Taxation in ancient Athens

Here's a quote from the book Radical Markets: Uprooting Capitalism and Democracy for a Just Society to ponder:

Most of us think of the liturgy as the words chanted by members of a religious community. But the term originated in ancient Athens where it meant roughly "public works" and referred to the responsibility of the roughly 1000 wealthiest citizens to fund the operations of the state, particular the army and navy. How did the Athenians determine which citizens were the wealthiest? According to Demosthenes, any member of the liturgical class could challenge any other citizen he believed was wealthier to antidosis or "exchange." The person being challenged would have to either assume the liturgical responsibility or exchange all possessions with the challenger. The system gives everyone an incentive to be honest despite the burdens of the liturgy. If you falsely claimed to be poorer than the top 1000 so as to avoid the liturgical burdens then you could end up being forced to exchange your possessions with someone who is poorer than you are.