|Chapter 3||The Eternal Duties of a Human Beings||Verse 21|
Rudra Vaisnava Sampradaya:
How the performance of prescribed Vedic actions acts as an incentive to the masses is what Lord Krishna is emphasising here. That line of reasoning that great personalities accept as authoritative people will also follow.
Brahma Vaisnava Sampradaya:
The great personalities naturally set the example for the common man to follow in the manner in which they speak and in the way in which they act. This is Lord Krishna's meaning.
Sri Vaisnava Sampradaya:
So understanding that the whole Earth benefits from the performance of prescribed Vedic activities, one should act altruistically not for themselves but for the welfare of the world. This is the meaning Lord Krishna is conveying. The word sresthah means great personality expert in the conclusions of the Vedas. Whatever actions such a great person performs others will try to follow. It may be that a certain activity should be performed on a special day. The common people will wait to see how a great person takes the initiative on such an action and then they will follow suit. Hence the great personalities should always act in an exemplary manner to set the standard for the world. In this way they inspire everyone to perform prescribed Vedic actions according to the qualification of one's varna or caste in life and one's asrama or stage in life. If one fails to do this by neglect or omission one commits sin by omitting to help benefit the welfare of the world by their example and the consequence will be one will fall down from the path they achieved after many lifetimes.
Kumara Vaisnava Sampradaya:
How Lord Krishna performing actions helps the maintenance of the world is explained here. Whatever actions a great personality performs is accepted by the common people as the path to follow due to their looking up to people in positions of leadership, royalty and fame etc. Why should they think this way when it is a known fact that the Vedic scriptures are the authority on all aspects of life? They think this way because they do not rely on the scriptures they depend upon the actions ot the visibly prominent in society to base their judhements. So whatever a prominent member of society postualtes whether it is Vedic or concocted the ignorant not being knowlegeable will undoubtedly follow correct or not.