How should we judge between the altruism and the egoism? What evidence or arguments might adjudicate between these two positions? How might we try to combine them?
In my opinion, most acts combine both altruistic and egoistic motives. For instance, when I give money to the local food bank, I'm doing it to help feed the hungry, but I also feel good about myself and see myself as a generous person.
I don't think it's necessary to judge a person's motives on the basis of altruism or egoism. All acts are on a continuum between the two extremes.
You might take a look at our presidential candidates and try to discern whether their motives for running for office are largely altruistic or egoistic. What about the great presumably altruistic historical figures of Mahatma Gandhi and Mother Teresa? What about the evil Adolf Hitler? Did he have some altruistic motives?