General alternatives:
* Unreasonably
* Unsoundly
* Illogically
* Unintelligibly
* Absurdly
* Foolishly
* Unwisely
Emphasis on emotion:
* Impulsively
* Emotionally
* Passionately
* Blindly
* Instinctively
Emphasis on lack of logic:
* Preposterously
* Ridiculously
* Incoherently
* Inconsistently
* Unjustifiably
Emphasis on being stubborn:
* Doggedly
* Obstinately
* Tenaciously
* Headstrong
Emphasis on being foolish:
* Carelessly
* Recklessly
* Thoughtlessly
* Rashly
The best word will depend on the specific situation. For example, if you are talking about someone who is making a decision based on their emotions, "emotionally" might be a good choice. If you are talking about someone who is making a decision that makes no logical sense, "illogically" might be a better choice.