Kondorset usuli - Condorcet method

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Kondorset usuli bo'yicha ovoz berish byulleteni namunasi. Bo'sh ovozlar ushbu nomzodni oxirgi o'rinda turishiga teng.

A Kondorset usuli (Ingliz tili: /kɒnd.rˈseɪ/; Frantsiya:[kɔ̃dɔʁsɛ]) bir nechta saylov usullari har bir boshchiligidagi saylovda boshqa nomzodlarning har biriga qarshi ovozlarning ko'pchiligini qo'lga kiritgan nomzodni, ya'ni bunday nomzod mavjud bo'lganda, boshqa har bir kishidan ko'ra ko'proq saylovchilar afzal ko'rgan nomzodni tanlaydi. Ushbu mulkka ega bo'lgan nomzod juftlik bo'yicha chempion yoki hamma g'olib, rasmiy ravishda Kondorets g'olibi.^[1] Shuni ta'kidlash kerakki, boshma-bosh saylovlari alohida ravishda o'tkazilmaydi; har bir juftlik nomzodi o'rtasida saylovchilarning afzalligini, ulardan nomzodlarni reytingini so'rab, so'ngra har bir juftlik uchun yuqori darajadagi nomzodga ovoz berishini taxmin qilish orqali topish mumkin.^[2]

Kondorets g'olibi ma'lum bir saylovda har doim ham mavjud bo'lmasligi mumkin, chunki ikkitadan ortiq variantni tanlagan saylovchilar guruhining afzalligi davriy bo'lishi mumkin - ya'ni har bir nomzodda ularni mag'lubiyatga uchratadigan raqib bo'lishi mumkin (lekin juda kam) ikki nomzod tanlovi.^[3](Bu o'yinga o'xshaydi tosh qog'oz qaychi, bu erda har bir qo'l shakli faqat bitta raqibga qarshi g'alaba qozonadi va boshqasiga yutqazadi). Bir guruh saylovchilarda bunday davriy imtiyozlar ehtimoli quyidagicha tanilgan Kondorset paradoksi. Shu bilan birga, guruhda bo'lmagan barcha nomzodlarni mag'lub etgan eng kichik nomzodlar guruhi doimo mavjud bo'lib, ular nomi bilan tanilgan Smit o'rnatdi, unda faqat bitta mavjud bo'lganda Kondorset g'olibi bo'lishi kafolatlanadi; ko'plab Kondorset usullari har doim Kondorset g'olibi bo'lmagan taqdirda Smit to'plamida bo'lgan nomzodni tanlaydi va shu tariqa "Smit-samarador" deb aytiladi. ^[4] Condorcet g'olibi ham odatda, lekin shart emas foydali g'olib (maksimal darajaga ko'taradigan) ijtimoiy ta'minot ).^[5][6]

Kondorset ovoz berish usullari 18-asr frantsuzlari uchun nomlangan matematik va faylasuf Mari Jan Antuan Nikola Karitat, Markiz de Kondorset, kim bunday ovoz berish tizimlarini qo'llab-quvvatlagan. Biroq, Ramon Lull eng qadimgi Kondorset usulini 1299 yilda o'ylab topgan.^[7] Bu teng edi Kopeland usuli juftlik rishtalari bo'lmagan hollarda.^[8]

Kondorset usullari imtiyozli (tartiblangan) ovoz berish (va odatda ovoz berish) yoki ikkinchi bosqich saylovlarining alohida turlaridan foydalanishi mumkin.

Kondorset usullarining ko'pchiligida bitta tur imtiyozli ovoz berish davri mavjud bo'lib, unda har bir saylovchi o'z nomzodlarini eng ko'p tanlanganlardan (1 raqami bilan belgilangan) eng kam holatiga (yuqori raqam bilan belgilangan) saralaydi. Saylovchilarning reytingi ko'pincha ularning deb nomlanadi imtiyoz tartibi, Garchi bu ularning samimiy imtiyozlari tartibiga to'g'ri kelmasa ham, saylovchilar o'zlari tanlagan har qanday tartibda tartibda erkin bo'lishlari va imtiyozlarni noto'g'ri talqin qilish uchun strategik sabablari bo'lishi mumkin. G'olibni topish uchun ovozlarni ko'p jihatdan to'plash mumkin. Ba'zilar - Condorcet usullari - agar mavjud bo'lsa, Condorcet g'olibini tanlaydi. Shuningdek, ular Kondorset g'olibi bo'lmagan taqdirda ham g'olibni tanlashlari mumkin va Kondorsetga mos keladigan turli xil usullar tsiklda turli xil g'oliblarni tanlashi mumkin - Kondorset usullari boshqa qaysi mezonlarga muvofiqligi bilan farq qiladi.

Berilgan tartib Robertning tartib qoidalari Saylovchilar o'zlarining ustunliklarini bildirish orqali ovoz bermasliklariga qaramay, takliflar va tuzatishlar bo'yicha ovoz berish ham Kondorset usuli hisoblanadi.^[9] Ovoz berishning bir necha bosqichlari mavjud va har bir turda ovoz berish ikkita muqobil variant orasida bo'ladi. Juftlikning yutqazuvchisi (ko'pchilik qoidalari bo'yicha) yo'q qilinadi va juftlikning g'olibi boshqa turga qarshi keyingi turda juftlik hosil qilish uchun omon qoladi. Oxir-oqibat faqat bitta alternativa qoladi va u g'olibdir. Bu bitta g'olib yoki davra bo'yicha o'tkaziladigan turnirga o'xshaydi; juftlikning umumiy soni alternativalar sonidan bittaga kam. Kondorset g'olibi har bir juftlikda ko'pchilik qoidalari bilan g'alaba qozonganligi sababli, u hech qachon Robertning qoidalari bilan yo'q qilinmaydi. Ammo bu usul a ni aniqlay olmaydi ovoz berish paradoksi unda Kondorset g'olibi yo'q va ko'pchilik g'olibga nisbatan erta yutqazuvchini afzal ko'radi (garchi u har doim kimnidir tanlasa Smit o'rnatdi ). Ijtimoiy tanlov nazariyasiga oid adabiyotlarning katta qismi ushbu uslubning xususiyatlari haqida, chunki u keng qo'llanilgan va muhim tashkilotlar (qonun chiqaruvchi organlar, kengashlar, qo'mitalar va boshqalar) tomonidan qo'llaniladi. Bu ommaviy saylovlarda foydalanish uchun amaliy emas, chunki uning ko'p bosqichli ovoz berishlari saylovchilar, nomzodlar va hukumatlar tomonidan boshqarilishi uchun juda qimmatga tushar edi.

Xulosa

A va B nomzodlari o'rtasida bo'lib o'tgan tanlovda Kondorset usuli bo'yicha imtiyozli ovoz berish shaklidan foydalaniladi, agar ko'proq saylovchilar o'z byulletenlarini o'z nomzodlarini B nomzodiga nisbatan afzal deb belgilasalar, aksincha o'z byulletenlarini belgilagan saylovchilar sonidan, u holda B nomzod saylanmagan (saylanishi kerak).

Biroq, ehtimolligi sababli Kondorset paradoksi, mumkin, lekin mumkin emas,^[10] ushbu maqsadni aniq bir saylovda amalga oshirish mumkin emasligi. Bunga ba'zan a deyiladi Kondorset tsikli yoki shunchaki tsikl va deb o'ylash mumkin Nomzod nomzod qaychi, nomzod qog'ozni urgan nomzod qaychi va nomzod toshni kaltaklagan nomzod qaychi. Faqatgina turli xil Kondorset usullari bunday tsiklni qanday hal qilishlari bilan ular samarali farq qiladi (garchi ko'p saylovlarda tsikllar mavjud emas; qarang Condorcet paradox # Paradoksning ehtimoli taxminlar uchun). Agar tsikl bo'lmasa, barcha Kondorset usullari bir xil nomzodni tanlaydi va operativ jihatdan tengdir.

