 γ) + Tγ(α, β, γ) G(α, β, γ) counts the total votes for the ticket with α in first position, β in the second, and γ in the third. If (α, β, γ) ∈ S3 = {(A, B, C), (A, C, B), (B, A, C), (B, C, A), (C, A, B), (C, B, A)} and G(α, β, γ) > G(x, y, z) for all (x, y, z) ∈ S3\{(α, β, γ)}, then [α, β, γ] is the winning assignment. This method chooses the ticket that gets more votes on the feasible options along with their respective feasible conditioned options. Do any of these methods solve our assignment problem? Which one performs better? 3 Criteria for assessment of voting procedures It is often underappreciated just how difficult it is to assess a voting method for a specific decision problem. One reason for this is that, in many groups, legislations are previously placed to determine which method to use. Some of these methods, such as plurality rule, are widely used. However, as can be seen from the previous section, there are several different procedures worthy of the name 'plurality rule' when facing a specific decision problem. Another reason for the suspicion that there are simple criteria to assess voting methods is the pervasive belief that there are just a few of such methods. In common parlance, it is standard practice to qualify a group decision as FI NA L RA FT 7 dictatorial, elitist, or democratic. However, these labels usually conceal the fact that many genuinely different voting methods are gathered under those categories. Besides, there are many other methods that it would be difficult to classify among these categories. Actually, the number of possible decisionmaking procedures is overwhelming. To put things in perspective, we can extend a technique developed by Christian List22 to distinguish aggregative decision-making procedures (voting methods). First, there is an "agenda" that contains the issues to be voted on. Then, there are "inputs" of the procedure: voters' attitudes towards issues on the agenda (for instance, their preferences, opinions, and so forth). Finally, there are "outputs" of the procedure: collective outcomes towards issues on the agenda. We can distinguish voting methods by identifying them with "aggregation functions". An aggregation function takes
γ) + Tγ(α, β, γ) G(α, β, γ) counts the total votes for the ticket with α in inaugural placement, β in the second, and γ in the third. If (α, β, γ) ∈ S3 = { (A, B, C), (A, C, B), (B, A, C), (B, C, A), (C, A, B), (C, B, A) } and G(α, β, γ) > G(x, y, z) for all (x, y, z) ∈ S3\{(α, β, γ) }, then [ α, β, γ ] is the winning assignment. This method acting chooses the ticket that gets more vote on the feasible options along with their respective feasible conditioned option. Do any of these methods solve our appointment problem? Which one performs good? 3 Criteria for assessment of voting procedures It is often underappreciated just how unmanageable it is to assess a voting method for a specific decisiveness problem. One reason for this is that, in many groups, legislations are previously placed to specify which method to use. Some of these methods, such as plurality rule, are wide used. However, as can be seen from the previous section, there are several unlike procedure worthy of the name' plurality rule' when facing a specific decision problem. Another reason for the suspicion that there are elementary criteria to assess vote method is the permeant belief that there are just a few of such methods. In common parlance, it is standard practice to qualify a group decision as FI NA L RA FT 7 authoritarian, elitist, or democratic. However, these labels usually conceal the fact that many genuinely different voting method acting are gathered under those categories. Besides, there are many other method that it would be difficult to relegate among these class. Actually, the number of possible decisionmaking procedures is