Am I obligated to give up my seat on public transportation for an old man, and would I be sinful if I did not do so?

Standing up from a seat in public transportation for an elderly person or others is not obligatory; rather, it is recommended due to the good deed it entails and the preference given to others. This is among the righteous deeds for which Allah praised those who perform them, saying: "and prefer [them] over themselves, even though they are in [dire] poverty. And whoever is protected from the stinginess of his soul - it is those who will be the successful."