• Har bir saylovchi nomzodlarni imtiyozlar tartibida (yuqoridan pastgacha, yoki eng yaxshidan yomongacha yoki 1, 2, 3 va hokazo) saralaydi. Saylovchiga nomzodlarni tenglashtirishi, ular o'rtasida befarqligi (afzalligi yo'qligi) bildirilishi mumkin. Vaqtni tejash uchun saylovchi tomonidan o'tkazib yuborilgan nomzodlarga saylovchi ularni pastki qatorga qo'ygandek munosabatda bo'lish mumkin.^[11]
• Nomzodlarning har bir juftligi uchun (a kabi davra bo'yicha musobaqa ) har bir nomzodni boshqa nomzoddan qancha ovoz bilan hisoblashini hisoblash. Shunday qilib, har bir juftlik ikkita jami bo'ladi: ularning ko'pligi va ozchilikning kattaligi^{[iqtibos kerak ][12]} (yoki galstuk bo'ladi).

Kondorset usullarining ko'pchiligida bu hisoblar odatda tugatish tartibini to'liq aniqlash uchun kifoya qiladi (ya'ni kim g'olib bo'ldi, kim 2-o'rinni egalladi va hokazo) Ular har doim Kondorset g'olibi bor yoki yo'qligini aniqlash uchun etarli.

Agar aloqalar yuzaga kelsa, qo'shimcha ma'lumot kerak bo'lishi mumkin. Aloqalar ko'pchilik bo'lmagan juftliklar bo'lishi mumkin yoki ular bir xil o'lchamdagi ko'pchilik bo'lishi mumkin; saylovchilar ko'p bo'lganda bu aloqalar kamdan-kam bo'ladi. Ba'zi Kondorset usullari boshqa turdagi bog'lanishlarga ega bo'lishi mumkin; masalan, bilan Kopeland usuli, Kondorset g'olibi bo'lmagan taqdirda, bir xil miqdordagi juftlikda ikki yoki undan ortiq nomzod g'olib chiqishi kamdan kam bo'lmaydi.^{[iqtibos kerak ]}

Ta'rif

Kondorset usuli bu har doim Kondorset g'olibini tanlaydigan ovoz berish tizimi (agar mavjud bo'lsa); bu saylovchilar bir-birlariga taqqoslaganda, saylovchilar bir-biridan afzal ko'rgan nomzod. Ushbu nomzodni (agar ular mavjud bo'lsa; keyingi xatboshiga qarang) boshqa barcha nomzodlarni mag'lub etgan nomzod borligini tekshirish orqali topish mumkin; bu yordamida amalga oshirilishi mumkin Kopeland usuli va keyin "Copeland" g'olibi "Copeland" ning eng yuqori balliga ega ekanligini tekshiradi. Yuqorida tavsiflangan Robertning tartib qoidalarida keltirilgan protseduradan foydalanib, ularni juft-juft taqqoslashlar o'tkazish orqali ham topish mumkin. Uchun N nomzodlar, bu talab qiladi N - 1 juft gipotetik saylov. Masalan, 5 nomzod bilan 4 juft taqqoslash o'tkazilishi kerak, chunki har bir taqqoslashdan keyin nomzod o'chiriladi va 4 chiqarib tashlanganidan so'ng dastlabki 5 nomzoddan faqat bittasi qoladi.

Kondorset g'olibi ma'lum bir saylovda mavjudligini tasdiqlash uchun avval Robertning "Buyurtma qoidalari" protsedurasini bajaring, qolgan oxirgi nomzodni protsedura g'olibi deb e'lon qiling va keyin qo'shimcha ravishda qo'shimcha qiling. N - protsedura g'olibi va ular bilan hali taqqoslanmagan nomzodlar o'rtasida ikkita juft taqqoslash (ilgari chiqarilgan barcha nomzodlarni hisobga olgan holda). Agar protsedura g'olibi barcha juftlik o'yinlarida g'olib chiqmasa, unda Kondorset g'olibi saylovda yo'q (va shu tariqa Smit to'plamida bir nechta nomzodlar mavjud).

Barcha juft taqqoslashlarni hisoblash uchun $ Delta $ talab qilinishini unutmangN(N−1) uchun juftlik bilan taqqoslash N nomzodlar. 10 nomzod uchun bu 0,5 * 10 * 9 = 45 taqqoslashni anglatadi, bu ko'plab nomzodlar bilan saylovlarni ovozlarni hisoblash qiyin bo'lishi mumkin.

Kondorset usullari oilasi, shuningdek, Kondorset usuli deb ham yuritiladi. Kondorset g'olibini har doim bor bo'lganda tanlaydigan ovoz berish tizimi saylov olimlari tomonidan Kondorset mezonini qondiradigan tizim sifatida tavsiflanadi.^{[iqtibos kerak ][13]} Bundan tashqari, ovoz berish tizimi har qanday Condorcet g'olibini tanlasa, Kondorset konsistentsiyasiga ega yoki Kondorset izchil bo'lishi mumkin.^[14]

Muayyan sharoitlarda saylovlarda Kondorset g'olibi bo'lmaydi. Bu "a" deb nomlanuvchi bog'lash turi natijasida yuzaga keladi ko'pchilik qoidalari aylanishitomonidan tasvirlangan Kondorset paradoksi. Keyinchalik g'olibni tanlash usuli har xil Kondorset usulidan boshqasiga qarab farq qiladi. Ba'zi Kondorset usullari quyida tavsiflangan asosiy protsedurani o'z ichiga oladi va Kondorset g'olibi bo'lmagan taqdirda g'olibni topish uchun foydalaniladigan Kondorset tugatish usuli bilan birlashtiriladi. Boshqa Condorcet usullari hisoblashning mutlaqo boshqa tizimini o'z ichiga oladi, ammo Condorcet usullari yoki Condorcet izchil deb tasniflanadi, chunki agar ular mavjud bo'lsa, ular Kondorset g'olibini tanlaydilar.^[14]

Shuni ta'kidlash kerakki, bitta g'olib ham emas, ovoz berish tizimlari Condorcet usullari. Masalan, bir zumda ovoz berish va Borda hisoblash Condorcet usullari emas.^[14][15]

Asosiy protsedura

Ovoz berish

Kondorset saylovlarida saylovchi nomzodlar ro'yxatini afzalligi bo'yicha tartiblaydi. Masalan, saylovchi birinchi afzalliklariga "1", ikkinchi afzalliklariga "2" va hokazolarni beradi. Shu nuqtai nazardan, bu Kondorset usulida bo'lmagan saylovlar bilan bir xil bir zumda ovoz berish yoki bitta o'tkaziladigan ovoz. Kondorsetning ba'zi usullari saylovchilarga bir nechta nomzodlarni teng ravishda reytingga qo'yishga imkon beradi, masalan, saylovchi bitta emas, balki ikkita birinchi afzallikni bildirishi mumkin.^{[iqtibos kerak ]} Buning o'rniga saylovchilarga nomzodlarga o'xshash shkala bo'yicha baho berishlari yoki ball to'plashlariga imkon berish mumkin Balli ovoz berish, ko'proq imtiyozni ko'rsatadigan yuqori reytingga ega.^[16]

Odatda, saylovchi imtiyozlarning to'liq ro'yxatini bermasa, hisoblash uchun, ular reytingga kiritgan nomzodlarni ular kiritmagan barcha nomzodlardan afzal ko'rishlari va ular tanlagan nomzodlar o'rtasida hech qanday afzalliklarga ega bo'lmasliklari kerak. unvon. Ba'zi Kondorset saylovlariga ruxsatnoma yozish uchun nomzodlar Ammo, buni amalga oshirish qiyin bo'lishi mumkinligi sababli, Kondorset saylovlarini o'tkazish uchun mo'ljallangan dasturiy ta'minot ko'pincha ushbu parametrga yo'l qo'ymaydi.^{[iqtibos kerak ]}

