Where the principle is not applied consistently by one person's definition, it is almost always because by another person's definition the people to whom the law applies unequally are not equals. From one end of the political spectrum to the other, horizontal equity is a universally accepted principle. There are no sides, no division between conservatives or liberals, or between advocates of big or small government. Usually the principle is so taken for granted and understood that it is not even explicitly examined. If a person can prove that she is just like another, then almost no one will deny that she has a strong case for equality under all laws applying to the two of them.
Horizontal equity is the most basic of the applications of equal justice.
When it comes to vertical equity and progressivity, on the other hand, agreement quickly breaks down. Everyone has his own version of how progressive government should be, how much it should be involved in assessing different amounts of tax on individuals with different means, or helping differentially those with different needs. The debate over progressivity at one level or another has often dominated the public debate and even led to the toppling of governments. It has been a major issue in the debate between socialism and capitalism and the resulting compromise that is sometimes called a mixed economy. If governmental action is invoked to try to rectify some vertical inequity, then some amount of redistribution is almost inevitable.