 priority of positions for assignment, and 2) another without priority of positions for assignment. As an example of the former, we can picture the election of president, vice president, and secretary when one position is more important than the other(s) or must take office beforehand. As for the latter, we can think about the assignment of positions to players in a team sport, such as being in the far left, in the middle, in the far right, where it makes no sense to compare the relative importance of each position. In the literature on operational research we can find the assignment problem as one in which there is a performance data table among candidates and positions, and only one person, the decision-maker, looks for a solution that maximizes performance.20(pp435-445) However, in this paper we analyze preferences (probability distributions) among the n voters that will make the decision. The approach we develop in Section 4 uses computational simulation to display conditions for the voters' preference distribution that warrant, for each method, that the probability of choosing the best assignment (on the assumption that there is one) approaches 1. When investigating the frequency with which each method chooses the ideal assignment, we assume that assignment to be the one that is objectively correct or more accurate than the alternative options to be voted on. Even though the nature and extent of the collective decision problems in which there is such an assignment are controversial, there is broad agreement in acknowledging that some public problems are of this kind.21(pp38-47) In developing our approach to examine several voters' preference distributions, we assume that we know what the ideal assignment is –actually, we fix it– and then we compare the performance of the methods. However, the ability of the methods to choose the ideal assignment does not require that someone knows which one it is, but only that such an assignment exists and that the voters' preference distribution (even if their preferences are subjective) surpasses a certain competence threshold in identifying it. We will first define the notation that we use to describe the voting methods: • T = {A, B, C}, the set of "candidates". • A "feasible option" will be any vector with one or three components, each component will be a member of T and each member of T will appear at most once. Thus, each voter will approve or reject a feasible option, with the following interpretation: o (α): Indicates that candidate α (with α ∈ T) is being chosen for the first position. o
priority of positions for assignment, and 2) another without priority of position for grant. As an example of the former, we can picture the election of president of the united states, vice president, and repository when one position is more important than the other(s) or must take agency beforehand. As for the latter, we can think about the appointment of positions to players in a team fun, such as being in the far leave, in the middle, in the far right, where it makes no sense to compare the relative importance of each military position. In the literature on operational research we can find the appointment problem as one in which there is a performance data mesa among candidates and positions, and only one person, the decision - maker, look for a solution that maximizes performance.20(pp435 - 445) However, in this paper we analyze preferences (probability distributions) among the n voter that will form the decision. The approach we develop in Section 4 uses computational simulation to display conditions for the voter' predilection distribution that warrant, for each method, that the probability of choosing the good assignment (on the assumption that there is one) approach 1. When investigating the frequency with which each method chooses the ideal assignment, we wear that assignment to be the one that is objectively correct or more accurate than the alternative options to be voted on. Even though the nature and extent of the collective decisiveness problems in which there is such an assignment are controversial, there is broad agreement in acknowledging that some public problems are of this kind.21(pp38 - 47) In develop our approach to examine several voters' preference distribution, we assume that we know what the ideal assignment is – actually, we specify it – and then we compare the performance of the methods. However, the ability of the methods to choose the ideal assignment