 population grows. (3) Fast-rate convergence. The method's ability to arrive at the ideal outcome has a fast rate convergence to 1 (it does not require a very large population). This criterion provides a further refinement on Convergence to optimum. It offers a comparative basis to acknowledge when a voting method is better at capitalizing the initial reliability of the preference distribution than others. (4) Initial low competence. The initial competence of the voting population to ensure that their collective output matches the ideal outcome converging to 1 is less demanding than that of alternative voting methods. This criterion is also a refinement on Convergence to optimum. It allows to compare the initial threshold of competence required for the group to improve on the average voter. (5) Constant behavior. The probabilistic results of applying the same method to the same initial values are consistent on many trials. This is to ensure that the qualities praised by the aforementioned criteria are not merely random results. How do the voting methods we described in Section 2 perform according to these criteria? 4 Comparing voting methods through simulations In order to illustrate these criteria of assessment, we ran simulations in MATLAB of the voting methods for the decision problem described in Section 2. Here is an outline of how our simulations worked. 4.1 General settings and procedure Different sizes for a population can be specified. For each simulation, a population ranging from 1 to n individuals is selected. A random number corresponding to one of the six possible ticket choices is assigned to every individual, according to the intended proportions. Assuming voter competence, the ideal ticket is always assigned as a default to a greater number of individuals. If the outcome of the voting procedure matches the ideal ticket, the simulation is deemed to be successful. In order to assess the procedures according to their instrumental epistemic value, we assume that there is an ideal ticket. Without loss of generality, we always assume that (A, B, C) is the ideal assignment ‒but only a percentage of the population knows it; alternatively, the general population is reliable tracking that ideal assignment up to a certain degree. Then, we run computer simulations of the voting methods. Each voting procedure is repeated in k FI NA L DR AF T 10 iterations for each population of n individuals, preserving the intended proportions. In our experiment, we always used 100 iterations of each procedure. The probability of choosing the ideal ticket for each population of n individuals is determined as the ratio of successful outcomes divided by the total number of iterations. A selection performance curve is then drawn with the ordered pairs (n, Pw
population grows. (3) Fast - rate convergence. The method acting's ability to arrive at the ideal result has a fast pace convergence to 1 (it does not want a very large population). This criterion leave a further refinement on Convergence to optimum. It offers a relative footing to acknowledge when a voting method acting is better at capitalizing the initial dependability of the preference distribution than others. (4) Initial low competence. The initial competence of the voting population to ensure that their collective output matches the ideal result converging to 1 is less demanding than that of alternative voting method acting. This criterion is also a refinement on Convergence to optimum. It allows to compare the initial doorway of competence required for the group to improve on the average voter. (5) Constant behavior. The probabilistic result of applying the same method to the same initial values are consistent on many trials. This is to ensure that the qualities praised by the aforementioned criteria are not merely random results. How do the voting methods we described in part 2 perform according to these criteria? 4 compare vote method acting through simulations In order to exemplify these criteria of appraisal, we ran simulations in MATLAB of the vote methods for the decision problem described in Section 2. Here is an outline of how our simulations worked. 4.1 General settings and procedure Different sizes for a population can be assign. For each simulation, a population range from 1 to n individuals is selected. A random number corresponding to one of the six possible tag choices is assigned to every individual, harmonize to the intended proportions. Assuming voter competence, the ideal ticket is constantly assigned as a default option to a greater number of person. If the outcome of the vote procedure matches the ideal ticket, the simulation is deem to be successful. In order to assess the procedures accord to their instrumental epistemic value, we bear that there is an ideal slate. Without loss of generality, we always assume that (A, B, C) is the ideal grant ‒but only a percentage of the population know it; alternatively, the general population is reliable tracking that ideal assignment up to a certain degree. Then, we prevail computer simulations of the voting methods. Each voting procedure is repeat in k FI NA L DR AF T 10 iteration for each population of nitrogen individuals, preserving the intended proportions. In our experiment, we always used 100 iteration of each procedure. The probability of choosing the ideal ticket for each population of n individual is determined as the ratio of successful outcomes divided by the total issue of iterations. A selection performance bend is then drawn with the ordered pair (n, Pw