G'olibni topish

Hisoblash gipotetik yakkama-yakka tanlovlarda har bir nomzodni boshqa nomzodlarga qarshi qo'yish orqali amalga oshiriladi. Har bir juftlikning g'olibi saylovchilarning ko'pchiligi tomonidan afzal ko'rilgan nomzod hisoblanadi. Agar ular bog'lamasalar, faqat ikkita tanlov mavjud bo'lganda har doim ko'pchilik bo'ladi. Har bir saylovchi tomonidan afzal ko'rilgan nomzod, saylovchilarning saylov byulletenlarida reytingi (yoki baholari) yuqoriroq bo'lgan juftlikdagi nomzod sifatida qabul qilinadi. Masalan, agar Elis Bobga qarshi juft bo'lsa, Elisni Bobdan yuqori bo'lgan saylovchilar sonini ham, Bobni Elisdan yuqori bo'lganlarni ham sanash kerak. Agar Elisni ko'proq saylovchilar afzal ko'rishsa, u bu juftlikning g'olibi hisoblanadi. Nomzodlarning barcha mumkin bo'lgan juftliklari ko'rib chiqilganda, agar bitta nomzod ushbu bahslarda boshqa nomzodlarni mag'lub etsa, ular Kondorset g'olibi deb e'lon qilinadi. Yuqorida ta'kidlab o'tilganidek, agar Kondorset g'olibi bo'lmasa, saylov g'olibini topish uchun qo'shimcha usuldan foydalanish kerak va bu mexanizm har xil Kondorset usulidan boshqasiga farq qiladi.^[14] O'tkaziladigan har qanday Condorcet usulida Smit tomonidan boshqariladigan alternativalarning mustaqilligi, ba'zan buni aniqlashga yordam beradi Smit o'rnatdi boshdan-oyoq matchuplardan va ushbu Kondorset usuli uchun protsedurani bajarishdan oldin barcha nomzodlarni yo'q qiling.

Juftlik bilan hisoblash va matritsalar

Kondorset usullari juft hisoblash usulidan foydalanadi. Mumkin bo'lgan har bir juft nomzod uchun bitta juftlik bilan hisoblash, qancha nomzod boshqa nomzoddan ko'ra juftlangan nomzodlardan birini afzal ko'rishini, yana bir juftlik bilan hisoblash esa qancha saylovchilarning qarama-qarshi afzalliklarga ega ekanligini ko'rsatadi. Nomzodlarning mumkin bo'lgan barcha juftliklari bo'yicha hisob-kitoblar barcha saylovchilarning barcha juftlik afzalliklarini umumlashtiradi.

Juftliklar soni ko'pincha a-da ko'rsatiladi juft taqqoslash matritsasi^[17] yoki ustun matritsa^[18] Quyidagi kabi. Bularda matritsalar, har bir satr har bir nomzodni "yuguruvchi", har bir ustun har bir nomzodni "raqib" sifatida ifodalaydi. Qator va ustunlar kesishgan katakchalarning har biri ma'lum juft taqqoslash natijasini ko'rsatadi. Nomzodni o'zlari bilan taqqoslaydigan hujayralar bo'sh qoldiriladi.^[19][20]

Tasavvur qiling, to'rtta nomzod o'rtasida saylovlar bo'lib o'tmoqda: A, B, C va D. Quyidagi birinchi matritsada bitta byulletenda ko'rsatilgan afzalliklar qayd etilgan bo'lib, unda saylovchilarning istaklari (B, C, A, D); ya'ni saylovchi birinchi o'rinda B, C ikkinchi, A uchinchi va D to'rtinchi o'rinni egalladi. Matritsada a '1' yuguruvchining 'raqib' dan ustunligini, '0' esa yuguruvchining mag'lub bo'lganligini bildiradi.^[19][17]

Yuqoridagi kabi matritsadan foydalanib, saylovning umumiy natijalarini topish mumkin. Har bir saylov byulleteni ushbu matritsaning uslubiga aylantirilishi va undan keyin boshqa barcha saylov matritsalariga qo'shilishi mumkin matritsa qo'shilishi. Saylovdagi barcha byulletenlarning yig'indisi summa matritsasi deb ataladi.

Faraz qilaylik, xayoliy saylovlarda yana ikkita saylovchi bor. Ularning afzalliklari (D, A, C, B) va (A, C, B, D). Birinchi saylovchiga qo'shilgan ushbu saylov byulletenlari quyidagi summa matritsasini beradi:

Summa matritsa topilganda, har bir juft nomzod o'rtasidagi bahs ko'rib chiqiladi. Raqib ustidan yuguruvchi (yuguruvchi, raqib) uchun berilgan ovozlar soni Kondorset g'olibini topish uchun yuguruvchi (raqib, yuguruvchi) ustidan berilgan ovozlar soni bilan taqqoslanadi. Yuqoridagi summa matritsasida A Kondorset g'olibi hisoblanadi, chunki A har bir boshqa nomzodni mag'lub etadi. Condorcet g'olibi bo'lmasa, reyting juftlari va Schulze usuli kabi Kondorsetni to'ldirish usullari g'olibni tanlash uchun yig'indisi matritsasidagi ma'lumotlardan foydalaning.

Yuqoridagi matritsalarda '-' belgisi qo'yilgan katakchalar '0' qiymatiga ega, ammo chiziqcha ishlatiladi, chunki nomzodlar hech qachon o'zlaridan ustun bo'lmaydi. Bitta byulleteni ifodalaydigan birinchi matritsa teskari nosimmetrik: (yuguruvchi, raqib) ¬ (raqib, yuguruvchi). Yoki (yuguruvchi, raqib) + (raqib, yuguruvchi) = 1. Jami matritsa quyidagi xususiyatga ega: (yuguruvchi, raqib) + (raqib, yuguruvchi) = N saylovchi uchun N, agar barcha yuguruvchilar har bir saylovchi tomonidan to'liq tartiblangan bo'lsa.

Misol: Tennessi poytaxti joylashgan joyda ovoz berish

Buni tasavvur qiling Tennessi uning joylashgan joyi bo'yicha saylov o'tkazmoqda poytaxt. Tennesi shtati aholisi shtat bo'ylab tarqalgan to'rtta yirik shahar atrofida to'plangan. Ushbu misol uchun, deylik saylovchilar bu to'rtta shaharda yashaydi va har kim imkon qadar poytaxtga yaqin joyda yashashni xohlaydi.

Poytaxtga nomzodlar:

• Memfis, shtatning eng katta shahri, saylovchilarning 42 foizi ishtirok etgan, ammo boshqa shaharlardan uzoqda joylashgan
• Neshvill, saylovchilarning 26% ishtirokida, shtat markaziga yaqin
• Noksvill, saylovchilarning 17% ishtirok etdi
• Chattanuga, 15% saylovchilar bilan

Saylovchilarning afzalliklari quyidagicha taqsimlanadi:

Kondorset g'olibini topish uchun har bir nomzod xayoliy yakkama-yakka tanlovlarning barcha boshqa nomzodlariga mos kelishi kerak. Har bir juftlikda g'olib ovoz beruvchilarning ko'pchilik ovozi bilan afzal bo'ladi. Har qanday mumkin bo'lgan juftlik natijalari aniqlanganda ular quyidagilar:

Natijalar matritsa shaklida ham ko'rsatilishi mumkin:

Yuqoridagi ikkala jadvaldan ko'rinib turibdiki, Nashvill har bir boshqa nomzodni mag'lubiyatga uchratmoqda. Bu shuni anglatadiki, Nashvill Kondorset g'olibidir. Shunday qilib, Nashvill har qanday mumkin bo'lgan Kondorset usuli ostida o'tkazilgan saylovda g'olib chiqadi.

Kondorsetning har qanday usuli Nashvillni g'olib deb tanlaydi, agar uning o'rniga bir xil ovozlar asosida saylovlar o'tkazilsa birinchi o'tgan yoki bir zumda ovoz berish, ushbu tizimlar Memfisni tanlaydi^[21] va Noksvill^[22] navbati bilan. Aksariyat odamlar Neshvillni o'sha "g'olib" lardan birini afzal ko'rishlariga qaramay, bu sodir bo'lar edi. Kondorset usullari bu afzalliklarni e'tiborsiz qoldirish yoki bekor qilish o'rniga aniqroq qiladi.

