Step 1: Understand disproportionation reaction.
A disproportionation reaction is a redox reaction in which the same species undergoes both oxidation and reduction simultaneously.
For disproportionation to occur, the element must be in an intermediate oxidation state so that it can be oxidized to a higher oxidation state and reduced to a lower oxidation state.
Step 2: Calculate the oxidation state of chlorine in each species.
For \(ClO^{-}\),
\[
x-2=-1
\]
\[
x=+1
\]
For \(ClO_2^{-}\),
\[
x+2(-2)=-1
\]
\[
x=+3
\]
For \(ClO_3^{-}\),
\[
x+3(-2)=-1
\]
\[
x=+5
\]
For \(ClO_4^{-}\),
\[
x+4(-2)=-1
\]
\[
x=+7
\]
Step 3: Analyze the possibility of disproportionation.
The oxidation state \(+7\) is the highest possible oxidation state of chlorine.
Therefore, chlorine in \(ClO_4^{-}\) cannot be oxidized further.
Since disproportionation requires simultaneous oxidation and reduction, \(ClO_4^{-}\) cannot undergo disproportionation.
On the other hand,
\[
ClO^{-} \; (+1),
\quad
ClO_2^{-} \; (+3),
\quad
ClO_3^{-} \; (+5)
\]
are intermediate oxidation states and can undergo disproportionation reactions.
For example,
\[
3ClO^{-}\rightarrow 2Cl^{-}+ClO_3^{-}
\]
is a disproportionation reaction.
Step 4: Final conclusion.
Since chlorine is already in its maximum oxidation state \((+7)\) in perchlorate ion,
\[
\boxed{ClO_4^{-}}
\]
does not show disproportionation reaction.
Hence, the correct option is
\[
\boxed{(3)}
\]