For whom is beneficial to deduct the amount paid in state income tax from their income for purposes of computing federal income tax?

Obvious advantages stem from being able to deduct the full cost of state and local taxes you have to pay each year. Every deduction from taxable income helps, and these taxes can sometimes be significant. It's something of a double hit if you have to pay taxes to your state and also pay federal tax on taxes you paid to your state.

The state and local tax deduction (SALT) prevents that from happening, at least to some extent.

Rules for the SALT Deduction

All income taxes that are imposed by a state, local, or foreign jurisdiction can be deducted subject to a few rules.

First, you must itemize your deductions on Schedule A to claim them. This means foregoing the standard deduction, which is often more than the total of a taxpayer's itemized deductions for the tax year. Don't be penny wise and pound foolish and give the Internal Revenue Service more money than you have to. Make sure your total itemized deductions exceed the standard deduction for your filing status so itemizing is worth your while. Otherwise, you'll be paying taxes on more income than you have to, which was what you were trying to avoid in the first place.

The tax must be imposed on you personally. You can't claim a deduction for income taxes paid by one of your dependents—and in some cases, even by your spouse. You must have paid them during the tax year for which you're filing.  

Eligible expenses that can be deducted as state and local income taxes include:

Withholding for state and local income taxes as shown on Form W-2 or Form 1099

Estimated tax payments you made during the year

Extension tax payments you made during the year

Payments made during the year for taxes that arose in a previous year

Mandatory contributions to state benefit funds