does not want that someone knows which one it is, but entirely that such an assignment exists and that the voter' preference distribution (even if their preferences are subjective) surpasses a sealed competence threshold in identifying it. We will foremost define the notation that we use to describe the voting method acting: • T = { A, B, C }, the set of " candidates ". • A " feasible option " will be any vector with one or three components, each component will be a member of T and each member of T will appear at most once. therefore, each voter will approve or reject a feasible option, with the following rendition: o (α ): Indicates that candidate α (with α ∈ T) is being choose for the first position. o
 prlority of positions for xssignment, and 2) anothec withoht priorkty of positions for assignmxnt. Qs an example of the former, we can ppcture thw eltction of presideif, vice ixesidskt, anb wecretary when one posithon is more im[oftcnt than the other(s) or must take offyce befprfhand. As for tre lseter, we can think about the assignment of posptions to players in a team sport, such as bfing in the far left, ij the middlg, in rhe far righg, where it makes no sehse to compare the relative impurtanee of each koaihhon. In the oiterwture on opevstionan reseatch we can finc tie awsignment problem as mne in which there is a perxoxmance data table amobg candhdatas ave pusiuiois, znd onpy kne person, the decisiin-maker, looks for a sjoution that mzximizqs performance.20(pp435-445) However, in this paper we anzlyze preferences (probavility distributions) wmong the n voters that will make the decision. The approacv we vexelip kb Dection 4 uses computational simulation to dis[mau bonditions for thc voters' preferencr fixjribution that warrauf, ror each method, thwt the krobabulity of shooxing the best assignment (on the assumptpon rhat there is one) cpproaches 1. Chen imvestogating the frequency wnth whjch each mehhod chooads the ideal asskgnkett, we assume that assignmegt to be vhe oue that ks onjectidely correft or more accurate than the cltertative optlons to be voted on. Even though the nature anc axtvnt of thz collcctive decision problems in wkich thexe is ruch an asaignmenv are controdersial, there ls broad agrxement in ackbowlwdging gfat some publiv problems are of tyis kind.21(pp38-47) In devekopkhg our approach to examine severak vutews' pceferqtce distribudionr, wd assuoe that we jvow ehat the ideal assigtmenf is –actually, we fox it– and jhen we cjmpare the petformance of the mtthods. Hoxever, yhe ability of the methods to chokse the ifeaj assignment doew not requirz that someone knows which one it is, but only that such an assignment exists cnc that the toters' preferenwe distribution (even if their preferekces are subjective) sudpassev a cfrtain competence threshold in identifying it. We will first define the noration that we use to cescrpbe che votyng lxthods: • T = {A, B, C}, nhe set of "candidates". • A "feasiblx option" whlj be any vector with one or yhfee componentr, each component will be a membet of T and each member of T wilk appear at most once. Thms, each viter sill aikrote or reject a feasinle opcion, wuth the folpowing interpfetstlon: o (α): Indlcatts tkat candidate α (with α ∈ T) is being xhosen flr the first posmtion. o
priority of positions for assignment, and 2) priority positions for As an example picture election of president, president, and secretary one position is more important than other(s) or must take office beforehand. As for the latter, we can think the assignment of positions to players in a team sport, such as being the left, the in the far right, where it makes no sense to compare the relative importance of each In the literature on operational research we can the assignment problem as in which there is a data among candidates positions, only person, the decision-maker, for a solution that maximizes performance.20(pp435-445) However, in this paper we analyze preferences (probability distributions) among the voters that the decision. approach develop Section 4 uses to display conditions for the voters' warrant, for each method, that the probability of the best (on the assumption that there is approaches 1. When investigating the frequency with which method chooses the ideal assignment, we assume that assignment to be the one that is or more accurate than alternative options to voted Even the and extent the collective decision problems in which there is such an assignment