Implementing direct democracy via representation

Today, several social movements in western democracies argue that traditional representative democracy has failed to adequately represent the will of the "people", and instead support direct democracy as the only political system to restore the will of the majority. We analyze under what conditions the policy –a vector of decisions on every issue– implemented by the winner of a bipartisan electoral competition coincides with the policy that citizens would choose by means of direct democracy. We find necessary and sufficient conditions for this equivalence to hold, implying that, as long as at least one of them is not fulfilled, a divergence of outcomes between direct and representative democracy arises. The first condition requires that the outcome of majority voting issue-by-issue is the Condorcet winner relative to the voters' preference profile over the set of policies. The second requires that either that outcome is the preferred policy for at least one of the candidates, or that candidates' preferred policies differ on every single issue. We reinterpret some findings in the literature in the light of our model and present them as potential reasons why the equivalence between direct and representative democracy may fail.