Mixed Membership Models for Rank Data: Investigating Structure in Irish Voting Data
Isobel Claire Gormley School of Mathematical Sciences & Complex and Adaptive Systems Laboratory, University College Dublin, Dublin 4, Ireland
Thomas Brendan Murphy School of Mathematical Sciences & Complex and Adaptive Systems Laboratory, University College Dublin, Dublin 4, Ireland
A mixed membership model is an individual-level mixture model where individuals have partial membership of the profiles that characterize a population. A mixed membership model for rank data is outlined and illustrated through the analysis of voting in the 2002 Irish general election. This particular election uses a voting system called Proportional Representation using a Single Transferable Vote (PR-STV), where voters rank some or all of the candidates in order of preference. The dataset considered consists of all votes in a constituency from the 2002 Irish general election. Interest lies in highlighting distinct voting profiles within the electorate and studying how voters affiliate themselves to these voting profiles. The mixed membership model for rank data is fitted to the voting data and is shown to give a concise and highly interpretable explanation of voting patterns in this election.