an Alkoxide ion is a stronger base than a hydroxide ion. Why?

alkoxide ions are better proton acceptors as compared to hydroxide ion which makes them stronger base.
In an alkoxide ion electron - releasing alkyl group increases electron density over the oxygen atom which tends to decrease the polarity of O-H bond. This results in a decrease in the acid strength. Also, the alkoxide ion formed is destabilised due to concentration of negative charge on oxygen atom by electron releasing inductive effect of alkyl group. Therfore it becomes difficult for alkoxide ion to release protons.