 pooulation grows. (3) Fast-rate convergence. Thg nethod'v abiljty to afrive at the ideal outcome hes a fast rate convergence to 1 (kt does nlt requiee a cery large populatljn). Tgls crntxrion provides s further sefinement on Wovvzrgence to optimum. It offers a compawative nadis to acknowlgdge eren z voting method is better at capitzlizing the initial teliability of the preferejce fistribution than lthers. (4) Inijjal oow competenze. The iniuicl competende of the voting population to dnsurz that theit dopnective out'ut manches the ideal outcoke convrrging to 1 is kesv dwmanding than that of alternative votind methods. Tkis criterion is also a refitemett ov Covvedgxncs to ootijum. It allkws to compqre the initial thrtshjod of competehce rezuyred for the group to improve on the avtrage voter. (5) Constant behaviir. The probabilistic tesults of applying the same method to the same initial valges ace couwistevr ln many trials. This is to ensure that the quajjtoex praised by tme aforementioned vrltrtia are not metely rausoj results. How do tje votigg merhods we qesctibed in Section 2 perform axcording to nhesw criteria? 4 Comparnng voting mzthods throigh simulations In ordex to imlustrate tjese critsfia of assessmeng, wv rat simulaukons in MATLAB of the votiig mechods fof thg decisyon problel desgsibed in Section 2. Jere ns an outline ov how our simulations worked. 4.1 Gxieral settingx dnd proceduxe Difnerent sizes fow a population can be speckfied. For vach simunation, a po[ulation ranghjg from 1 to i individtals is welectea. A random numbrr corresiouding to ine of the six posxibus ticket choicew iw assigned to eferh igdpvivual, wwcording to dhe kntdmded oroportions. Xssuking voter competenca, ths ideal ticket is slrays assugned as a default to a greater number lf invividuels. If thg outcome of the voting procedude matched tme ideal tickqt, tme symulation ns deemed to be successful. In order to awsess the procedutes according to theit ikstrumental xpisteiic value, we assume that therw is an ideal ticlet. Without loss of gsneralhty, wf always assume that (A, B, C) is the ideal assignment ‒but only a percentage if the population inowx it; dlceruativelr, thx jeneral populatiom is reliable tracking that ideel assignmanc up to a certain degree. Then, wd run computet simulations of the votinf methodx. Each voting procedure is repested in k FI NA L DR AF B 10 iteratuons ror eabg 'opulation of n indifidualv, prewerving the intended proooryilns. In oug exkerijent, we always used 100 iterations if eacy orocedure. The prmbability on ghoosihg the ideal ticket fod eadj popolation of n imdividuals is cetermined as the ranio of successful kutcomes divoded by the total nnmber of itesations. A selection performance curve is then drawn with the ordered 'airs (n, Pw
population grows. (3) Fast-rate convergence. The method's arrive the ideal has a fast does require a very population). This criterion a further refinement on Convergence to It offers a comparative basis to acknowledge when a voting method is better capitalizing the initial reliability of the preference distribution than others. (4) Initial low The competence the population to ensure that their collective output matches the ideal outcome converging to 1 is less than that of alternative voting methods. This criterion also a refinement on to optimum. It allows to the threshold of required the to improve on average voter. (5) Constant behavior. The probabilistic results of applying the same method to the same initial are consistent trials. This to that qualities praised by criteria are not merely random results. voting methods we described in Section 2 perform to these 4 Comparing voting methods through simulations order to illustrate these criteria of assessment, we simulations in MATLAB of the voting methods for the decision problem described in Section 2. an outline of how simulations worked. 