 from this it could be argued that "the computational experiment (...) offers no support for the social applications proposed by the authors".29(p1025) Although there is a kernel of truth in this concern, our approach might withstand such setback by recognizing such concern as the inevitable result of using idealization to formally represent complex phenomena. This commonly occurs in mathematical practice, and it also has widely acknowledged remedies: we can explore several extensions and alternatives to the original setting. Nonetheless, when the aim is to apply the results outside of the Math Lab, some cautionary warning and a reminder of this is always advisable. Although we address an aspect of this in (e), below, it is important to keep in mind that our assessment criteria are not primarily meant to be used as a descriptive tool for predicting voting behavior, but rather as providing insights into the optimality of the voting methods themselves. (b) The procedure for assessing voting methods here outlined is not exhaustive. As the remarks on Section 3 concerning the number of voting methods make plain, there remains a vast uncharted territory of non-explored voting methods. In fact, when we designed our example, there were several brainstorming meetings to propose alternative voting methods to compete. Our proposal provides some insight on how well a voting method performs, conditional on there being "well-behaved" methods in our initial pool for assessment. Using this procedure does not warrant that the best method will be selected. But this should not overshadow some remarkable qualities of our criteria for assessment. First, the methodology we outlined does identify non-comparative traits of some "good" voting methods, provided they are considered for assessment. That task is performed by our criteria of Triviality validation, Convergence to optimum and Constant behavior. In addition, there are other criteria that allow for comparative assessment. While this comparison must be made considering a small number of methods, it could prove useful. Finally, although the procedure of assessment is contingent on conceivable voting methods, there is a pragmatic requirement that would probably discard "unimaginable" voting methods. In order to be incorporated in a democratic society, a voting method should be "transparent". In this sense, its details should be easily explainable to the voting population; otherwise, the method could be construed as a black box that does not accurately reflect the views of the overall group. FI NA L DR AF T 17 (c) Some simulations require additional information than that of (initial) competence and aggregation function. In order to compare the performance
from this it could be argued that " the computational experiment (...) offers no support for the social applications aim by the authors".29(p1025) Although there be a kernel of truth in this concern, our approach might resist such setback by recognizing such business as the inevitable result of using idealization to formally represent complex phenomenon. This commonly occurs in numerical practice, and it also has widely acknowledged redress: we can explore several extensions and alternatives to the original setting. however, when the aim is to apply the results outside of the Math Lab, some admonitory warning and a reminder of this is always advisable. Although we address an aspect of this in (vitamin e), below, it is important to keep in mind that our assessment standard are not primarily meant to be used as a descriptive tool for predicting voting behavior, but rather as providing insights into the optimality of the voting methods themselves. (b) The procedure for assessing voting methods here outlined is not exhaustive. As the remark on Section 3 concerning the issue of vote method acting make plain, there remain a vast uncharted territory of non - explored voting method. In fact, when we designed our example, there were several brainstorming meetings to propose alternate voting methods to compete. Our proposal provides some insight on how well a voting method perform, conditional on there being " well - behaved " methods in our initial pool for assessment. practice this procedure does not warrant that the best method will be selected. But this should not overshadow some remarkable qualities of our criterion for assessment. foremost, the methodology we outlined does identify non - comparative traits of some " good " vote methods, provided they are considered for assessment. That job is performed by our criteria of Triviality validation, Convergence to optimum and Constant demeanor. In addition, there are other criterion that allow for comparative assessment. While this