We differentiate between policies and platforms at two levels: incorporating a non-trivial policy-setting process, and modelling voters who care about the implemented policy and the platform they support with their vote. We show that platform convergence is a non-robust feature of the winner-takes-all assumption. Some influence of the opposition in policy-making provokes a divergent tendency in platform writing. Platforms can be even more extreme than candidates' ideal policies. With purely pragmatic voters, parties radicalize their positions but the implemented policy is moderate and consistently differs from the median voter ideal policy. When voters care about both policy and platforms, parties announce differentiated yet non-extreme policies, voters concentrate around the platforms, and substantial turnouts are generically obtained even with positive costs of voting. Abstention occurs among voters with extreme views and with moderate views.