Disproportionation occurs when an element in an intermediate oxidation state simultaneously undergoes oxidation and reduction.

• $\text{BrO}^-$ (Br = +1): can disproportionate to Br$^-$ ($-1$) and BrO$_3^-$ ($+5$) ✓
• $\text{BrO}_2^-$ (Br = +3): can disproportionate to $\text{BrO}^-$ and $\text{BrO}_3^-$ ✓
• $\text{BrO}_3^-$ (Br = +5): can disproportionate under certain conditions ✓
• $\text{BrO}_4^-$ (Br = +7): Br is in its highest oxidation state for bromine — it cannot be further oxidised, so disproportionation is not possible.

$\text{BrO}_4^-$ does not undergo disproportionation.