What is the significance of the fact that Athenians allowed poor and common man to win a position in the government by lot?

It was a modern ideal of democracy to allow the poor and common man to win a position in the government by lot.

It was also sign by the Athenians that they had the different idea about the citizenship that everyone must be included in the politics.

Anyone who doesn't involve in the politics of the country is a useless man. They treated rich and poor men as an equal candidate for the country's election and any other activities.