In what ways are

In janapadas, men became ‘rajas’ by performing the Ashvamedha sacrifice. The rajas who let the ashvamedha horse pass through their lands meant that they accepted that the raja who wanted to perform the sacrifice was stronger than them.

In the modern times, we have a democratic system for electing our leaders. Each citizen who is 18yrs old (or older) has the right to cast his/her vote. The contesting candidate with majority of votes wins the election, thus becoming the public leader.