Uniformity: the argument that does not need an appraisal
The Illinois Constitution requires property to be taxed uniformly. That is a ground in its own right.
Most owners think an appeal means proving what their house is worth. There is a second ground, it is often stronger, and it needs no appraisal.
The rule
The Illinois Constitution requires that taxes on real property be levied uniformly by valuation. In practice: two properties that are alike should be assessed alike. Where they are not, the over-assessed one has a claim — regardless of what either would sell for.
Why it is easier to prove
A market-value argument requires evidence about the market: recent arm's-length sales of genuinely comparable properties, or an appraisal. A uniformity argument requires only the county's own records. You are not contradicting the assessor with outside information; you are pointing at an inconsistency inside their own file.
What makes a strong uniformity case
Comparable properties that match on the attributes the assessor recorded — class, town or neighbourhood, lot size, building size, age — and are assessed materially less. The tighter the match, the harder it is to explain away. Three or four tight matches beat a dozen loose ones.
The honest caveat
Mass appraisal is not expected to be identical. A few per cent of spread is tolerance, not injustice. The argument works when the gap is large and the properties are genuinely alike — and if half your comparables are assessed more than you, you do not have this case.