Introduction Models Evaluation Conclusion Mergers, Migration, and Signaling ChristopherAhern UniversityofPennsylvania March23,2013 Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 1/36 Introduction Models Evaluation Conclusion Outline 1 Introduction 2 Models 3 Evaluation 4 Conclusion Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 2/36 Introduction Models Evaluation Conclusion Overview Overview Goal Gainabetterunderstandingofsoundchangethroughmathematicalmodeling. Mergers Well-studied. Notablyfreefromsocialawareness. Migration Contact-inducedchangethroughmigration. Mergedspeakersmigrateto non-mergedpopulations. SignalingGames Frameworkforbuildingmodelsofmergers. Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 3/36 Introduction Models Evaluation Conclusion Overview Two Models Cognitive Misunderstandingsbetweenmergedandnon-mergedindividualsdrivethe spreadofthemerger(Herold,1990) Social Accommodationbetweenmergedandnon-mergedindividualsdrivesthe spreadofthemerger(Trudgill,1986) Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 4/36 Introduction Models Evaluation Conclusion Overview Cognitive Mergedspeakerandnon-mergedhearer. Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 5/36 Introduction Models Evaluation Conclusion Overview Social Mergedspeakerandnon-mergedhearer. Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 6/36 Introduction Models Evaluation Conclusion Overview Signaling Games (Lewis, 1969) Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 7/36 Introduction Models Evaluation Conclusion Signaling Games SignalingGame: (cid:104){S,R},T,δ,M,A,U ,U (cid:105) S R Sisthesender,andRisthereceiver. Tisasetofstates δ isaprobabilitydistributionoverthosestates Misasetofmessages Aisasetofactions U andU aretheutilityfunctionsofSandR S R Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 8/36 Introduction Models Evaluation Conclusion Merged speaker (Blue), Non-merged hearer (Red) Merger: A,O→A. δ cot caught S S [kAt] [kOt] [kAt] [kOt] R R R R cot caught cot caught cot caught cot caught 1,1 0,0 1,1 0,0 0,0 1,1 0,0 1,1 Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 9/36 Introduction Models Evaluation Conclusion Cognitive Cognitive Factors Yang(2009) Bulkofmisunderstandingsoccurbetweenmergedspeakersand non-mergedlisteners(Labov,2010). Misunderstandingsleadlistenerstoadjuststrategy. Wecancalculatethefrequencyofthesemisunderstandingsgiven minimalpairwordfrequenciesandvowelconfusabilitymeasures. Ahern(UPENN) Mergers,Migration,andSignaling March23,2013 10/36