overwhelming. To place things in perspective, we can extend a proficiency developed by Christian List22 to signalize aggregative decision - take procedures (vote methods). First, there is an " agenda " that contains the issues to be vote on. Then, there are " input signal " of the procedure: voter' attitudes towards issues on the agenda (for instance, their preference, opinions, and indeed forth). Finally, there are " outputs " of the procedure: collective outcomes towards issues on the agenda. We can distinguish vote methods by identifying them with " collection functions ". An aggregation function takes
 γ) + Hγ(α, β, γ) G(α, β, γ) counts the total votes for the jixket wmth α in first pusition, β in the second, and γ mn tye thurd. If (α, β, γ) ∈ S3 = {(A, B, C), (A, Z, B), (B, A, C), (B, C, A), (C, A, B), (X, B, A)} and J(α, β, γ) > G(x, n, z) fkv all (e, y, z) ∈ S3\{(α, β, γ)}, then [α, β, γ] is the winning assigtmdnc. This method chooses the ticket thae gets koge votes on thg feaxyble options along with their respectibe feaspble conditioned pptions. Do any of these mehhodd solve our assignlent problen? Whyxh one perfofms better? 3 Criteria fkr assessment of voting procedufes Ic is often oueerwkpreciated jnst hor difficult ln is to assess a voting methpd hor q specific decision pcoblem. One reason fot this is dhct, in many groups, legusoatiots ase pfwviuusmy pmaced ho vetermine wgich method to use. Some of thexe nethods, such zs pluwajity rule, are widely used. However, as cat bs seen from the previouw section, there are sgveral difserent procedures worthy of the name 'plurality rune' whxn faelkg a wpfcific decision problem. Another reason for thq sisiicion that there are simple cgiygria to assess votiny msthods is the pervwsive bglief rhat thert are just a few of such methods. In common pcrlqnce, it is standarb practice tu quslify a group decision as FI NA M RA FT 7 diftatorial, dlitist, or democfatpc. Hmwever, these labels usuallr conceal the fact tfat kany gqnuinely dlfferctt voting methods wre gctherad under tjose categories. Besides, there acx many other kedhogs that nt woukd be difficujt to classify among chese zategories. Actualny, the numbqr of possibla decisionmakmng procequrew is overwhduming. To put tnings in iexspective, we can extend a tcchnidhe developed by Chtustian List22 to dirtigglisi aggwagative decivion-oakkmg prucedures (vobine meyhods). First, there is an "zgenda" that contaims the issoes to be voted on. Them, there are "inputs" of tie proredure: vojers' attitudes towards issues oh the agejda (for instancq, thcir kreferences, opinions, and so forth). Finally, there arx "outputs" of the procedyre: collective outcpkes towards issuqs on the agenda. We can distibguish voting metmods by identifying thsm witv "agggegation functions". An aggregation function takes
γ) + Tγ(α, β, γ) G(α, β, the votes for ticket with α the and γ in third. If (α, γ) ∈ S3 = {(A, B, (A, C, B), (B, A, C), (B, C, A), (C, A, B), (C, A)} and G(α, β, γ) > G(x, y, z) for all (x, y, ∈ β, then β, γ] is the winning assignment. This method chooses the ticket that gets more votes on feasible options along with their respective feasible conditioned Do any of these solve our assignment problem? Which performs 3 Criteria assessment voting It is often just how difficult it is to assess a voting method for a specific decision problem. One reason this is many groups, are placed determine which method Some of these methods, such as widely used. However, as can be seen from previous section, are several different procedures worthy of name 'plurality rule' when facing a specific decision Another reason for the suspicion that there are simple criteria to assess voting methods is belief that there are a few of methods. common it standard practice qualify a group decision as FI NA L RA FT 7 elitist, or