controversial, there is broad agreement in acknowledging that some public of kind.21(pp38-47) In developing approach to examine several preference we assume that we the assignment fix and we compare the performance the methods. However, the ability the methods to choose require that someone knows which one it is, only that such an assignment exists and the voters' preference distribution (even if their preferences are subjective) surpasses a competence threshold it. We will first define the notation that use to describe the methods: • T = {A, B, C}, the set "candidates". A "feasible will be any with one or components, each component a member T each will appear at most once. Thus, voter approve or reject a feasible with interpretation: o (α): Indicates that candidate α (with α ∈ T) is being chosen for position. o
 priority of positions for assIgnment, and 2) AnothEr wIthOuT priOritY of positions foR AssiGnment. As an example of the FormeR, wE Can pICtUre thE electiON oF PResIdEnT, viCe PReSidenT, anD secretAry when one PosItIon is more impORtAnt than the OthEr(s) or must takE ofFice beFoRehANd. As fOr tHe latTer, we cAN think About the aSsIGnment OF positiONS tO plaYers in a team sport, sUCh AS being in the far Left, in ThE MiDDLe, iN thE far right, wHeRe it mAKes no seNSe TO COmpARe the relative Importance oF EacH positIoN. In THe liteRaturE oN OpeRational resEarcH we can finD the asSIgnment PRoblem aS one in WhiCh tHere IS a PeRfoRmANce DAtA taBLe aMong candIdAtEs and PosiTIONS, and OnlY one PersoN, the decision-mAkeR, looKS foR a solUtion That MaXimizEs perfOrmanCe.20(Pp435-445) However, in this PapeR we analyzE prEfEreNcEs (proBAbilitY diStrIbutionS) among tHE n vOtERS ThAt will make the decisIoN. tHe Approach We deveLOp In sEction 4 usEs ComPutaTIOnal sImulATiOn to dispLay conDItIoNs for thE vOters' pReFerEncE distRIbutIon thaT warrant, For eaCH method, that the PRobability of cHOoSINg THe beSt aSsignment (on The aSSumpTion THaT thERe is oNe) appRoAChES 1. When investigating tHe FrequeNcy wiTh which each meThod chooseS THE ideal asSignMEnT, We assume that asSignmEnt to be the ONe that is ObjecTively coRrect or moRE Accurate ThaN thE alTerNATiVe options to be VOTed oN. EVen thouGh tHe naturE anD exTenT of ThE collectiVe decisiOn PrObLeMs iN whicH There is sUcH an AsSigNment ARe contRoverSial, ThErE Is bRoad agrEEmENT in aCkNoWledGinG tHat soMe puBLic ProblemS are of thiS kiND.21(pp38-47) IN dEvEloping Our approach to ExAmine severAl VotErs' preFERence disTributions, we assume that wE Know whaT thE ideaL assIgnment is –ActUally, wE fiX It– and tHen we cOmparE tHe pERFormaNCE oF thE mEthods. HoweVER, thE abilItY of tHe methoDs to choose the ideal ASsiGnment does not ReqUire THAt SomEOnE KnoWs WHicH ONe it is, but only thAt such an asSiGNmEnt exists aND thAt The voteRs' prefeRence DIstribuTion (even iF their preFeRencES Are Subjective) SurpasseS a certain COmpetENcE threShoLd in idEnTifYing iT. We wilL FirSt defIne the NoTation That wE uSe to descRibe the voting methods: • T = {A, B, c}, the seT of "caNdiDates". • A "feaSibLE opTion" will bE any Vector with One Or tHree cOmpONents, Each COmPonENt wilL be a MEmber of T aND eAch MEMbEr of T will apPEAR at Most oNce. tHus, eacH votEr will approve or reJEct a feasible opTion, WITh tHe fOLlowInG interpretatioN: o (α): inDICates thaT cAndidate α (wiTh α ∈ T) is beInG ChoseN for thE first PositioN. O
 priority of positions for  assignmen t, an d 2 ) a no ther  wit hout priorityo f po sitions for assignment . Asan exam p le  of t he form e r, w e c an  p ict ur e  t he el ect ion ofpresident,  vi ce  president,a nd  secretary  wh en one posit ion  is mo re  im p ortan t t han t he oth e r(s) o r must ta ke office beforeh a n d.  Asfor the latter, w e  c a n think aboutthe as si g nm e n t o f p ositions t oplaye r s in at ea m s por t , such as bei ng in the f a r l eft, i nthe middle , inth e  fa r right, wh ereit makesno sen s e to co m pare th e rela tiv e i mpor t an ce  of  e a chp os iti o n.In the l it er ature  ono p e r atio nal  res earch  we can findthe  ass i gnm ent p roble m as  o ne in  which  ther eis a performanc e da ta tableamo ng  ca nd idate s  and p osi tio ns, and  only o n e p er s o n ,the decision-maker ,l o ok s for asoluti o nth a t maximi ze s p erfo r m ance. 20(p p 43 5-445) H owever ,  i nthis pa pe r we a na lyz e p refer e nces  (prob abilitydistr i butions) among the n voterst ha t wi l l ma kethe decisio n. T h e ap proa c hwed evelo p inSe c ti o n 4 uses computatio na l simu latio n to displayconditions f o r the vo ters '  p r eference distr ibuti on that wa r rant, fo r eac h method , that th e probabil ity  of  ch oos i n gthe best assi g n ment  ( on theass umption  th atthe reis  one) app roaches1.  