Why was solon chosen to be a leader of athens?

Solon was chosen to design a system for Athens (which would eventually become democracy under Cleisthenes) because at the time, indebted Athenians were being sold into slavery and resentment for the upper class amongst poor people were building and the aristocrats feared a revolution. Solon was chosen because he was both of aristocratic birth and trusted by the common Athenians, acting as the link between both. 

The ratio is 112 to 410