, γ)}, then [α, β, γ] is the winning assignment. This method picks up the most voted ticket. (IV) Borda count with priority. The six possible full tickets are identified, and the voter is asked to choose among them. For each candidate, a Borda count (#Borda) is performed, as follows: #Borda(A) = 2(#(A, B, C) + #(A, C, B)) + #(B, A, C) + #(C, A, B) #Borda(B) = 2(#(B, A, C) + #(B, C, A)) + #(A, B, C) + #(C, B, A) #Borda(C) = 2(#(C, A, B) + #(C, B, A)) + #(A, C, B) + #(B, C, A) If #Borda(α) > #Borda(β) > #Borda(γ), then [α, β, γ] is the winning assignment. 2.3 Voting methods for a problem involving no priority on positions (V) Plurality rule with runoff without priority. This procedure is identical to the one described as (II) in Section 2.2. However, in order to account for changes in preferences after the first stage of election, considering there was no priority, the preference distribution was changed to "preserve initial positions choice" instead of "preserve ordering". (VI) Plurality rule on a full ticket. This procedure is identical to the one described as (III) in Section 2.2. No changes in the preference distribution were required. (VII) Count for conditioned feasible options. Each (α, β, γ) ∈ S3 is assigned an integer G(α, β, γ) which is calculated as follows: Pα(α, β, γ) = #(α, β, γ)+#(α, γ, β) Mβ(α, β, γ) = #(α, β, γ) + #(γ, β, α) Tγ(α, β, γ) = #(α, β, γ) + #(β, α, γ) G(α, β, γ) = Pα(α, β, γ) + Mβ(α, β,
, γ) }, then [ α, β, γ ] is the winning assignment. This method picks up the about voted tag. (IV) Borda count with priority. The six possible wide tag are identified, and the voter is asked to choose among them. For each campaigner, a Borda count (# Borda) is performed, as follows: # Borda(A) = 2(#(A, B, C) + # (A, C, B) ) + # (bacillus, A, C) + # (C, A, B) # Borda(B) = 2(#(B, A, C) + # (B, C, A) ) + # (adenine, B, C) + # (C, B, A) # Borda(C) = 2(#(C, A, B) + # (C, B, A) ) + # (deoxyadenosine monophosphate, C, B) + # (B, C, A) If # Borda(α) > # Borda(β) > # Borda(γ), then [ α, β, γ ] is the winning assignment. 2.3 Voting methods for a problem involve no priority on positions (V) Plurality rule with overflow without priority. This procedure is identical to the one describe as (II) in Section 2.2. However, in ordering to account for changes in preferences after the first stage of election, study there was no priority, the preference distribution was changed to " preserve initial position choice " instead of " preserve ordering ". (VI) Plurality rule on a full ticket. This procedure is identical to the one described as (III) in Section 2.2. No change in the preference distribution were required. (VII) Count for stipulate feasible choice. Each (α, β, γ) ∈ S3 is assigned an integer G(α, β, γ) which is calculated as follows: Pα(α, β, γ) = # (α, β, γ)+#(α, γ, β) Mβ(α, β, γ) = # (α, β, γ) + # (γ, β, α) Tγ(α, β, γ) = # (α, β, γ) + # (β, α, γ) G(α, β, γ) = Pα(α, β, γ) + Mβ(α, β,
