I suppose this an attempt to, in a way, force the people of Hamilton to research and learn about past citizens and history of their community. And, with this, be able to nominate a worthy candidate for the "greatest" Hamiltonian. Although I think that it is a good idea for people to know about their history, selecting a "greatest" Hamiltonian is impossible.
Individuals have many different interests and goals and, therefore, have had different influences in throughout their lives. For example, a foot-ball fanatic would probably vote for Russ Jackson (CFL Hall of Fame quarterback and broadcaster) while a dancer would vote for Karen Kein (international ballet star) What I'm trying to say is that a person would think the Greatest Hamiltonian would be the person who most influenced them / their interests.
This is a clip from the original contest, "The Greatest Canadian":
As you can see, each individual has a different idea as to who the "greatest" Canadian is. Therefore, there is no "Greatest" Hamiltonian but a long list of great Hamiltonians.
But, I must say, that if I were forced to pick the greatest Hamiltonian, it would be George Hamilton. Why? Because without the founder of Hamilton, there'd be no Hamiltonians to nominate!