Arrange the following in decreasing order of stability: (I) tropylium cation, (II) benzyl cation, (III) $(\mathrm{CH}{}_3){}_2\mathrm{CH}{}^{+}$, (IV) $\mathrm{CH}{}_3-\mathrm{CH}{}_2{}^{+}$.

Tropylium is aromatic (6 $\pi$ electrons over 7 carbons), which makes it the most stable. Benzyl cation is stabilised by delocalisation into the ring but is not aromatic. Among the alkyl cations, secondary is more stable than primary through more hyperconjugation and +I effect. The order is I > II > III > IV.