Boshqa tomondan, ushbu misolda Chattanooga ushbu shaharlarga qarshi juftlik paytida Noksvill va Memfisni ham mag'lub etganiga e'tibor bering. Agar biz imtiyozni aniqlash uchun asosni o'zgartirib, Memfis saylovchilari Chattanugani uchinchi tanlov sifatida emas, balki ikkinchi tanlov sifatida afzal ko'rishganini aniqlasak, Chattanooga Kondorset g'olibi bo'lar edi, garchi post-postdan oldingi saylovlarda oxirgi o'rinni egallagan bo'lsa ham.

Ushbu misol haqida fikr yuritishning muqobil usuli, agar a Smit-samarali Kondorset usuli ISDA g'olibni aniqlash uchun ishlatiladi, bu saylovchilarning 58%, a o'zaro ko'pchilik, Memfisni oxirgi o'rinda (Memfisni shunday qiladi) ko'pchilik yutqazgan ) va Memfis ustidan hukmronlik qilgan Neshvill, Chattanuga va Noksvill. O'sha paytda Memfisni 1-tanlovi sifatida tanlagan saylovchilar faqat Nashvill, Chattanuga va Noksvill o'rtasida g'olibni tanlashda yordam berishlari mumkin edi va ularning barchasi Nashvillni o'sha uch kishining birinchi tanlovi sifatida tanlagani uchun, Nashvill 68 foizga ega bo'lar edi. qolgan nomzodlar orasida 1-tanlovning aksariyati va ko'pchilikning 1-tanlovi sifatida g'olib bo'ldi.

Dumaloq noaniqliklar

Yuqorida ta'kidlab o'tilganidek, ba'zida saylovlarda Kondorset g'olibi bo'lmaydi, chunki saylovchilar tomonidan boshqa barcha nomzodlardan ustun bo'lgan nomzod yo'q. Bu sodir bo'lganda, vaziyat "ko'pchilik qoidalari tsikli", "dumaloq noaniqlik", "dumaloq taqish", "Kondorset paradoks" yoki oddiygina "tsikl" deb nomlanadi. Bu holat, barcha ovozlar to'plangandan so'ng, ba'zi nomzodlarga nisbatan saylovchilarning afzalliklari doirani shakllantirganda paydo bo'ladi, unda har bir nomzod kamida bitta nomzod tomonidan kaltaklanadi.(O'zgaruvchanlik ).

Masalan, uchta nomzod bo'lsa, Nomzod rok, nomzod qaychi va nomzod qog'ozi, agar saylovchilar nomzod qaychi va qog'oz o'rniga qaychi o'rniga nomzod qog'ozni afzal ko'rishsa, nomzod qog'ozi toshdan ustun bo'lsa, Condorcet g'olibi bo'lmaydi. Saylovlar o'tkaziladigan kontekstga qarab, dumaloq noaniqliklar keng tarqalgan bo'lishi mumkin yoki bo'lmasligi mumkin, ammo tartiblangan ovoz berish bilan hukumat saylovlari bo'yicha ma'lum bir holat mavjud emas, unda tartiblangan saylov byulletenlari yozuvlaridan dumaloq noaniqlik ko'rinadi. Shunga qaramay, tsikl har doim ham mumkin va shuning uchun har qanday Condorcet usuli g'olibni aniqlab berishi mumkin. Noma'lumlikni hal qilish mexanizmi noaniqlik rezolyutsiyasi, tsiklni hal qilish usuli yoki Kondoretsni to'ldirish usuli.

Dumaloq noaniqliklar natijasida paydo bo'ladi ovoz berish paradoksi - barcha individual saylovchilar tranzitiv ustunlikni bildirgan bo'lishiga qaramay, saylov natijalari o'zgaruvchan bo'lishi mumkin (tsiklni shakllantirish). Kondorset saylovlarida bitta saylovchining afzalliklari tsiklik bo'lishi mumkin emas, chunki saylovchi barcha nomzodlarni tartibda, eng yuqori tanlovdan pastgacha tanlovgacha saralashi kerak va har bir nomzodni faqat bir marta saralashi mumkin, ammo ovoz berish paradoksi saylovchilarning saylov natijalarida haligacha dumaloq noaniqlik paydo bo'lishi mumkinligini anglatadi.

A ning idealizatsiyalangan tushunchasi siyosiy spektr ko'pincha siyosiy nomzodlar va siyosatni tavsiflash uchun ishlatiladi. Bunday spektr mavjud bo'lgan joyda va saylovchilar spektrda o'z pozitsiyalariga eng yaqin bo'lgan nomzodlarni afzal ko'rishganda, Kondorset g'olibi bor (Blekning yagona tepalik teoremasi ).

Kondorset usullarida, aksariyat saylov tizimlarida bo'lgani kabi, oddiy galstuk ehtimoli ham mavjud. Bu ikki yoki undan ortiq nomzodlar bir-biri bilan bog'lab turganda, lekin boshqa nomzodlarni mag'lubiyatga uchratganda yuz beradi. Boshqa tizimlarda bo'lgani kabi, buni tasodifiy usul bilan, masalan, qur'a tashlash orqali hal qilish mumkin. Bog'larni boshqa usullar bilan ham hal qilish mumkin, masalan, bog'langan g'oliblardan qaysi biri eng ko'p ovoz berganini ko'rish, ammo bu va boshqa tasodifiy bo'lmagan usullar taktik ovoz berishni qayta kiritishi mumkin, ayniqsa saylovchilar poyga yaqin bo'lishini bilsalar. .

Dumaloq noaniqliklarni hal qilish uchun ishlatiladigan usul turli Kondorset usullari orasidagi asosiy farqdir. Buni amalga oshirishning son-sanoqsiz usullari mavjud, ammo har qanday Kondorset usuli kamida ikkita juftlik bilan o'tkazilgan saylovlarda saylovchilar bildirgan ko'pchilikka e'tibor bermaslikni o'z ichiga oladi. Ba'zi tsikllarni hal qilish usullari Smit tomonidan samarali bo'ladi, ya'ni ular o'tishni anglatadi Smit mezonlari. Bu tsikl bo'lganida (va juftlik aloqalari bo'lmaganida), faqat tsikldagi nomzodlar g'alaba qozonishini kafolatlaydi va agar mavjud bo'lsa o'zaro ko'pchilik, ularning afzal ko'rgan nomzodlaridan biri g'olib chiqadi.

Kondorset usullari ikki toifaga to'g'ri keladi:

• Ikki usulli tizimlar, bu holda Condorcet g'olibi bo'lmagan hollarda alohida usulni qo'llaydi
• Bir usulli tizimlar, har qanday maxsus ishlov bermasdan har doim g'olibni Kondorset g'olibi sifatida aniqlaydigan yagona usuldan foydalanadi

Ko'p bitta usulli tizimlar va ba'zi ikki usulli tizimlar davra galstugida 4 dan kam nomzod bo'lsa va barcha saylovchilar alohida ravishda ushbu nomzodlarning ikkitasini ajratib ko'rsatadigan bo'lsalar, bir-birlari bilan bir xil natijani beradi. Bularga Smit-Minimaks (Minimax, ammo Smit to'plamida bo'lmagan barcha nomzodlar yo'q qilinganidan keyingina amalga oshiriladi), Reyting juftlari va Shults kiradi. Masalan, Smitdagi uchta nomzod bilan Kondorset tsikli o'rnatilgan, chunki Schulze va Rank Pairs o'tadi ISDA, avval Smit to'plamiga kirmagan barcha nomzodlarni yo'q qilish mumkin, so'ngra Shultsga uchta kuchsiz mag'lubiyatni tashlab qo'yish, o'sha eng zaif mag'lubiyatga ega bo'lgan nomzodga boshqa nomzodlarni mag'lubiyatga uchratadigan yoki bog'laydigan yagona nomzod bo'lishiga imkon beradi. Juftliklar, dastlabki ikkita kuchli mag'lubiyat qulflangandan so'ng, kuchsizlar buni qila olmaydi, chunki bu tsiklni yaratadi va shuning uchun eng zaif mag'lubiyatga uchragan nomzod ularga qarshi yopiq mag'lubiyatlarga ega bo'lmaydi).