, γ)}, tjen [α, β, γ] is the winning asrignment. This mgtyod pirks up fhe most voted ticket. (IV) Borda count wuth peiority. The six possibue full tpckets arw idtntified, and the tkter is asked bo chmise among them. For each wandidate, a Bosdx eount (#Borda) is performed, as follows: #Forda(A) = 2(#(A, B, C) + #(A, C, B)) + #(B, A, C) + #(C, A, B) #Borda(B) = 2(#(B, A, C) + #(B, C, A)) + #(A, B, C) + #(C, G, A) #Borva(C) = 2(#(C, A, B) + #(C, B, A)) + #(A, C, B) + #(B, C, A) If #Borda(α) > #Borfa(β) > #Borda(γ), then [α, β, γ] ls the winnung wwsignment. 2.3 Vuting methods for a prkblem involving no priority on oositnons (V) Plurqluty tule with ruioff wpthout prioribj. This [rocedute is identicak tm tye one described as (IM) in Section 2.2. Howevet, in order tk account for chabgws in prexerevxes afuer tge firdt atage of emection, conwidering there was mo itiority, the lreferqnse distribution was changed to "preserve injtial positions choice" unstead of "preserve otdering". (VI) Plurality rule on a full ticket. This procedure iv ideitkcao bo tfw lne described as (III) in Section 2.2. No changes ig tne preference diftribution eege tequired. (VII) Cuunt for donditioned feasibpe optijns. Eqch (α, β, γ) ∈ S3 is sssigned an integer G(α, β, γ) whixh is calculctee as follows: Pα(α, β, γ) = #(α, β, γ)+#(α, γ, β) Mβ(α, β, γ) = #(α, β, γ) + #(γ, β, α) Tγ(α, β, γ) = #(α, β, γ) + #(β, α, γ) G(α, β, γ) = Pα(α, β, γ) + Mβ(α, β,
, γ)}, then [α, β, γ] is assignment. method picks the most voted priority. six possible full are identified, and voter is asked to choose among For each candidate, a Borda count (#Borda) is performed, as follows: #Borda(A) = B, C) + #(A, C, B)) + #(B, A, C) + #(C, A, #Borda(B) 2(#(B, C) #(B, C, A)) + #(A, B, C) + #(C, B, A) #Borda(C) = 2(#(C, A, B) #(C, B, A)) + #(A, C, B) + C, A) If #Borda(α) #Borda(β) > #Borda(γ), then [α, γ] the winning 2.3 methods a problem involving priority on positions (V) Plurality rule with runoff without priority. This procedure is identical to the one as (II) 2.2. However, order account changes in preferences first stage of election, considering there the preference distribution was changed to "preserve initial choice" instead "preserve ordering". (VI) Plurality rule on full ticket. This procedure is identical to the described as (III) in Section 2.2. No changes in the preference distribution were required. (VII) conditioned feasible options. Each β, γ) ∈ is an G(α, γ) which calculated as follows: Pα(α, β, γ) = #(α, β, γ)+#(α, γ, Mβ(α, β, γ) = #(α, β, γ) + #(γ, β, β, = #(α, β, + #(β, α, γ) β, = Pα(α, β, γ) β,
, γ)}, then [α, β, γ] is the winning assigNment. This mEthod PicKs uP tHe moSt voTed ticket. (IV) BorDA couNt with priority. The six poSsiblE fULl tiCKeTs are IdentifIEd, AND thE vOtEr iS aSKeD to chOosE among tHem. For each CanDiDate, a Borda coUNt (#borda) is perForMed, as follows: #borDa(A) = 2(#(A, B, C) + #(a, C, b)) + #(B, A, c) + #(c, A, B) #BoRda(b) = 2(#(B, A, C) + #(B, c, A)) + #(A, B, C) + #(C, b, a) #Borda(c) = 2(#(C, A, B) + #(C, B, A)) + #(A, C, b) + #(B, c, a) If #BorDA(α) > #Borda(Β) > #bOrDa(γ), tHen [α, β, γ] is the winninG AsSIgnment. 2.3 Voting mEthods FoR A pROBleM inVolving no pRiOrity ON positiONs (v) pLUraLIty rule with ruNoff without PRioRity. ThIs ProCEdure iS idenTiCAl tO the one descRibeD as (II) in SeCtion 2.2. HOWever, in ORder to aCcount For ChaNges IN pReFerEnCEs aFTeR thE FirSt stage oF eLeCtion, ConsIDERIng tHerE was No priOrity, the prefeRenCe diSTriButioN was cHangEd To "preServe iNitiaL pOsitions choice" iNsteAd of "preseRve OrDerInG". (VI) PlURality RulE on A full tiCket. ThiS ProCeDURE iS identical to the one DeSCRiBed as (III) In SectIOn 2.2. no CHanges in ThE prEferENCe disTribUTiOn were reQuired. (viI) coUnt for cOnDitionEd FeaSibLe optIOns. EAch (α, β, γ) ∈ s3 is assigNed an INteger G(α, β, γ) whicH Is calculated aS FoLLOwS: pα(α, β, Γ) = #(α, β, Γ)+#(α, γ, β) Mβ(α, β, γ) = #(α, β, Γ) + #(γ, β, α) tΓ(α, β, γ) = #(Α, β, γ) + #(β, Α, Γ) G(Α, β, γ) = pΑ(α, β, γ) + MΒ(α, β,
