Motivated by the restoration of $SU(2)\times U(1)$ at high energy, we suggestthat certain ratios of diboson differential cross sections can be used ashigh-precision observables at the LHC. We rewrite leading-order dibosonpartonic cross sections in a form that makes their $SU(2)\times U(1)$ andcustodial $SU(2)$ structure more explicit than in previous literature, andidentify important aspects of this structure that survive even in hadroniccross sections. We then focus on higher-order corrections to ratios of$\gamma\gamma$, $Z\gamma$ and $ZZ$ processes, including fullnext-to-leading-order corrections and $gg$ initial-state contributions, andargue that these ratios can likely be predicted to better than $5\%$, whichshould make them useful in searches for new phenomena. The ratio of $Z\gamma$to $\gamma\gamma$ is especially promising in the near term, due to large ratesand to exceptional cancellations of QCD-related uncertainties. We argue thatelectroweak corrections are moderate in size, have small uncertainties, and canpotentially be observed in these ratios in the long run.