Ikki usulli tizimlar

Kondorset usullarining bir oilasi avval bir necha juft taqqoslashni o'tkazadigan tizimlardan iborat bo'lib, keyin Kondorset g'olibi bo'lmasa, g'olibni aniqlash uchun butunlay boshqacha, Kondorset uslubiga qaytadi. Bunday eng sodda usullar juft taqqoslash natijalariga umuman e'tibor bermaslikni o'z ichiga oladi. Masalan, Qora usuli Kondorset g'olibini tanlaydi, agar u mavjud bo'lsa, lekin ishlatsa Borda hisoblash buning o'rniga tsikl bo'lsa (usul nomi berilgan Dunkan Qora ).

Ikki bosqichli murakkab jarayon - bu tsikl bo'lgan taqdirda, g'olibni topish uchun alohida ovoz berish tizimidan foydalanish, ammo bu ikkinchi bosqichni juftlik bilan taqqoslash natijalarini sinchkovlik bilan o'rganish orqali topilgan nomzodlarning ma'lum bir qismiga cheklash. Shu maqsadda foydalaniladigan to'plamlar shunday aniqlanganki, agar u mavjud bo'lsa, unda har doim faqat Kondorset g'olibi bo'ladi va har doim, har holda, kamida bitta nomzod bo'ladi. Bunday to'plamlarga quyidagilar kiradi

• Smit o'rnatdi: Belgilangan saylovda bo'sh bo'lmagan nomzodlarning eng kichik to'plami, chunki to'plamdagi har bir nomzod to'plamdan tashqaridagi barcha nomzodlarni mag'lub etishi mumkin. Har bir saylov uchun faqat bitta Smit to'plami mavjudligini osongina ko'rsatish mumkin.
• Shvarts o'rnatdi: Bu ichki mag'lubiyatsiz to'plam va odatda Smit to'plami bilan bir xil. Bu barcha mumkin bo'lgan nomzodlar birlashmasi sifatida belgilanadi, chunki har bir to'plam uchun:
  1. To'plam ichidagi har bir nomzod to'plamdan tashqaridagi boshqa nomzodlar tomonidan juftlik bilan mag'lub bo'lmaydilar (ya'ni bog'lashga ruxsat beriladi).
  2. To'plamning to'g'ri (kichikroq) kichik to'plami birinchi xususiyatni bajarmaydi.
• Landau o'rnatdi (yoki yopiq to'plam yoki Fishburn to'plami): nomzodlar to'plami, har bir a'zo boshqa har bir nomzod uchun (shu qatorda nomzodlar qatorida) ushbu nomzodni mag'lub etadi yoki o'zi nomzodni mag'lubiyatga uchratmagan uchinchi nomzodni mag'lub qiladi.

Mumkin bo'lgan usullardan biri bu qo'llashdir bir zumda ovoz berish turli yo'llar bilan, masalan, Smit to'plamining nomzodlariga. Ushbu usulning bir varianti "Smit / IRV" deb ta'riflangan, boshqasi esa Tidemanning muqobil usullari. Shuningdek, "Smit / Tasdiqlash" ni saylovchilarga nomzodlarni saralashga ruxsat berish va qaysi nomzodlarni ma'qullashlarini ko'rsatish orqali amalga oshirish mumkin, masalan, eng ko'p saylovchilar tomonidan tasdiqlangan Smit to'plamidagi nomzod g'olib chiqadi; bu ko'pincha tasdiqlash chegarasi yordamida amalga oshiriladi (ya'ni, agar siz 3-tanlovingizni ma'qullasangiz, siz o'zingizning 1-chi va 2-chi tanlovlaringizni avtomatik ravishda tasdiqlashingiz mumkin). Smit / Skorda Smit nomzodi eng yuqori umumiy ballni qo'lga kiritdi, natijada juftlik bilan taqqoslash amalga oshirildi, natijada nomzodlar boshqalarnikidan yuqori to'plandi.

Bir usulli tizimlar

Ba'zi Kondorset usullari Kondorset mezonlariga mos keladigan yagona protseduradan foydalanadi va ortiqcha protsedurasiz, shuningdek, ular paydo bo'lganda dumaloq noaniqliklarni hal qiladi. Boshqacha qilib aytganda, ushbu usullar turli vaziyatlar uchun alohida protseduralarni o'z ichiga olmaydi. Odatda bu usullar o'zlarining hisob-kitoblarini juft hisoblashlar asosida amalga oshiradi. Ushbu usullarga quyidagilar kiradi:

• Kopeland usuli: Ushbu oddiy usul eng ko'p juftlik bilan mos keladigan nomzodni tanlashni o'z ichiga oladi. Biroq, ko'pincha galstuk ishlab chiqaradi.
• Kemeny-Young usuli: Ushbu usul eng ommabop va ikkinchi eng ommabopdan eng ommabopgacha bo'lgan barcha tanlovlarni saralaydi.
• Minimaks: Shuningdek, deyiladi Simpson, Simpson-Kramerva Oddiy Condorcet, bu usul eng yomon juftlik mag'lubiyati boshqa barcha nomzodlarga qaraganda yaxshiroq bo'lgan nomzodni tanlaydi. Ushbu uslubni takomillashtirish, uni Smit to'plami orasidan g'olib tanlash bilan cheklashni o'z ichiga oladi; bu chaqirildi Smit / Minimax.
• Nanson usuli va Bolduin usuli Borda Count-ni tez oqadigan tartib bilan birlashtirish.
• Dodgson usuli nomzodlarni almashtirish orqali Kondorset g'olibi topilguncha Kondorset usulini kengaytiradi. G'olib minimal miqdordagi svoplarni talab qiladigan nomzod hisoblanadi.
• Saralangan juftliklar har ikkala tsiklni juftlik bo'yicha afzallik grafigida tsikldagi eng zaif ko'pchilikni tashlab, buzadi va shu bilan nomzodlarning to'liq reytingini beradi. Ushbu usul shuningdek sifatida tanilgan Tideman, uning ixtirochisidan keyin Nikolay Tideman.
• Schulze usuli g'olib aniq aniqlanmaguncha, juftlik bilan ustunlik grafigidagi eng zaif ko'pchilikni takroriy ravishda tushiradi. Ushbu usul shuningdek sifatida tanilgan Shvarts ketma-ket tushib ketish (SSD), Shvarsning ketma-ket tushishi (CSSD), beatpath usuli, beatpath g'olibi, ovoz berish yo'li va yo'l g'olibi.

Rank Pairs va Schulze protseduraviy jihatdan bir-biriga qarama-qarshi yondashuvlardir (garchi ular juda tez-tez bir xil natijalarni berishadi):

• Reytingli juftliklar (va uning variantlari) eng kuchli mag'lubiyatlardan boshlanadi va noaniqlik yaratmasdan iloji boricha ko'proq ma'lumotlardan foydalanadi.
• Shulze noaniqlik olib tashlanmaguncha eng zaif mag'lubiyatni bir necha bor olib tashlaydi.

Minimaxni ushbu yondashuvlarning har ikkisiga qaraganda ko'proq "to'mtoq" deb hisoblash mumkin edi, chunki mag'lubiyatlarni olib tashlash o'rniga, eng kuchli mag'lubiyatlarni ko'rib chiqish bilan nomzodlarni darhol chiqarib tashlash (garchi ularning g'alabalari hanuzgacha keyingi nomzodlarni yo'q qilish uchun ko'rib chiqilmoqda). Mag'lubiyatlarni olib tashlash nuqtai nazaridan o'ylashning bir usuli shundaki, Minimax har bir nomzodning eng zaif mag'lubiyatlarini olib tashlaydi, ular orasida faqat juft juftlik rishtalari bo'lgan ba'zi nomzodlar guruhida mag'lubiyat qolmaguncha, guruh g'alaba qozonish uchun bog'lanadi.^[23]

Kemeny-Young usuli

Kemeny-Young usuli har qanday tanlov ketma-ketligini ko'rib chiqadi, qaysi tanlov eng mashhur bo'lishi mumkin, qaysi tanlov ikkinchi eng mashhur bo'lishi mumkin va shuning uchun qaysi tanlov eng ommabop bo'lishi mumkin. Har bir bunday ketma-ketlik yig'indisiga teng bo'lgan Kemeny ballari bilan bog'liq juftlik bilan hisoblash belgilangan ketma-ketlikka tegishli. Eng yuqori ball to'plagan ketma-ketlik eng ommabopdan eng ommabopgacha bo'lgan umumiy reyting sifatida aniqlanadi.

