The path and the desire to reduce the suffering of others?

It seems to me that the Noble Eight-fold Path is designed to reduce the suffering of the self. But how do we use its guidance to reduce the suffering of others? If the Buddha was walking down a road after enlightenment and saw a strong man fighting a weaker man, or two equally strong men fighting, would he: - Desire to help one escape the other (and follow that desire)? - Desire to help one defeat the other (and follow that desire)? - Or (having no desire at all), keep on walking down the road? And how should one who is still following The Path act in this situation?