Preface Over th e pas t decad e o r so , topic s fro m th e socia l science s hav e graduall y made thei r wa y into a number o f mathematics texts , bot h a t th e secondar y and collegiat e levels . I n college , thes e topic s ar e ofte n taugh t a s a uni t i n a liberal arts mathematics cours e intende d fo r non-mathematic s majors . I n high school, they are used as an exercise in mathematical modeling and prob- lem solving , typicall y i n a wa y tha t directl y addresse s th e NCT M proces s standards o f reasonin g an d proof , communication , connections , an d repre - sentation. Som e college s an d universitie s hav e eve n begu n offerin g entir e semester-length course s devote d t o th e mathematic s o f politic s an d socia l choice. Gran d Valle y Stat e Universit y recentl y adde d suc h a cours e t o it s curriculum, an d thi s book was written i n response to a need create d b y tha t course. Grand Valley' s course , entitle d The Mathematics of Voting and Elec- tions^ i s a junior/senio r leve l cours e aime d a t student s fro m a variet y o f mathematical backgrounds . I t ca n b e take n a s par t o f a student' s gen - eral educatio n requirements , an d it s onl y mathematica l prerequisit e i s th e completion o f a course in the university' s mathematic s foundatio n category , which includes college algebra, liberal arts mathematics, introductory statis - tics, logi c (taugh t b y th e philosoph y department) , an d eve n Visua l Basi c programming. Thi s bein g the case , the audienc e fo r th e cours e i s highly di - verse. I n its initial offering, student s came from a variety of major programs , including accounting , business , compute r science , economics , engineering , English, geography , history , mathematics , philosophy , an d politica l scienc e (all i n a clas s o f onl y 1 7 students!) . A t th e sam e time , a simila r course , but wit h a n audienc e consistin g almos t entirel y o f mathematics majors , wa s taught a t Appalachia n Stat e University . We believe that thi s book is appropriate for both settings. Student s wit h more mathematical training will approach the problems from a different per - spective tha n thos e wh o ar e no t a s mathematicall y inclined . Furthermore , IX
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