Tanlovlar eng ommabop (yuqori va chap) dan eng ommabop (pastki va o'ng) dan ketma-ketlikda paydo bo'ladigan matritsaga joylashtirilganda, g'olib bo'lgan Kemeny ballari yuqori o'ngdagi, uchburchakdagi hisoblar yig'indisiga teng matritsaning yarmi (bu erda yashil fonda qalin harflar bilan ko'rsatilgan).

Ushbu misolda Nashvill> Chattanooga> Noksvill> Memfis ketma-ketligining Kemeni reytingi 393 ga teng bo'ladi.

Har bir Kemeny balini hisoblash bir nechta tanlovni o'z ichiga olgan hollarda hisoblash uchun juda ko'p vaqtni talab qiladi. Biroq, asoslangan tez hisoblash usullari butun sonli dasturlash 40 ta tanlov bilan ba'zi holatlar uchun hisoblash vaqtini bir necha soniya ichida bering.

Saralangan juftliklar

Tugatish tartibi, ko'pchilikni kichikdan ko'pgacha (juftlik bilan) ko'pchilikni birma-bir ko'rib chiqib, bir vaqtning o'zida bir qismga quriladi. Har bir ko'pchilik uchun ularning yuqori darajadagi nomzodlari marraga (qisman tuzilgan) tartibda quyi darajadagi nomzodlaridan oldinroq joylashadilar, faqat quyi darajadagi nomzodlari ilgari yuqori darajadagi nomzodlaridan oldinroq joylashtirilgan hollar bundan mustasno.

Masalan, saylovchilarning imtiyozli buyruqlari 75% dan B darajaga, 65% A dan B ga va 60% A dan yuqori darajaga teng deb taxmin qiling (uchta ko'pchilik a tosh qog'oz qaychi tsikl.) tartiblangan juftliklar eng katta ko'pchilikdan boshlanadi, ular B ni C dan yuqori darajaga ko'taradilar va tugatish tartibida B ni C dan oldinroq qo'yadilar. Keyin A ni B dan yuqori darajadagi ikkinchi o'rinni egallaydi va tugatish tartibida A ni B dan ustun qo'yadi. Shu nuqtada A, B va B oldilarida tugaydi, bu A ning ham S ga teng kelishini bildiradi, shuning uchun reyting juftlari C dan A dan pastroq o'rinlarni egallagan uchinchi ko'pchilikni hisobga olganda nomzod A allaqachon yuqori darajadagi nomzod C dan oldinroq joylashtirilgan, shuning uchun C A dan oldin joylashtirilmagan. Tugatish tartibi "A, B, C" va A g'olib hisoblanadi.

Ekvivalent ta'rif bu eng katta teskari ko'pchilik hajmini minimallashtiradigan tugatish tartibini topishdir. ("Lug'atshunoslik tartibi" ma'nosida. Agar tugatishning ikkita tartibida teskari yo'naltirilgan aksariyat qismi bir xil bo'lsa, tugatishning ikki buyrug'i ikkinchi katta teskari ko'pchilik bilan taqqoslanadi va hokazo. Leksikografik buyurtma maqolasining "Motivatsiya va foydalanish" bo'limida MinMax, MinLexMax va Rank juftliklarini muhokama qilish ). (Masalan, "A, B, C" tugatish tartibi A dan yuqori bo'lgan 60% ni teskari tomonga o'zgartiradi, boshqa har qanday tugatish tartibi aksariyat ko'pchilikni qaytaradi.) Ushbu ta'rif Rankning ba'zi dalillarini soddalashtirish uchun foydalidir. Juftlik xususiyatlari, ammo "konstruktiv" ta'rifi ancha tezroq bajariladi (kichik polinom vaqti).

Schulze usuli

The Schulze usuli ovozlarni quyidagicha hal qiladi:

Har bir bosqichda biz quyidagicha harakat qilamiz:

1. Har bir olib tashlangan X va Y nomzod juftliklari uchun: Agar X nomzoddan Y nomzodga yo'naltirilmagan yo'nalishlarning yo'nalishi bo'lsa, biz "X → Y" ni yozamiz; aks holda biz "X → Y emas" deb yozamiz.
2. V va W olib tashlanmagan har bir juftlik nomzodlari uchun: Agar "V → W" va "emas W → V" bo'lsa, unda W nomzod o'chiriladi va W nomzod bilan boshlanadigan yoki tugaydigan barcha havolalar o'chiriladi.
3. Eng zaif ochilmagan havola o'chiriladi. Agar bir nechta ochilmagan havolalar eng zaif bo'lsa, ularning hammasi o'chiriladi.

Jarayon barcha havolalar o'chirilgandan so'ng tugaydi. G'oliblar tanlanmagan nomzodlardir.

Boshqacha qilib aytadigan bo'lsak, ushbu protsedura bir necha bor eng zaif juftlik mag'lubiyatini yuqori to'plam ichida tashlab yuboradi, natijada qolgan ovozlar aniq qarorga kelguniga qadar.

Kuchni mag'lub et

Ba'zi juft usullar, shu jumladan minimax, Rank Pairs va Schulze usuli - doiraviy noaniqliklarni mag'lubiyatlarning nisbiy kuchiga qarab hal qiladi. Har bir mag'lubiyatning kuchini o'lchashning turli xil usullari mavjud va ularga "g'alaba qozongan ovoz" va "ustunlik" ni hisobga olish kiradi:

• Ovozlarni yutib olish: Mag'lubiyatning g'olib tomonidagi ovozlar soni.
• Chegaralar: Mag'lubiyatning mag'lubiyat tomonidagi ovozlar sonini olib tashlagan holda, mag'lubiyat tomonidagi ovozlar soni.^[24]

Agar saylovchilar barcha nomzodlar uchun o'zlarining afzalliklarini belgilashmasa, ushbu ikki yondashuv turli xil natijalarga olib kelishi mumkin. Masalan, quyidagi saylovlarni ko'rib chiqing:

Ikkala mag'lubiyat quyidagicha:

• B A ni 55 dan 45 gacha mag'lub etdi (55 g'olib ovoz, 10 ovoz farqi)
• C - 45 dan 44 gacha (45 g'olib ovoz, 1 ovoz farqi)
• C B ni 29 dan 26 gacha mag'lub etdi (29 g'olib ovoz, 3 ovoz farqi)

Using the winning votes definition of defeat strength, the defeat of B by C is the weakest, and the defeat of A by B is the strongest. Using the margins definition of defeat strength, the defeat of C by A is the weakest, and the defeat of A by B is the strongest.

Using winning votes as the definition of defeat strength, candidate B would win under minimax, Ranked Pairs and the Schulze method, but, using margins as the definition of defeat strength, candidate C would win in the same methods.

If all voters give complete rankings of the candidates, then winning votes and margins will always produce the same result. The difference between them can only come into play when some voters declare equal preferences amongst candidates, as occurs implicitly if they do not rank all candidates, as in the example above.

The choice between margins and winning votes is the subject of scholarly debate. Because all Condorcet methods always choose the Condorcet winner when one exists, the difference between methods only appears when cyclic ambiguity resolution is required. The argument for using winning votes follows from this: Because cycle resolution involves disenfranchising a selection of votes, then the selection should disenfranchise the fewest possible number of votes. When margins are used, the difference between the number of two candidates' votes may be small, but the number of votes may be very large—or not. Only methods employing winning votes satisfy Woodall's plurality criterion.

