Using data from U.S. presidential elections, we show how seemingly insignificant changes to what we call the "architecture" of the Electoral College can cause different candidates to be elected President, even when no one changes how they vote. We consider varying the size of the House of Representatives, the method of apportionment, the number of "Senate" electoral votes cast by each state, and the lower bound on the number of "House" electoral votes cast by each state. We consider, in particular, elections with a "referendum paradox". In these elections, the electoral vote winner is not the popular vote winner. Our work extends Neubauer and Zeitlin (2003) who analyzed the case of the 2000 election. We give an explanation for the effects that we observe in the data. (C) 2013 Elsevier Ltd. All rights reserved.