According to Molecular Orbital Theory, the stability of a species is directly proportional to its bond order. Bond order is calculated as $\frac{1}{2}(N_b - N_a)$, where $N_b$ is the number of bonding electrons and $N_a$ is the number of antibonding electrons.

• $\text{O}_2$ (16 electrons): The configuration is $\sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 (\pi 2p_x^2 = \pi 2p_y^2) (\pi^* 2p_x^1 = \pi^* 2p_y^1)$. Bond order = $\frac{10 - 6}{2} = 2.0$.
• $\text{O}_2^+$ (15 electrons): Formed by removing one electron from the antibonding $\pi^*$ orbital. Bond order = $\frac{10 - 5}{2} = 2.5$.
• $\text{O}_2^-$ (17 electrons): Formed by adding one electron to the antibonding $\pi^*$ orbital. Bond order = $\frac{10 - 7}{2} = 1.5$.
• $\text{O}_2^{2-}$ (18 electrons): Formed by adding two electrons to the antibonding $\pi^*$ orbitals. Bond order = $\frac{10 - 8}{2} = 1.0$. Since stability increases with an increase in bond order, the decreasing order of stability is $\text{O}_2^+ \text{ (2.5)} > \text{O}_2 \text{ (2.0)} > \text{O}_2^- \text{ (1.5)} > \text{O}_2^{2-} \text{ (1.0)}$.