$$ \textbf{Oxidation States:} $$

In $$\mathrm{ClO_4^-}$$ (perchlorate), chlorine is in the +7 oxidation state.

In $$\mathrm{ClO_3^-}$$ (chlorate), chlorine is in the +5 oxidation state.

In $$\mathrm{ClO_2^-}$$ (chlorite), chlorine is in the +3 oxidation state.

In $$\mathrm{ClO^-}$$ (hypochlorite), chlorine is in the +1 oxidation state.

$$ \textbf{Disproportionation Reaction:} $$

A disproportionation reaction is one in which a species simultaneously undergoes oxidation and reduction. For this to occur, the element must be in an intermediate oxidation state such that it can be oxidized to a higher state and reduced to a lower one.

In $$\mathrm{ClO^-}$$ and $$\mathrm{ClO_2^-}$$, chlorine is in lower oxidation states (+1 and +3, respectively), making them susceptible to disproportionation. For example, hypochlorite can disproportionate in basic solution as follows:

$$ 3\,\mathrm{ClO^-} \rightarrow 2\,\mathrm{Cl^-} + \mathrm{ClO_3^-} $$

In $$\mathrm{ClO_3^-}$$, chlorine is in an intermediate oxidation state (+5) that, under certain conditions, can undergo disproportionation.

However, in $$\mathrm{ClO_4^-}$$, chlorine is in its highest possible oxidation state (+7) and cannot be oxidized further. Since disproportionation requires one part of the species to be oxidized and the other reduced, $$\mathrm{ClO_4^-}$$ is thermodynamically stable and does not undergo disproportionation.

$$ \boxed{\mathrm{ClO_4^-} \text{ (perchlorate ion) does not undergo disproportionation.}} $$