W he ninv estig a ting the  f req ue ncy  with whicheachmeth od  c h oos es thei de a l  ass ig nm ent,  we  a ssume  tha t  as signmen t to be t heo ne t ha tis obje ctively corre ct  or more a cc ura te tha n the alte rnative options to be v o ted on.  Ev en th ough  the natu reand ex ten t  of th e coll ectiv edec i s ion p r o bl ems  i n which th e r e i s suc han a ssignme nt are controversi a l,there is broa d a gree m e nt  in ac k now le d gin g that some publi c problems  a r eof this ki n d.2 1( pp38-47 ) In de velop i ng ourapproachto examin eseve r a l v oters' pre ferencedistribut i ons,w eassum e t hat we  k now  what  the i d eal  assi gnment  i s –act ually ,we fix i t– and then we comparethe pe rform anc e of themet h ods . However , th e abilityofthe  meth ods to ch oose th e i d eal a ssig n ment does no t r e q ui re that som e o n e k nowswhi c h oneit i s, but only thats uch an assignm ente x ist s a n d th at  the voters' p ref er e n ce distr ib ution (even  if thei rp refer encesare su bjectiv e )  s u rpasse s acer tain comp ete nc e  thresh ol di n iden tify in g it.We wil l  fir s t  define the nota tiont h at we use  to d es cribe t h e vo ting metho ds: • T = { A, B,C},the s et of " ca ndidat es" .• A "feasi b le option " wil l be an yvect orwith o ne o r three  com po nen ts, eachc o mp o ne nt wil l be  a me mb er o f T and e a ch membe r o f  T will  a ppe a r  at mo s to n ce. Thus,eac h vot e r  will appr o ve o r  r e jecta feas ible o ption,w ith  t he foll owi n g  interpre tation: o (α) :Indi cates th at  can di dat eα (with α ∈ T)is being  chosenf o r thefir s t po s ition.  o 
 priority_of positions_for assignment, and 2)_another without_priority_of positions_for_assignment. As an_example of the_former, we can picture_the election of_president,_vice president, and secretary when one position is more important than the other(s) or_must_take office_beforehand._As_for the latter, we can_think about the assignment of_positions to_players in a team sport, such as being_in_the far left,_in the middle, in the far right, where it_makes no sense to compare the_relative importance of_each_position._In the literature on_operational research we can find the_assignment problem as one in which_there is a performance data table among_candidates and positions, and only one_person, the decision-maker, looks for_a solution_that maximizes performance.20(pp435-445) However, in_this paper we_analyze preferences_(probability distributions) among_the n voters that will make_the decision. The_approach we develop in Section 4_uses_computational simulation to_display_conditions_for the_voters' preference distribution_that_warrant, for_each_method, that the probability of choosing_the_best assignment (on the assumption that there_is one) approaches 1._When_investigating the frequency with_which each method chooses the_ideal assignment, we assume that assignment_to be_the one_that is objectively correct or more accurate than the alternative options_to be voted on. Even though_the nature and extent_of the_collective_decision problems in_which_there is_such an assignment are controversial, there is_broad agreement_in acknowledging that some public problems_are of this kind.21(pp38-47)_In_developing our approach to examine several_voters' preference distributions, we assume that_we know what the ideal_assignment_is_–actually, we fix it– and_then we compare the performance of_the methods. However,_the ability of the methods to choose_the_ideal assignment does not require that_someone_knows which one it is, but_only_that_such an assignment exists and_that the voters' preference distribution (even_if their preferences are subjective) surpasses a certain competence_threshold in identifying_it. We will first define_the_notation_that we use to describe the voting methods: • T_= {A,_B, C}, the_set of "candidates". • A "feasible option" will be any_vector with one or three components, each_component will be a member of T and each member of_T will appear at most once. Thus, each_voter will approve or reject a feasible_option, with the following_interpretation:_o (α): Indicates that candidate α (with_α_∈_T)_is being chosen_for the first_position. o