This brief note intends to clarify what it means to say that the government is neutral with regard to the behavior of citizens and what it means to say that the government is discriminatory. As such, this is a mere logical exposition which does not entail any normative evaluation.

It should be noted that this discussion merely concerns neutrality in a certain respect, viz., neutrality with regard to the distribution of access to a given right between different groups of individuals. (By "group" is meant a number of individuals who have a certain defining characteristic, relevant to the gaining of access to some right, in common and may consist of only one individual.) Hence, the issue is not directly one of whether the government should value a certain phenomenon per se, but one of in what way different categories of citizens are treated. Neutrality, then, can be defined as a state of affairs where the government values and implements no right which, if implemented, would bestow a right on some subset of groups of people not identical to the whole set of groups of people.

We assume that the government in question is able to implement any set of rights it wants, that the term "rights" refers to created, and not "natural", rights, and that a right is a continuous variable being defined by a non-negative number on the real number scale.

• Define first a set of possible (positive or negative) rights x={x₁, x₂, …, x_n}, where x_i defines the legal right (and not the usage of it!) for group of people i. The legal right is, in itself, given and, if granted, identical in nature (but not necessarily in scope) for all concerned groups. x_i>0 means that group i has access to a given right to some extent.
• Then define a set of government evaluations of rights x, V(x)={V(x₁), V(x₂), ..., V(x_n)}. V(x_i)>0 means that the government values a given right for group i positively.
  

Consider next the following two cases.

1. x_i=0, i=1, 2, ...,n <-> V(x)=V(x₁)=V(x₂)=, ...,=V(x_n)=0
   In this case, there is no right for any group of citizens. This implies that the government is neutral.
2. x=x₁=x₂=, ...,=x_n>0 <-> V(x)=V(x₁)=V(x₂)=, ...,=V(x_n)>0
   In this case, there is a (positive or negative) right for all groups, and since each group is authorized to access this right in exactly the same way and to the exact same extent as any other group, if it so desires, the government is neutral.

It is clear from above that a government can be neutral with regard to the behavior of citizens in two different ways: (i) by not valuing and not implementing any right for any group; or (ii) by valuing a positive or negative right positively and by implementing it such that each group may access it in an equal fashion. Any other setting than the one described in the two cases implies that the government is not neutral, in the sense discussed here.

As pointed out in the second paragraph, there is another sense in which a government can be said to be neutral, which corresponds only to the first of the two cases outlined above. But, I argue, this is a thoroughly uninteresting sense in a discussion of neutrality, since neutrality in that setting holds if and only if anarchy prevails: any government right is a violation of neutrality. I agree that on this particular definition of neutrality, the second case above entails non-neutrality, but since I discuss the distribution of access to a given right, the second case, along with the first, define government neutrality.

Furthermore, the term discrimination can be defined fruitfully by means of the analytical apparatus developed above, in the following manner:

Non-neutrality <- Discrimination <-> No factual basis for non-neutrality (i.e., the exemption of at least one group of people without a factual basis)

In other words, non-neutrality does not necessarily imply that there is discrimination (although discrimination implies that there is non-neutrality). Rather, discrimination is defined as non-neutrality without a factual basis or invalid non-neutrality. Note first that "without a factual basis" and "invalid" are normative assessments which, as such, cannot be subjected to truth claims (as I explain in my essay On the Nature of Morality). Hence, the usage of the term "discrimination" necessarily entails a subjective evaluation. Note also that this reasoning only concerns implemented rights, i.e., x and not V(x).

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