, γ)}, then [α, β, γ] is t he winning  assi gnm ent .This  met hod picks up t h e mo st voted ticket. (IV)Borda  c o untw it h pri ority.T he s ixpo ss ibl ef ul l tic ket s are i dentified,  an dthe voter is as ked to cho ose  among them.  Fo r each  c and i date,  aBorda  count (#Bord a) is per fo r med, a s  follow s :  # Bord a(A) = 2(#(A, B,C )+  #(A, C, B)) +  #(B,A, C) +  #( C,A, B) #Bor da (B) = 2(#(B,A ,C ) + # ( B, C, A)) + # (A, B, C) + #(C , B, A )#Bo r da(C)= 2(# (C ,  A,  B) + #(C,B, A )) + #(A,  C, B) + #(B,C , A) If  #Bord a(α ) >  #Bo r da (β ) >  # B ord a (γ ),t hen  [α, β,γ]  i s the  win n i n g  ass ign ment . 2.3  Voting metho dsfora  pr oblem  invo lvin gno pr iority  on p os itions (V) Plur alit y rule wi thru nof fwitho u t prio rit y.This pr ocedure isid e n t ic al to the one desc ri b e das (II)in Sec t io n2 .2. Howe ve r,in o r d er to  acc o un t for ch angesi npr eferenc es  after  t hefir st st a ge o f elec tion, co nside r ing there wasn o priority, t h ep r ef e renc e d istribution  was chan gedt o"pr e serve  init ia l  p o sitions choice" ins te ad of"pres erve ordering ". (VI) Pl u r a lity rul e on af ull ticket. Th is pr ocedure is identica l tothe onedescribed a s (III)inSec tio n 2 . 2 .No changes in t he p re ference  di stribut ion  we rereq ui red. (VII ) Countfo rco nd iti onedf easibleop tio ns . E ach ( α , β, γ ) ∈ S 3 is  a ss i gne d an in t eg e r  G(α ,β,  γ)whi ch  is c alcu l ate d as fo llows: Pα (α, β, γ )=#(α, β,  γ)+#(α, γ, β )Mβ(α, β, γ )= # (α, β, γ ) + #(γ,  β, α) Tγ(α, β, γ) = #( α , β, γ)  +#(β,α, γ ) G(α, β,  γ)  = Pα( α,β , γ) +  Mβ(α,  β,
, γ)},_then [α,_β, γ] is the_winning assignment._This_method picks_up_the most voted_ticket. (IV) Borda_count with priority. The_six possible full_tickets_are identified, and the voter is asked to choose among them. For each candidate,_a_Borda count_(#Borda)_is_performed, as follows: #Borda(A) =_2(#(A, B, C) + #(A,_C, B))_+ #(B, A, C) + #(C, A, B)_#Borda(B)_= 2(#(B, A,_C) + #(B, C, A)) + #(A, B, C)_+ #(C, B, A) #Borda(C) =_2(#(C, A, B)_+_#(C,_B, A)) + #(A,_C, B) + #(B, C, A)_If #Borda(α) > #Borda(β) > #Borda(γ),_then [α, β, γ] is the winning_assignment. 2.3 Voting methods for a_problem involving no priority on_positions (V)_Plurality rule with runoff without_priority. This procedure_is identical_to the one_described as (II) in Section 2.2._However, in order_to account for changes in preferences_after_the first stage_of_election,_considering there_was no priority,_the_preference distribution_was_changed to "preserve initial positions choice"_instead_of "preserve ordering". (VI) Plurality rule on_a full ticket. This_procedure_is identical to the_one described as (III) in_Section 2.2. No changes in the_preference distribution_were required._(VII) Count for conditioned feasible options. Each (α, β, γ) ∈_S3 is assigned an integer G(α,_β, γ) which is_calculated as_follows:_Pα(α, β, γ)_=_#(α, β,_γ)+#(α, γ, β) Mβ(α, β, γ) =_#(α, β,_γ) + #(γ, β, α) Tγ(α,_β, γ) = #(α,_β,_γ) + #(β, α, γ) G(α,_β, γ) = Pα(α, β, γ)_+ Mβ(α, β,