In what way is this shard of pottery evidence of democracy in Ancient Greece

Because of ostracism

Explanation:

Apart from the usual institutional guarantees, against the threat of a coup in the 6th century BC. Athenian lawmaker Kleisthenes created another peculiar thing: ostracism.

An extraordinary National Assembly would be convened each spring to look into the question of whether there was anyone among the citizens who could be dangerous to their freedom. If the assembly voted in the affirmative, it would gather again in six months and every citizen had the right to write the name of a potential tyrant. The one who had the most votes, at least six thousand, had to leave Attica for ten years.

But he did not lose his honor and property, he could live where he wanted and the assembly could grant him a return earlier. (Today, with hundreds of tiles excavated on the Agora, we can trace the political struggles of that time and their class character. The names of Democratic politicians are on the shards of fine tableware, and the names of aristocratic ones on the clefts of roughly baked clay pots.)