An argument in favour of using margins is the fact that the result of a pairwise comparison is decided by the presence of more votes for one side than the other and thus that it follows naturally to assess the strength of a comparison by this "surplus" for the winning side. Otherwise, changing only a few votes from the winner to the loser could cause a sudden large change from a large score for one side to a large score for the other. In other words, one could consider losing votes being in fact disenfranchised when it comes to ambiguity resolution with winning votes. Also, using winning votes, a vote containing ties (possibly implicitly in the case of an incompletely ranked ballot) doesn't have the same effect as a number of equally weighted votes with total weight equaling one vote, such that the ties are broken in every possible way (a violation of Woodall's symmetric-completion criterion ), as opposed to margins.

Under winning votes, if two more of the "B" voters decided to vote "BC", the A->C arm of the cycle would be overturned and Condorcet would pick C instead of B. This is an example of "Unburying" or "Later does harm". The margin method would pick C anyway.

Under the margin method, if three more "BC" voters decided to "bury" C by just voting "B", the A->C arm of the cycle would be strengthened and the resolution strategies would end up breaking the C->B arm and giving the win to B. This is an example of "Burying". The winning votes method would pick B anyway.

Tegishli shartlar

Other terms related to the Condorcet method are:

Kondorset yutqazgan

^{[iqtibos kerak ]} the candidate who is less preferred than every other candidate in a pairwise matchup (preferred by fewer voters than any other candidate).

Weak Condorcet winner

^{[iqtibos kerak ]} a candidate who beats or ties with every other candidate in a pairwise matchup (preferred by at least as many voters as any other candidate). There can be more than one weak Condorcet winner.^[25]

Weak Condorcet loser

^{[iqtibos kerak ]} a candidate who is defeated by or ties with every other candidate in a pairwise matchup. Similarly, there can be more than one weak Condorcet loser.

Improved Condorcet winner

^{[iqtibos kerak ]} in improved condorcet methods, additional rules for pairwise comparisons are introduced to handle ballots where candidates are tied, so that pairwise wins can not be changed by those tied ballots switching to a specific prerfence order. A strong improved condorcet winner in an improved condorcet method must also be a strong condorcet winner, but the converse need not hold. In tied at the top methods, the number of ballots where the candidates are tied at the top of the ballot is subtracted from the victory margin between the two candidates. This has the effect of introducing more ties in the pairwise comparison graph, but allows the method to satisfy the favourite betrayal criterion.

Condorcet ranking methods

Some Condorcet methods produce not just a single winner, but a ranking of all candidates from first to last place. A Condorcet ranking is a list of candidates with the property that the Condorcet winner (if one exists) comes first and the Condorcet loser (if one exists) comes last, and this holds recursively for the candidates ranked between them.

Methods that satisfy this property include:

• Kopeland usuli
• Kemeny-Young usuli
• Saralangan juftliklar
• Schulze usuli
• Condorcet Star method

Though there won't always be a Condorcet winner or Condorcet loser, there is always a Smith set and "Smith loser set" (smallest group of candidates who lose to all candidates not in the set in head-to-head elections). Some voting methods produce rankings that sort all candidates in the Smith set above all others, and all candidates in the Smith loser set below all others, with this holding recursively for all candidates ranked between them; in essence, this guarantees that when the candidates can be split into two groups, such that every candidate in the first group beats every candidate in the second group head-to-head, then all candidates in the first group are ranked higher than all candidates in the second group.^[26] Because the Smith set and Smith loser set are equivalent to the Condorcet winner and Condorcet loser when they exist, methods that always produce Smith set rankings also always produce Condorcet rankings.

Comparison with instant runoff and first-past-the-post (plurality)

Bu maqola kabi yozilgan shaxsiy mulohaza, shaxsiy insho yoki bahsli insho Vikipediya tahrirlovchisining shaxsiy his-tuyg'ularini bayon qiladigan yoki mavzu bo'yicha asl dalillarni keltiradigan. Iltimos uni yaxshilashga yordam bering uni qayta yozish orqali entsiklopedik uslub. (Noyabr 2020) (Ushbu shablon xabarini qanday va qachon olib tashlashni bilib oling)

Ko'p tarafdorlari bir zumda ovoz berish (IRV) are attracted by the belief that if their first choice does not win, their vote will be given to their second choice; if their second choice does not win, their vote will be given to their third choice, etc. This sounds perfect, but it is not true for every voter with IRV. If someone voted for a strong candidate, and their 2nd and 3rd choices are eliminated before their first choice is eliminated, IRV gives their vote to their 4th choice candidate, not their 2nd choice. Kondorets ovoz berish takes all rankings into account simultaneously, but at the expense of violating the later-no-harm criterion va keyinchalik yordam bermaslik mezonlari. With IRV, indicating a second choice will never affect your first choice. With Condorcet voting, it is possible that indicating a second choice will cause your first choice to lose.

Ko'pchilik ovoz berish is simple, and theoretically provides incentives for voters to compromise for centrist candidates rather than throw away their votes on candidates who can't win. Opponents to plurality voting point out that voters often vote for the lesser of evils because they heard on the news that those two are the only two with a chance of winning, not necessarily because those two are the two natural compromises. This gives the media significant election powers. And if voters do compromise according to the media, the post election counts will prove the media right for next time. Condorcet runs each candidate against the other head to head, so that voters elect the candidate who would win the most sincere runoffs, instead of the one they thought they had to vote for.

There are circumstances, as in the examples above, when both bir zumda ovoz berish va 'birinchi o'tgan ' plurality system will fail to pick the Condorcet winner. (In fact, FPTP can elect the Condorcet loser and IRV can elect the second-worst candidate, who would lose to every candidate except the Condorcet loser.^[27]) In cases where there is a Condorcet Winner, and where IRV does not choose it, a majority would by definition prefer the Condorcet Winner to the IRV winner. Proponents of the Condorcet criterion see it as a principal issue in selecting an electoral system. They see the Condorcet criterion as a natural extension of ko'pchilik hukmronligi. Condorcet methods tend to encourage the selection of centrist candidates who appeal to the o'rtacha saylovchi. Here is an example that is designed to support IRV at the expense of Condorcet:

B is preferred by a 501–499 majority to A, and by a 502–498 majority to C. So, according to the Condorcet criterion, B should win, despite the fact that very few voters rank B in first place. By contrast, IRV elects C and plurality elects A. The goal of a ranked voting system is for voters to be able to vote sincerely and trust the system to protect their intent. Plurality voting forces voters to do all their tactics before they vote, so that the system does not need to figure out their intent.

The significance of this scenario, of two parties with strong support, and the one with weak support being the Condorcet winner, may be misleading, though, as it is a common mode in plurality voting systems (see Dyverger qonuni ), but much less likely to occur in Condorcet or IRV elections, which unlike Plurality voting, punish candidates who alienate a significant block of voters.

Here is an example that is designed to support Condorcet at the expense of IRV:

B would win against either A or C by more than a 65–35 margin in a one-on-one election, but IRV eliminates B first, leaving a contest between the more "polar" candidates, A and C. Proponents of plurality voting state that their system is simpler than any other and more easily understood.

All three systems are susceptible to taktik ovoz berish, but the types of tactics used and the frequency of strategic incentive differ in each method.

Potential for tactical voting

Like all voting methods,^[28] Condorcet methods are vulnerable to murosa qilish. That is, voters can help avoid the election of a less-preferred candidate by insincerely raising the position of a more-preferred candidate on their ballot. However, Condorcet methods are only vulnerable to compromising when there is a majority rule cycle, or when one can be created.^[29]

All Condorcet methods are at least somewhat vulnerable to dafn qilish. That is, voters can sometimes help a more-preferred candidate by insincerely lowering the position of a less-preferred candidate on their ballot.

