wound Treatment
• Surgery
• First Aid
• Engineer
• Trade