comparison must be made considering a minor number of methods, it could raise useful. Finally, although the routine of assessment is contingent on conceivable voting methods, there be a pragmatic requirement that would probably discard " unimaginable " voting methods. In ordering to be incorporate in a democratic club, a voting method should be " transparent ". In this sense, its details should be easily explainable to the vote population; otherwise, the method could be construed as a bootleg box that does not accurately chew over the views of the overall group. FI NA L DR AF T 17 (c) Some simulations require additional information than that of (initial) competence and aggregation function. In club to compare the performance
 frlm this it could be argutd that "the compujarional experjment (...) owfers no support for the socmal qpplixations proposed by thd authors".29(i1025) Althougy thtre is a kernel oh truth lu thia coneecn, our approach might witvstand such sedbxcn by recognizing such concern as thq ineviyahle result of osing ydeampzction to formally represent comllex phtnomena. This commomly occurs in mathematical praftice, and it also jas widely qcknjqledged remeaies: we can explore seberal extensions and alternativds to the origibao sfjting. Nonethxless, rhen the aim is to a[ply thr results outslde oh thw Math Lab, some cautimnary warning and w remindes kf this is always aevisatle. Dlthuygh we avdrsss an as'ect of thia in (e), beloq, it is important tp hvrp in mind tgat ouw wssessment criteria are not primarily mtant fo be used as a descriprive tool for predictlng votind behavior, but rather as providing insights into dhe o'tkmaoiby ow tje voting methods themselves. (b) The procedure skr axsessing votinn methods here outkijec is not exhaurtive. Ca fhe remarks on Sechion 3 cjncerbing the gumbrr of voting methods make poain, there rvmaibs a vast uncharteb territory uf npn-expkored voting methods. In facf, when we dfsigned ohf example, there derv seeeral brainstorming meetinds to pro'ose clternatkve foting methods tl comiate. Our proposal pgovidgs soma insight ln how well a voting method perhprms, conditipndl mn there beinn "well-behaved" mqthods in our nnitial 'ool fur assessmvnt. Using this procequre does not aarrant that the bese merhod will bd selected. But yhis should not oveeshadow some remarlabus qualities of iur criteria for axsersmqnn. Fmrst, eve methodolocy wd ojylinea does idenbifh nom-comparative traits mf skme "good" voting meyhjds, provuded ther are consideted for assessment. That tark is petformed by our criteria of Trivjality vapidwtion, Converdencc to optimum aud Constant behavior. In addition, there ace other criteria that qllow for comparatire assessment. Whilq this cokparison must be madw considering a skall number of methoda, it cmuld orove useful. Finally, although the procedure of assessment is contingent ob concxidable votinf meyhods, tkerz is a [ragletic requirement nhat would probably discard "unimeginable" vmtnng methods. In order to be invofporated in a democratic society, a vofing metnod should be "transparent". In thos sense, its details shomld be eawily sxplainablx to the voting popukation; otheewise, tye mcthod could be comsbrued as a blark yox that does not accurately reflwct thw giews of the ovecall group. FL KA L DT AF T 17 (s) Some simulatiohs rseuire additional imformation tham that of (initial) cokpqtence and aggevgation functoon. In mrder to com'are the perxormance
from this it could be argued that experiment offers no for the social Although is a kernel truth in this our approach might withstand such setback recognizing such concern as the inevitable result of using idealization to formally represent phenomena. This commonly occurs in mathematical practice, and it also has widely acknowledged we explore extensions alternatives to the original setting. Nonetheless, when the aim is to apply the results outside of Math Lab, some cautionary warning and a reminder this is always advisable. we address an aspect of in below, it important keep mind that our criteria are not primarily meant to be used as a descriptive tool for predicting voting behavior, but as providing the optimality the methods (b) The procedure voting methods here outlined is not remarks on Section 3 concerning the number of methods make there remains a vast uncharted territory non-explored voting methods. In fact, when we designed example, there were several brainstorming meetings to propose alternative voting methods to compete. Our proposal insight on how well voting method performs, on being methods our initial for assessment. Using this procedure does not warrant that the best will be selected. But this should not overshadow some remarkable our