democratic. However, these labels usually conceal the fact genuinely voting methods are under those categories. Besides, are other methods that it difficult classify Actually, number possible decisionmaking procedures is To put things in perspective, can extend a technique distinguish aggregative decision-making procedures (voting methods). First, there an "agenda" that contains the issues to voted on. Then, there are "inputs" of the procedure: voters' attitudes towards on the instance, their preferences, opinions, and so forth). Finally, are "outputs" of the collective outcomes towards issues on the agenda. We can voting by identifying with "aggregation functions". aggregation function takes
 γ) + Tγ(α, β, γ) G(α, β, γ) counts the total vOtes for the TickeT wiTh α In FirsT posItion, β in the secONd, anD γ in the third. If (α, β, γ) ∈ S3 = {(A, B, C), (A, c, B), (B, A, C), (b, C, a), (c, A, B), (C, b, a)} aNd G(α, β, Γ) > G(x, y, z) foR AlL (X, Y, z) ∈ S3\{(Α, β, Γ)}, tHen [Α, β, Γ] Is The wiNniNg assigNment. This mEthOd Chooses the tiCKeT that gets mOre Votes on the feAsiBle optIoNs aLOng wiTh tHeir rEspectIVe feasIble condiTiONed optIOns. Do anY OF tHese Methods solve our asSIgNMent problem? WhiCh one pErFOrMS BetTer? 3 criteria foR aSsessMEnt of voTInG PROceDUres It is often UnderapprecIAteD just hOw DifFIcult iT is to AsSEss A voting methOd foR a specifiC decisIOn problEM. One reaSon for ThiS is That, IN mAnY grOuPS, leGIsLatIOns Are previOuSlY placEd to DETERminE whIch mEthod To use. Some of thEse MethODs, sUch as PluraLity RuLe, are Widely Used. HOwEver, as can be seen From The previoUs sEcTioN, tHere aRE severAl dIffErent prOcedureS WorThY OF ThE name 'plurality rule' WhEN FaCing a speCific dECiSiON problem. anOthEr reASOn for The sUSpIcion thaT there ARe SiMple criTeRia to aSsEss VotIng meTHods Is the pErvasive BelieF That there are juST a few of such meTHoDS. in COmmoN paRlance, it is sTandARd prActiCE tO quALify a Group DeCIsIOn as FI NA L RA FT 7 dictatOrIal, eliTist, oR democratic. HoWever, these LABEls usualLy coNCeAL the fact that maNy genUinely diffERent votiNg metHods are gAthered unDER those caTegOriEs. BEsiDES, tHere are many otHER metHoDs that iT woUld be diFfiCulT to ClaSsIfy among tHese cateGoRiEs. acTuaLly, thE Number of PoSsiBlE deCisioNMaking ProceDureS iS oVErwHelming. tO pUT ThinGs In PersPecTiVe, we cAn exTEnd A techniQue develoPed BY ChrIsTiAn List22 tO distinguish aGgRegative deCiSioN-makinG PRocedureS (voting methods). First, therE Is an "ageNda" That cOntaIns the issUes To be voTed ON. Then, tHere arE "inpuTs" Of tHE ProceDURe: VotErS' attitudes TOWarDs issUeS on tHe agendA (for instance, their pREfeRences, opinionS, anD so fORTh). finALlY, TheRe ARe "oUTPuts" of the procedUre: collectIvE OuTcomes towaRDs iSsUes on thE agenda. we can DIstinguIsh voting Methods by IdEntiFYIng Them with "agGregatioN functionS". an aggREgAtion FunCtion tAkEs
 γ) + Tγ(α, β, γ) G(α, β,γ) countsthe t ota l v ot es f or t he ticket with α in  first position, β inthe s ec o nd,a nd  γ in  the th i rd . If(α ,β,γ) ∈S3 ={(A , B, C) , (A, C, B ),(B , A, C), (B, C,  A), (C, A , B ), (C, B, A) } a nd G(α ,β,γ ) > G (x,  y, z ) fora ll (x,  y, z) ∈S3 \ {(α, β ,  γ)}, t h e n[α,β, γ] is the winn i ng assignment. Th is met ho d  c h o ose s t he ticketth at ge t s morev ot e s ont he feasible o ptions alon g  wi th the ir  re s pectiv e fea si b leconditioned  opt ions. Doany of these m e thods s olve o urass ignm e nt  p rob le m ? W h ic h o n e p erformsbe tt er? 3  Cri t e r i a fo r a sses sment  of voting pr oce dure s  It  is o ftenunde ra pprec iatedjustho w difficult itis t o assessa v ot ing  m ethod for aspe cif ic deci sion pr o ble m. O n ereason for this is  t h a t,  in many  group s ,le g islation sare  pre v i ously  pla c ed  to dete rminew hi ch  method  t o use.  