4.1 settings procedure sizes a population be specified. For each simulation, a population ranging from 1 to individuals is selected. A random number corresponding to one of possible choices is assigned every individual, according to intended Assuming voter competence, the is assigned to greater of individuals. If the of the voting procedure matches ideal ticket, the simulation In order to assess the procedures according to instrumental epistemic value, we assume that there an ideal ticket. Without loss of generality, we always assume that (A, C) is assignment ‒but only a percentage of the population it; alternatively, the general is reliable tracking that ideal assignment up to a degree. we run simulations of the methods. Each voting is repeated in NA L AF 10 population of n individuals, preserving the proportions. our experiment, we always used iterations procedure. The probability of choosing the ideal ticket for each population of n individuals is the ratio of successful divided the total number of iterations. A selection performance curve is then drawn ordered pairs (n,
 population grows. (3) Fast-rate coNvergence. THe metHod'S abIlIty tO arrIve at the ideal oUTcomE has a fast rate convergenCe to 1 (iT dOEs noT ReQuire A very laRGe POPulAtIoN). ThIs CRiTerioN prOvides a Further refIneMeNt on ConvergeNCe To optimum. IT ofFers a comparaTivE basis To AckNOwledGe wHen a vOting mEThod is Better at cApITaliziNG the iniTIAl ReliAbility of the prefeREnCE distribution tHan othErS. (4) inITIal Low Competence. thE initIAl compeTEnCE OF thE Voting populatIon to ensure THat Their cOlLecTIve outPut maTcHEs tHe ideal outcOme cOnverging To 1 is leSS demandINg than tHat of aLteRnaTive VOtInG meThODs. THIs CriTEriOn is also A rEfInemeNt on cONVErgeNce To opTimum. it allows to comParE the INitIal thReshoLd of CoMpeteNce reqUired FoR the group to imprOve oN the averaGe vOtEr. (5) COnStant BEhavioR. ThE prObabiliStic resULts Of APPLyIng the same method to ThE SAmE initial Values ARe CoNSistent oN mAny TriaLS. this iS to eNSuRe that thE qualiTIeS pRaised bY tHe aforEmEntIonEd criTEria Are not Merely raNdom rESults. How do the vOTing methods we DEsCRIbED in SEctIon 2 perform aCcorDIng tO theSE cRitERia? 4 CoMpariNg VOtINg methods through simUlAtions in ordEr to illustratE these critERIA of assesSmenT, We RAn simulations iN MATLaB of the votINg methodS for tHe decisiOn problem DEScribed iN SeCtiOn 2. HEre IS An Outline of how oUR SimuLaTions woRkeD. 4.1 GeneraL seTtiNgs And PrOcedure DiFferent sIzEs FoR a PopUlatiON can be spEcIfiEd. for Each sIMulatiOn, a poPulaTiOn RAngIng from 1 TO n INDiviDuAlS is sEleCtEd. A raNdom NUmbEr correSponding tO onE Of thE sIx PossiblE ticket choiceS iS assigned tO eVerY indivIDUal, accorDing to the intended proporTIons. AssUmiNg votEr coMpetence, tHe iDeal tiCkeT Is alwaYs assiGned aS a DefAULt to a GREaTer NuMber of indiVIDuaLs. If tHe OutcOme of thE voting procedure maTCheS the ideal tickEt, tHe siMULaTioN Is DEemEd TO be SUCcessful. In order To assess thE pROcEdures accoRDinG tO their iNstrumeNtal ePIstemic Value, we asSume that tHeRe is AN IdeAl ticket. WiThout losS of generaLIty, we ALwAys asSumE that (A, b, C) Is tHe ideAl assiGNmeNt ‒but Only a pErCentagE of thE pOpulatioN knows it; alternatively, thE generAl popUlaTion is relIabLE trAcking thaT ideAl assignmeNt uP to A certAin DEgree. then, WE rUn cOMputeR simULations of THe VotING mEthods. Each vOTINg pRocedUre IS repeaTed iN k FI NA L DR AF T 10 iteraTIons for each popUlatION of N inDIvidUaLs, preserving thE inTeNDEd proporTiOns. In our expEriment, wE aLWays uSed 100 iteRationS of each PROcEDure. ThE proBabIlity of chOosInG The ideaL tIcKEt for eAch pOpUlatioN of n inDIvidUALs is determined as The raTIO of suCCesSful oUtComes diVIded By the total Number of iteRationS. A seLectiOn perfoRmAnce cuRve Is Then drawn wITh the ordeRed paIrs (n, Pw
 population grows. (3) Fas t-rate con verge nce . T he  met hod' s ability to a r rive  at the ideal outcomehas a  f a st r a te  conv ergence to 1  (i tdo esno t  r equir e a  very l arge popul ati on ). This crit e ri on provide s a  further ref ine ment o nCon v ergen ceto op timum. It off ers a com pa r ativeb asis to a ck nowl edge when a votin g  m e thod is better  at ca pi t al i z ing  th e initialre liabi l ity oft he p r efe r ence distribu tion than o t her s. (4)  I nit i al low  comp et e nce . The initi al c ompetence  of th e  voting populat ion to  en sur e th a tth eir  c o lle c ti veo utp ut match es  t he id ealo u t c omecon verg ing t o 1 is less d ema ndin g  th an th at of  alt er nativ e voti ng me th ods. This crite rion  is alsoa r ef ine me nt on Conver gen ceto opti mum. It all ow s t ocompare the initia lt h re shold of  compe t en ce required  f ortheg r oup t o im p ro ve on th e aver a ge  v oter. ( 5)  Const an t b eha vior. Theprobab ilisticresul t s of applyingt he same metho d  t o th e  sam e i nitial valu es a r e co nsis t en t o n  many  tria ls .  T h is is to ensure tha tthe qu aliti es praised by  the afore m e n tioned c rite r ia are not merely  rand om results .  