Slate asks why Chicago is so corrupt, and how we measure corruption:
The most straightforward way to measure corruption is to check the number of convicted local officials. Between 1995 and 2004, 469 politicians from the federal district of Northern Illinois were found guilty of corruption. The only districts with higher tallies were central California (which includes L.A.), and southern Florida (which includes Miami). Eastern Louisiana (and New Orleans) rank somewhat further down the list.
But a high conviction count doesn't necessarily mean more corruption. It could mean that a district happens to have very strict transparency laws or a zealous and effective federal prosecutor—like Patrick Fitzgerald in Chicago. You might try to measure corruption by checking the number of city employees per 1,000 people. (Bigger governments suggest patronage-style politics.) Or you could check to see how long it takes to acquire a construction permit through legal means. (Long delays may reflect a system of rampant bribery.)
Public perception may be the most useful measure. If the inhabitants of a city view corruption as a given, they'll be more inclined to forgive politicians who have already been tainted by scandal, like Chicago's current mayor, Richard Daley.