Question

Due to a budget problem, a committee is recommending to the school board ways to reduce expenses. The options are A, reduce sports programs; B, reduce fin preference table to determine the choice that the committee recommends using the plurality-with-elimination method. Then determine whether Condorcet's criteri Which option is selected using the plurality-with-elimination method? B OD ОА С Using Condorcet's criterion, which option is selected? O A D ОВ, А Ос. с ODB

Answer 1

A Sieppsose due to budget problem, a committee is recomending to school board ways to reduce expensest reduce sport programs Ba reduce fine arts programs increases class size D - defer maintenance on building tale prefrence table to determine choice of Commitee that should be recommended Number of ballots preference 9 ist с A B second A third B fourth Use 13 4 3 L 3 с A А В B с D B A Ac D O By Plurality method with elimination method total votes 9+13+4 +3+3+1 = 33 Majority = total votes - 16.5 → a 2 --- 17 voter needs to been win by this method Now с D 34356 В has 944=13 first place roter has 13 first place votes A has forst place votes hast first place vote. Eliminate By Plurrality with elimination method, elimintate comme thee with leash vote commette B95 eliminated Above table become,

Number of ballats Preference ។ 13 4 3 3 - Bedsrus LSE с D c A A 0 1 2nd A A bo 3rd ath D C This become D CA A CDD 13 4. 3 3 1 Prefrence LSE second D A A D tuad А. D А third D A one A has 6 first place whes eliminate c has at 94 =18 finot place voles D har 13 host place votes None of get majority So eliminate commette co with kast vote table become Number of ballots no. of ballots 4 prefience g 13 4 3 D Prefrence 9 13 3 3 3 28€ C c ISE C C D C s and Luio D о с D and Iu 3rd C 6D has 13+3 =16 first place votes has 9+4+3+1 = 17 first place voter c got majority By Plurality with elimination method, comme tee should recomend By Condorcef criterion - We compare every two commette separately & eliminate other two commetter

A versus B Celiminate Go) 2 Preference 33 13 v g Preference 13 - 4 3 3 B A А A A B LBL B AA ABIB A B B A A second B B LSE and 3rd 4th В B A А 9+13+ 3+3+= 28 votes A has B has 4+1 = 5 votes coins -. A rers us C. & fill empty places B & D Eliminate every entry of by lower entries of B &D Prefrence 4 3 13 3 A А U A LSL olut с A A A с and has U sk has gfhfls 14 first place roter 19 fost place votes La coing 13 + 373 versus & fill empty places by D Eliminate every entry of B &D lower entrier of A &C Preference 13 3 LSE D D A second A D g 4 3 А A D ch A og +3+3+1 has has is first place votes first place voter D 13+4=17 D wins B versus D Eliminate every entry power entries of of A&C and fill empty places by B&D

B Versus Eliminate D every entry entries of of A&C and fill empty places by louar B & D Preference 3 13 4 3 3 ISh B D B B 3 D D D B B 2nd D - B has 9+4+3+1 F 17 first place votes P has 1 3-3 Pirst place voter B wins B Versus с Eliminate erery entry of A&D, fill empty places by lower entries of B &C Preference g 13 4 3 3 1 B B B З LSE end U♡ с B с --- B has 13 +3 + 3+1 2o first place voter gth=13 first place vote's (3 coins c versus Eliminate every entry of A & B & fill empty places by lower entries of C&D preference 4 3 13 D с C Isk and Gle C c has D har gta + 3+1 -17 first place voter 13+3 c6 first place notes Ć wins حامي A :. two times & B win two times But A war prefered orer B commettee A should be recommed by this method