The only common interests amongst all rational human beings are the equal protection of individual rights. No rational individual wants to have their rights violated; all rational individuals wish to be left free to enter and compete in any market they choose to; all rational individuals wish not to have their property looted from them. This is the only proper meaning of the “public interest”: the interests that all rational individuals have in common.
What statists mean by the “public interest” is the unequal protection of rights, by granting government privileges to one group (who is represents the “public”) at the expense of another group (who is not the “public” and left disenfranchised).
The statist version of the “public interest” is a myth. Outside the equal protection of individual rights, there are only the social and economic interests of various individuals. Any attempt by the government to implement the ‘public interest’ by the violation of individual rights, will lead to a civil war of lobbying pressure groups.