How dothe v oting me thods wed e scribedinSec tio n 2 p er form accordin g to t he se crit eri a? 4 Co mpa rin g v oti ng  methodsthroughsi mu la ti ons  In o r der to i ll ust ra tethese criter ia of  ass es sm e nt,  we ran si m u lati on sin M ATL AB  of t he v o tin g metho ds for th e d e cisi on  p roblemdescribed inSe ction 2. H er e i s an o u t line ofhow our simulations wor k ed. 4.1  Ge neral  set tings and  pr ocedur e D i fferen t size s for  a  po p u latio n ca n b especified. F oreachsi mula tion, a  population rangin g  fr om 1 to n ind ivi dual s is  se l ec t ed.  A ran d o m number corres ponding to  o n eof the six pos si ble tic ket cho icesi s assig ned to ev ery indiv id ual, a cco rding to t he inten ded propo r tions .  A ssumi ngvoterco mpe tence , thei dea l tic ket is  a lwaysassig ne d as a d efault to a greater num ber of  indi vid uals. Ifthe out come of t he v oting proc edu rematch est he id ealt ic ket ,  thesimu l ation isd ee med t obe successf u l .  In  orde r t o  asses s th e procedures acco r ding to theirinst r u men tal epis te mic value, weass um e that the re  is an idea l ticket .W ithou t loss  of ge neralit y ,  w e  alway s as sum e that (A , B ,C ) is th eid e al ass ignm en t ‒but  onlya  per c e ntage of the pop ulati o n  know s  it ; alt er nativel y , th e generalpopulationis rel iabl e tra cking t ha t idea l a ss ignment up to a cert ain d egree.Th en,werun co mput e r  simu lati on s o f the vot i n gm et ho d s.Each  voti ng  pro cedure is repeated  in k FI NA  L  DR A F T 10 it e r ations for  ea ch po p u lation ofn  ind i vi d uals,  prese rvingthe int e nde dproport ion s .  In our e xperiment ,  we  a lway s used 1 00  ite ra tio ns  of each proced ure. The  probabi l i ty ofcho o sing the id ea l ticket for  each  p o pulatio n ofn indiv i dua lsisdete rmi neda s the ratio of successfu l ou tcome s  di vided  by t he  total n u mber  of iter a tions. A sele ction performan c e c u rveist he ndrawn wit h t h e ord ered  pa irs(n,  Pw
 population_grows. (3)_Fast-rate convergence. The method's_ability to_arrive_at the_ideal_outcome has a_fast rate convergence_to 1 (it does_not require a_very_large population). This criterion provides a further refinement on Convergence to optimum. It offers_a_comparative basis_to_acknowledge_when a voting method is_better at capitalizing the initial_reliability of_the preference distribution than others. (4) Initial low_competence._The initial competence_of the voting population to ensure that their collective_output matches the ideal outcome converging_to 1 is_less_demanding_than that of alternative_voting methods. This criterion is also_a refinement on Convergence to optimum._It allows to compare the initial threshold_of competence required for the group_to improve on the average_voter. (5)_Constant behavior. The probabilistic results_of applying the_same method_to the same_initial values are consistent on many_trials. This is_to ensure that the qualities praised_by_the aforementioned criteria_are_not_merely random_results. How do_the_voting methods_we_described in Section 2 perform according_to_these criteria? 4 Comparing voting methods through_simulations In order to_illustrate_these criteria of assessment,_we ran simulations in MATLAB_of the voting methods for the_decision problem_described in_Section 2. Here is an outline of how our simulations worked._4.1 General settings and procedure Different_sizes for a population_can be_specified._For each simulation,_a_population ranging_from 1 to n individuals is selected._A random_number corresponding to one of the_six possible ticket choices_is_assigned to every individual, according to_the intended proportions. Assuming voter competence,_the ideal ticket is always_assigned_as_a default to a greater_number of individuals. If the outcome_of the voting_procedure matches the ideal ticket, the simulation_is_deemed to be successful. In order_to_assess the procedures according to their_instrumental_epistemic_value, we assume that there_is an ideal ticket. Without loss_of generality, we always assume that (A, B, C)_is the ideal_assignment ‒but only a percentage_of_the_population knows it; alternatively, the general population is reliable tracking_that ideal_assignment up to_a certain degree. Then, we run computer simulations of the_voting methods. Each voting procedure is repeated_in k FI NA L DR AF T 10 iterations for_each population of n individuals, preserving the intended_proportions. In our experiment, we always used_100 iterations of each_procedure._The probability of choosing the ideal ticket_for_each_population_of n individuals_is determined as_the ratio of_successful outcomes_divided by the_total number_of iterations. A_selection_performance curve is then drawn with the ordered pairs (n, Pw