Why was the tyrant Peisistratus able to gain power in Athens and why might he be considered an important person in the evolution of democracy there?

Solon had been leader before Pisistratus and was largely unpopular with the lower common classes. Despite making things somewhat better for these people Athens was still in bad shape in terms of overpopulation and agricultural productivity so hunger and poverty were still a very real issue for the poor of Athens. Solon did not help his relations with the poor by introducing military conscription for all males aged between 18 and 60. His efforts to improve the situation, through efforts such as increased trade and the aforementioned military presence had lead to unrest in Athens. This unrest allowed Peisistrauts to seize power in a violent uprising. Peisistrauts had made his money in mining (see Ehrenberg on tyranny, pg.81) since being exiled from Athens by the ruling elite. With a hired army he successfully took Athens and drove it's previous rulers out. He was already of to a good start with the people of Athens as they were thankful that he had overthrown their oppressive rulers. He proved popular with the people by sponsoring public games and religious festivals. He also moved to tax everybody equally, previously the wealthy had enjoyed the privilege of lower taxes. Crucially, he also provided cheaper state loans for farmers in the city. This was doubly advantageous as he was looking out for the common man while also equipping the common man with the means to battle that which affected them, hunger and poverty. He provided stability for the farmers, farming was a precise and slow business which was often hindered by the interference of those in charge making demands on the farmers. He sought to put a stop to this and to achieve this he appointed district judges who were fairer to the farmers. In fact it was often said that Peisistratus himself would travel out to see the farmers. In further efforts to help the farmers he would grant land that had been confiscated from nobles and allow growing on certain parts of land that had previously been held for grazing. (Ehrenberg, page. 83) He sought to increase trade and was successful on doing so as well as showing success in claiming new lands for Athens, though this did also serve him as he appointed a rival of his over this newly gined land, nevertheless this new land allowed trade access with the Black Sea (Ehrenberg, page.82).
He won favour through his efforts in revamping the city's temples and he also sponsored sculptures throughout the city. (Ehrenberg, page 84 for quotes on Athenas temple). He minted coins also which an image of an owl the symbol of Athena further solidified his strong connection to the city of Athens and his religious beliefs. As previously mentioned he sponsored public games, these were also done as a tribute to Athena and the city itself (Ehrenberg, pg. 85 quote on festivals proving popular and solidifying his position)

See Ehrenberg page 84 about his popularity with the common people and how he tried to raise the living standard for these people.

Aristotle on Peisistratus: ‘In all matters he was willing to conduct all the affairs of state in accordance with the laws, granting himself no special privilege … and for these reasons he remained in power for a long time … For the majority of the notables and of the people favoured him, since he won over the former by diplomacy and the latter by his help in their private affairs; he was popular with both.’ (Aristotle, Ath. Pol., 15)

Thanks to the wealth he had accumulated and his desire to help Athens he also introduced a new and better water supply for the city and improved upon the agora, the market place which had been set up by Solon (Ehrenberg, pg. 86, Agora grew to centre of city life). These improvements demonstrated that he was willing to use his vast fortune towards bettering the city, of course he benefited too. He claimed new taxes on the improved agricultural produce but this was only achieved because of the great work carried out by him in establishing and maintaining better conditions for the farmers of the city. This was a leader who was just as concerned with the people of his city as he was himself. Through his efforts in improving many aspects of Athenian life for all it's citizens we see that he was a capable and very practical leader. (Ehrenberg, page 86, " The man whose reign.... foundations of Athenian greatness")

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