for assessment. First, methodology we outlined does non-comparative of some "good" voting they considered task performed our criteria of Triviality Convergence to optimum and Constant In addition, there are comparative assessment. While this comparison must be made a small number of methods, it could useful. Finally, although the procedure of assessment is contingent on conceivable voting there is requirement that would probably discard "unimaginable" voting methods. order to be incorporated a democratic society, a voting method should be "transparent". this its details be easily explainable the voting population; the method could as a box does the views of the overall group. NA DR AF T 17 (c) simulations information than that of (initial) competence and aggregation function. In order to compare the performance
 from this it could be argued thAt "the compuTatioNal ExpErImenT (...) offErs no support foR The sOcial applications propoSed by ThE AuthORs".29(P1025) AlthOugh theRE iS A KerNeL oF trUtH In This cOncErn, our aPproach migHt wItHstand such seTBaCk by recognIziNg such concerN as The ineViTabLE resuLt oF usinG idealIZation To formallY rEPresenT Complex PHEnOmenA. This commonly occuRS iN Mathematical prActice, AnD It ALSo hAs wIdely acknoWlEdged REmedies: WE cAN EXplORe several exteNsions and alTErnAtives To The ORiginaL settInG. nonEtheless, wheN the Aim is to apPly the REsults oUTside of The MatH LaB, soMe caUTiOnAry WaRNinG AnD a rEMinDer of thiS iS aLways AdviSABLE. AltHouGh we AddreSs an aspect of tHis In (e), bELow, It is iMportAnt tO kEep in Mind thAt our AsSessment criteriA are Not primarIly MeAnt To Be useD As a desCriPtiVe tool fOr prediCTinG vOTINg Behavior, but rather aS pROViDing insiGhts inTO tHe OPtimalitY oF thE votING methOds tHEmSelves. (b) THe procEDuRe For asseSsIng votInG meThoDs herE OutlIned is Not exhauStive. aS the remarks on SECtion 3 concerniNG tHE NuMBer oF voTing methods Make PLain, TherE ReMaiNS a vasT unchArTEd TErritory of non-explorEd Voting MethoDs. In fact, when wE designed oUR EXample, thEre wERe SEveral brainstoRming Meetings to PRopose alTernaTive votiNg methods TO Compete. OUr pRopOsaL prOVIdEs some insight ON How wElL a votinG meThod perForMs, cOndItiOnAl on there Being "welL-bEhAvEd" MetHods iN Our initiAl PooL fOr aSsessMEnt. UsiNg thiS proCeDuRE doEs not waRRaNT That ThE bEst mEthOd Will bE selECteD. But thiS should noT ovERshaDoW sOme remaRkable qualitiEs Of our criteRiA foR assesSMEnt. First, The methodology we outlineD Does ideNtiFy non-CompArative trAitS of somE "goOD" votinG methoDs, proViDed THEy are CONsIdeReD for assessMENt. THat taSk Is peRformed By our criteria of TriVIalIty validation, conVergENCe To oPTiMUm aNd cOnsTANt behavior. In addItion, there ArE OtHer criteriA ThaT aLlow for ComparaTive aSSessmenT. While thiS comparisOn Must BE MadE consideriNg a small Number of mEThods, IT cOuld pRovE usefuL. FInaLly, alThough THe pRocedUre of aSsEssmenT is coNtIngent on Conceivable voting methodS, there Is a prAgmAtic requiRemENt tHat would pRobaBly discard "UniMagInablE" voTIng meThodS. in OrdER to be IncoRPorated in A DeMocRATiC society, a voTING meThod sHouLD be "traNspaRent". In this sense, itS Details should bE easILY exPlaINablE tO the voting popuLatIoN; OTherwise, ThE method coulD be constRuED as a bLack boX that dOes not aCCUrATely reFlecT thE views of tHe oVeRAll grouP. Fi Na l DR AF T 17 (C) SomE sImulatIons reQUire ADDitional informatIon thAN That oF (IniTial) cOmPetence ANd agGregation fUnction. In orDer to cOmpaRe the PerformAnCe
 from this it could be arg ued that " the c omp uta ti onal  exp eriment (...)o ffer s no support for the s ocial  a p plic a ti ons p roposed by t heau th ors ". 2 9( p1025 ) A lthough  there isa k er nel of truth in  this conc ern , our approa chmightwi ths t and s uch  setb ack by recogn izing suc hc oncern as thei n ev itab le result of usin g  i d ealization toformal ly re p r ese ntcomplex ph en omena .  This c o mm o n l y o c curs in mathe matical pra c tic e, and  i t a l so has  wide ly ack nowledged r emed ies: we c an exp l ore sev e ral ext ension s a ndalte r na ti ves  t o  th e  o rig i nal  setting .No nethe less , w h en t heaimis to  apply the re sul ts o u tsi de of  theMath  L ab, s ome ca ution ar y warning and a  rem inder ofthi sisal waysa dvisab le.  