The Race to the Base

We study multi-district legislative elections between two office-seeking parties when one party has an initial valence advantage that may shift and even reverse during the campaign; and, each party cares not only about winning a majority, but also about its share of seats. When the initial imbalance favoring one party is small, each party targets the median voter. For moderate imbalances, the advantaged party maintains the centre-ground, but the disadvantaged party retreats to target its core supporters; and for large imbalances, the advantaged party advances toward its opponent, raiding its moderate supporters in pursuit of an outsized majority.