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Ambidentate Behaviour: Elimination vs Substitution 2
According to Pearsons hard soft [Lewis] acid base principle, hard Lewis acids have a strong affinity for hard Lewis bases and soft Lewis acids have a strong affinity for soft Lewis bases.

Hard alkoxide ion preferentially abstracts a hard proton, so initiating E2 elimination, whereas soft nucleophilic malonate carbanion preferentially displaces soft bromide ion nucleofuge. (Note that the pKa values of the conjugate acids, ethanol and diethyl malonate, a similar, around 16.)

Note that while hard vs soft comparisons can be made for carefully selected pairs of species and/or reactive centres, the HSAB analysis is NOT general. For more information look in the Chemogenesis webbook section on Pearson's HSAB principle.