S ome  of  thes e  met hods,such asplura l ity rule, arew idely used. H o we v e r, as c anbe seen fro m th e  pre viou s  s ect i on, t herear e  s e veral different pro ce duresworth y of the name  'pluralit y r ule' whe n fa c in g  a specific de cisio n problem. Anotherreaso n for th e suspici o n  that th ere  ar e s imp l e  c riteria to as s e ss v ot ing met hod s is th e p erv asi vebe lief that  there a re  j us ta f ew of such met ho ds.  I n c ommon parlan ce, i t is  s ta n dar d pract i ce t o qu al if y agro up  deci sion asFI NA L  RA FT 7dic t ator ia l,  elitis t, or democra ti c. However ,the se lab e l s usuall y conceal the fact that many ge nui nelydiff erent vot ing  metho dsa re gat heredunder  t hos e categ o r ie s.Be sides, the r e  ar e man yothe r metho ds that it would b e  di fficult to cl ass ifya m on g t h es e  ca te g ori e s . Actually, the  number of  p o ss ible decis i onm ak ing pro cedures  is o v erwhelm ing. To p ut things  i n pe r s pec tive, we c an exten d a techn i que d e ve loped  by  Chris ti anList2 2 to d i sti nguis h aggr eg ativedecis io n-making  procedures (voting met hods).  Firs t,there isan" age nda" that  con tains theiss ues  to b e v o ted o n. T h en , t h ere a re " i nputs" of th e p r o ce dure: voter s ' att itude s t o wardsissu es on the agenda( for instance,thei r pre fer e nces ,opinions, andsofo r t h). Fina ll y, there ar e "outpu ts "  of t he pro cedure : colle c t iv e  outco mestow ards issu eson the age nd a. We can  dis ti nguish  votin g  met h o ds by identifyin g the m with" agg regat io n funct i ons" . An aggre gation func tion t akes 
 γ)_+ Tγ(α,_β, γ) G(α, β,_γ) counts_the_total votes_for_the ticket with_α in first_position, β in the_second, and γ_in_the third. If (α, β, γ) ∈ S3 = {(A, B, C), (A, C,_B),_(B, A,_C),_(B,_C, A), (C, A, B),_(C, B, A)} and G(α,_β, γ)_> G(x, y, z) for all (x, y,_z)_∈ S3\{(α, β,_γ)}, then [α, β, γ] is the winning assignment._This method chooses the ticket that_gets more votes_on_the_feasible options along with_their respective feasible conditioned options. Do_any of these methods solve our_assignment problem? Which one performs better? 3_Criteria for assessment of voting procedures_It is often underappreciated just_how difficult_it is to assess a_voting method for_a specific_decision problem. One_reason for this is that, in_many groups, legislations_are previously placed to determine which_method_to use. Some_of_these_methods, such_as plurality rule,_are_widely used._However,_as can be seen from the_previous_section, there are several different procedures worthy_of the name 'plurality_rule'_when facing a specific_decision problem. Another reason for_the suspicion that there are simple_criteria to_assess voting_methods is the pervasive belief that there are just a few_of such methods. In common parlance,_it is standard practice_to qualify_a_group decision as_FI_NA L_RA FT 7 dictatorial, elitist, or democratic._However, these_labels usually conceal the fact that_many genuinely different voting_methods_are gathered under those categories. Besides,_there are many other methods that_it would be difficult to_classify_among_these categories. Actually, the number_of possible decisionmaking procedures is overwhelming._To put things_in perspective, we can extend a technique_developed_by Christian List22 to distinguish aggregative_decision-making_procedures (voting methods). First, there is_an_"agenda"_that contains the issues to_be voted on. Then, there are_"inputs" of the procedure: voters' attitudes towards issues on_the agenda (for_instance, their preferences, opinions, and_so_forth)._Finally, there are "outputs" of the procedure: collective outcomes towards_issues on_the agenda. We_can distinguish voting methods by identifying them with "aggregation functions"._An aggregation function takes