ANONYMITY, NEUTRALITY, AND MONOTONICITY 3 takes place . Unlik e a dictatorship , wher e a t leas t th e dictator' s vot e mat - ters, wit h impose d rul e nobody' s vot e matters . Sinc e the winne r i s decide d beforehand, impose d rul e suffer s fro m a differen t proble m tha n a dictator - ship - i t doesn' t trea t al l o f th e candidates equally . I t woul d b e quit e a n understatement t o sa y tha t Dowel l wa s favore d i n th e electio n describe d above i n truth, i t woul d b e impossibl e fo r Dowel l t o lose , even i f everyon e voted fo r Stutzman . Let me make just on e more proposal for deciding the winner of the Stick - eyville mayora l election : Eac h vote r shoul d cas t a ballo t fo r th e candidat e that the y wan t t o wi n th e election . Th e vote s fo r eac h candidat e shoul d then b e counte d an d th e candidat e wit h th e least numbe r o f vote s shoul d be declare d th e winner . (No t surprisingly , thi s metho d i s calle d minorit y rule.) Question 1.4.* Suppos e agai n that al l 101citizens of Stickeyville show u p at the polls, with 100 voting for Dowell and one (Stan ) votin g for Stutzman . Who woul d wi n the electio n unde r th e minorit y rul e method ? Question 1.5. Suppos e tha t Sta n convince s 5 0 o f th e 100 Dowel l voter s to chang e their mind s an d vot e fo r Stutzman . Wh o woul d wi n th e electio n now under minorit y rule ? Question 1.6. Doe s minorit y rul e trea t al l o f th e voter s equally ? Doe s i t treat al l of the candidate s equally ? Explain . Question 1.7. Unde r minorit y rule , i s i t beneficia l o r detrimenta l t o a candidate t o b e awarde d additiona l votes ? Explain . Anonymity, Neutrality , an d Monotonicit y In th e las t section , w e looke d a t thre e differen t method s fo r decidin g th e winner o f th e Stickeyvill e mayora l election . Suc h method s ar e typicall y called voting systems , althoug h it' s importan t t o not e tha t thi s terminol - ogy refer s no t onl y t o th e wa y vote s ar e cas t i n a particula r election , bu t also to th e wa y i n whic h th e winne r o f th e electio n i s determine d fro m th e individual ballots . One wa y t o evaluat e th e fairnes s o f a given votin g syste m i s to identif y certain desirabl e propertie s tha t w e thin k th e syste m shoul d satisfy , an d then se e if it actuall y doe s satisf y thos e properties . Recal l tha t w e did thi s for eac h o f th e thre e votin g system s w e considered i n th e previou s section .
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