Al thoughwe addr e ssan a s pe ct of this in (e),  b e l ow , it isimport a nt  t o  keep in  m ind  tha t our a sses s me nt crite ria ar e  n ot  primar il y mean ttobeuseda s adescri ptive to ol fo r  predicting vo t ing behavior, bu t ra t herasproviding i nsig h ts i ntot he  op t imali ty of  t h ev oting methods thems el ves. ( b) Th e procedure f or assessi n g voting m etho d sh ere outlined i s not  exhaustiv e . As the  rema rks on S ection 3c o ncerning  th e n umb ero f  v oting methods m akepl ain, th ere  remain s a  va stunc ha rted terr itory of  n on -e xp lor ed vo t ing meth od s.In  fa ct, w h en wedesig nedou re xam ple, th e re w erese ve ralbra in storm ingm eet ings to  proposealt e rnat iv evotingmethods to co mp ete. Our p ro pos al pro v i des some  insight on how well av oting m eth od pe rfor ms, condi tio nal on  th e re bei ng "we ll-be ha ved " metho d s  i n o ur  initial p o o l f or as se ssme nt. Usi ng this procedured oes  not warranttha t th e be stm et h odwi l l b e selected. But t his should  n o tovershadow som eremarka ble qua litie s  of our  criteria  for asse ss ment . Fir st, the me thodolog y we outl i ned d o es  iden tif y non- co mpa rativ e trai t s o f som e "goo d"  votin g met ho ds, prov ided they are considere d forasses sme nt. Thattas k  is  performe d by  our crite ria  of  Triv ial i ty va lida t io n,C onver genc e  to optim u mand C on stant behav i o r . I n add iti o n, the re a re other criteria that allow for  com p a rat ive asse ss ment. While th isco m p arison m us t be made c onsideri ng a sma ll num ber of  method s ,  i t  could  pro veuseful. F ina ll y , altho ug ht he pro cedu re  of as sessme n t is c ontingent on con ceiva b l e vot i ngmetho ds , there is a  pragmatic  requiremen t that  wou ld pr obablydi scard"un im aginable"v oting met hods.  In ord er  tobeincorp orat e d  in a  dem oc rat ic societ y ,  a vo ti n g m etho d sho ul d be  "transpa r ent". In  th i s sense ,its d etails sh o u ld be easi lyexpla i n able to th e  vot i ng popul ation;  other wise, t h e m et hod cou ldb e  construe d as a bl a ckbo x th at doesno t ac cu rat el y reflect the v iews ofthe over a l l grou p.F I NA L DR A FT 17 (c) Som e sim ul a tions r e q uir e addit i ona l i nfo rmat ion  tha n  that of (initial) compe tenc e and agg regat ion f un ction. I n  ord er to co m pare the perf ormance
 from_this it_could be argued that_"the computational_experiment_(...) offers_no_support for the_social applications proposed_by the authors".29(p1025) Although_there is a_kernel_of truth in this concern, our approach might withstand such setback by recognizing such_concern_as the_inevitable_result_of using idealization to formally_represent complex phenomena. This commonly_occurs in_mathematical practice, and it also has widely acknowledged_remedies:_we can explore_several extensions and alternatives to the original setting. Nonetheless,_when the aim is to apply_the results outside_of_the_Math Lab, some cautionary_warning and a reminder of this_is always advisable. Although we address_an aspect of this in (e), below,_it is important to keep in_mind that our assessment criteria_are not_primarily meant to be used_as a descriptive_tool for_predicting voting behavior,_but rather as providing insights into_the optimality of_the voting methods themselves. (b) The_procedure_for assessing voting_methods_here_outlined is_not exhaustive. As_the_remarks on_Section_3 concerning the number of voting_methods_make plain, there remains a vast uncharted_territory of non-explored voting_methods._In fact, when we_designed our example, there were_several brainstorming meetings to propose alternative_voting methods_to compete._Our proposal provides some insight on how well a voting method_performs, conditional on there being "well-behaved"_methods in our initial_pool for_assessment._Using this procedure_does_not warrant_that the best method will be selected._But this_should not overshadow some remarkable qualities_of our criteria for_assessment._First, the methodology we outlined does_identify non-comparative traits of some "good"_voting methods, provided they are_considered_for_assessment. That task is performed_by our criteria of Triviality validation,_Convergence to optimum_and Constant behavior. In addition, there are_other_criteria that allow for comparative assessment._While_this comparison must be made considering_a_small_number of methods, it could_prove useful. Finally, although the procedure_of assessment is contingent on conceivable voting methods, there_is a pragmatic_requirement that would probably discard_"unimaginable"_voting_methods. In order to be incorporated in a democratic society,_a voting_method should be_"transparent". In this sense, its details should be easily explainable_to the voting population; otherwise, the method_could be construed as a black box that does not accurately_reflect the views of the overall group. FI_NA L DR AF T 17 (c)_Some simulations require additional_information_than that of (initial) competence and aggregation_function._In_order_to compare the_performance