Learn Turkish: Mükellefler gelirleri arttığı oranda daha fazla vergi öder. - Taxpayers pay more tax to the extent that their incomes increase.

The target grammar here is verb + -dIk + possessive + oranda. We take artmak (to increase), add the participle -dık and the 3rd-person possessive -ı to get arttığı. Paired with oranda (at the rate / in the proportion), it literally translates to "at the rate of its increasing," which gives us "to the extent that" or "in proportion to how much".

Since gelirleri (their incomes) is plural, shouldn't the verbal noun be arttıkları instead of arttığı?

In Turkish, when a plural subject is non-human (like gelirler - incomes), the verb or verbal noun almost always stays in the singular form. That's why the singular possessive in arttığı is used; it correctly agrees with the non-human plural subject.

Why is the main verb öder in the aorist tense rather than the present continuous ödüyor?

The aorist tense (the -er in öder) is used for general facts, universal truths, and established rules. Since this sentence describes a systemic rule about how taxes work generally, rather than an action happening right now, the aorist is the most natural choice.

The subject Mükellefler (taxpayers) is a plural human subject. Why isn't the verb öderler?