Example with the Schulze usuli:

• B is the sincere Condorcet winner. But since A has the most votes and almost has a majority, with A and B forming a mutual majority of 90% of the voters, A can win by publicly instructing A voters to bury B with C (see * below), using B-top voters' 2nd choice support to win the election. If B, after hearing the public instructions, reciprocates by burying A with C, C will be elected, and this threat may be enough to keep A from pushing for his tactic. B's other possible recourse would be to attack A's ethics in proposing the tactic and call for all voters to vote sincerely. Bu chicken dilemma.

• B beats A by 8 as before, and A beats C by 82 as before, but hozir C beats B by 12, forming a Smith set bittadan kattaroq. Hatto Schulze usuli elects A: The path strength of A beats B is the lesser of 82 and 12, so 12. The path strength of B beats A is only 8, which is less than 12, so A wins. B voters are powerless to do anything about the public announcement by A, and C voters just hope B reciprocates, or maybe consider compromise voting for B if they dislike A enough.

Supporters of Condorcet methods which exhibit this potential problem could rebut this concern by pointing out that pre-election polls are most necessary with ko'pchilik ovoz berish, and that voters, armed with ranked choice voting, could lie to pre-election pollsters, making it impossible for Candidate A to know whether or how to bury. It is also nearly impossible to predict ahead of time how many supporters of A would actually follow the instructions, and how many would be alienated by such an obvious attempt to manipulate the system.

• In the above example, if C voters bury B with A, A will be elected instead of B. Since C voters prefer B to A, only they would be hurt by attempting the burying. Except for the first example where one candidate has the most votes and has a near majority, the Schulze method is very resistant to burying.

Evaluation by criteria

Scholars of electoral systems often compare them using mathematically defined ovoz berish tizimi mezonlari. The criteria which Condorcet methods satisfy vary from one Condorcet method to another. However, the Condorcet criterion implies the ko'pchilik mezonlari, and thus is incompatible with ahamiyatsiz alternativalarning mustaqilligi (though it implies a weaker analogous form of the criterion: when there is a Condorcet winner, losing candidates can drop out of the election without changing the result),^[30] later-no-harm, ishtirok etish mezonlari, va izchillik mezonlari.

Use of Condorcet voting

sample ballot for Wikimedia's Board of Trustees elections

Condorcet methods are not known to be currently in use in government elections anywhere in the world, but a Condorcet method known as Nanson usuli was used in city elections in the BIZ. shaharcha Market, Michigan 1920-yillarda,^[31] and today Condorcet methods are used by a number of private organizations. Organizations which currently use some variant of the Condorcet method are:

• The Vikimedia fondi ishlatilgan Schulze usuli to elect its Board of Trustees until 2013, when it switched to a reytinglar byulleteni with Support/Neutral/Oppose ballots.^[32]
• The Pirate Party of Sweden dan foydalanadi Schulze usuli for its primaries
• The Debian project uses the Schulze usuli for internal referenda and to elect its leader
• The Jamiyat manfaati uchun dasturiy ta'minot corporation uses the Schulze usuli for internal referenda and to elect its Board of Directors
• The Gentoo Foundation dan foydalanadi Schulze usuli for internal referenda and to elect its Board of Trustees and its Council
• The Bepul davlat loyihasi ishlatilgan Minimaks for choosing its target state
• The Buyuk Britaniya.* hierarchy of Usenet
• The Student Society of the University of British Columbia foydalanadi juftliklar for its executive elections.
• Kingman Hall va Hillegass Parker House, two loosely affiliated student housing cooperatives, each use the Schulze usuli to elect their management teams.

Boshqa fikrlar

• Condorcet election results show the win margins for every head to head runoff. If the Condorcet winner (A) is part of an A beats B beats C beats A Smith set, supporters of Candidate C will know that Candidate C would win a saylovni esga olish if candidate B is somehow kept off the ballot. If Condorcet voting is used, the rules for ballot access in recall elections may need to be evaluated to take the potential motives into consideration.

• If every seat in a legislature is elected (in separate elections, by the same pool of voters – use of districts will avoid this) by the Condorcet method, the legislators would all be centrists and might all agree with each on what laws to pass. Some voters prefer to have opposites in the legislature so they can't pass laws easily. These voters might prefer the Condorcet method for electing executive offices.

• If 10 candidates run for governor in a Condorcet race, ballot counters may need to count 9+8+7+6+5+4+3+2+1 = 45 head to head runoffs to find the winner. While this is doable, it might be more practical to still use ballot access laws or primaries, defeating some of the original intent of the Condorcet method. Possible solutions:
  • Computers can be used to speed up the counts, though some voters fear computers can be hacked and used for ballot counting fraud.
  • Another option would be to allow several independent scanner owners count the ballots and compare results. Volunteer hand counters could then spot check various candidates and ranks to make sure they match the subtotals reported by the scanners.
  • It is also possible to limit the number of ranks voters can use; for example, if every voter is only allowed to rank each candidate either 1st, 2nd, or 3rd, with equal rankings allowed, then only the runoffs between candidates ranked 1st and 2nd, 1st and 3rd, 1st and last, 2nd and 3rd, 2nd and last, and 3rd and last need be counted, as the runoffs between two candidates at the same rank will result in ties.
  • The negative vote-counting approach to pairwise counting may reduce the amount of work the vote-counters have to do.^[33] For example, with 10 candidates, a voter who ranks candidate A as their 1st choice and doesn't rank any other candidate prefers A over 9 other candidates. In the regular approach, this means recording those 9 preferences; but with negative counting, it can simply be recorded that A is marked on 1 voter's ballot and that no other candidate is preferred over A, with this itself indicating that A is preferred in every match-up. When a voter ranks a candidate 2nd, then a negative vote can be placed in the matchup between the 2nd choice and 1st choice to indicate that the 2nd choice is emas preferred to the 1st choice, such that it will cancel out with the support the 2nd choice would receive against the 1st choice from being marked on the voter's ballot. Negative votes can likewise be applied to matchups where both candidates are ranked equally.
  • If there are no more than 5 candidates ( or a larger number of candidates is short-listed to 5) then the amount of effort counting ballots could be reduced to normal acceptable levels by asking voters to select an order of preference from a predetermined list of the possibilities. This would mean that the ballots would just require to be counted once to determine the number of votes cast for each order of preference. The results would then be entered into a simple spreadsheet which would determine the Condorcet winner. For example where there are candidates A, B and C, there are six orders of preference, so voters could be asked to choose which of the six they wish to vote for. Counting would then be simply a matter of counting how votes were cast for each order of preference. The results could then be applied to a simple spreadsheet which revealed the Condorcet winner. If there were four candidates (options) then there would be 24 orders of preference; if there were five candidates then there would be 120 orders of preference and so on.

• Voters make an economic trade-off in the amount of time invested in researching and ranking candidates. If voters rank too few candidates or rank such as to inaccurately represent their preferences, the Condorcet candidate cannot be correctly discovered. Nominating primaries reduce the number of candidates to avoid this, and the style of nominating primary can impact whether the Condorcet candidate—or at least a similar candidate—remains or if all such candidates are eliminated in favor of polarized options.

Shuningdek qarang

• Kondorsetni yo'qotish bo'yicha mezon
• Ramon Lull (1232–1315) who, with the 2001 discovery of his lost manuscripts Ars notandi, Ars eleccionisva Alia ars eleccionis, was given credit for discovering the Borda count and Condorcet criterion (Llull winner) in the 13th century

Proportional forms of Condorcet

• CPO-STV
• Schulze STV

Izohlar va ma'lumotnomalar

Qo'shimcha o'qish

• Black, Duncan (1958). The Theory of Committees and Elections. Kembrij universiteti matbuoti.
• Farquarson, Robin (1969). Ovoz berish nazariyasi. Oksford.
• Sen, Amartya Kumar (1970). Kollektiv tanlov va ijtimoiy ta'minot. Holden-Day. ISBN  978-0-8162-7765-0.

Tashqi havolalar

• Johnson, Paul E, Ovoz berish tizimlari (PDF), Free faculty, olingan 2015-06-27.
• Lanphier, Robert ‘Rob’, Condorcet's Method.
• Loring, Robert ‘Rob’, Accurate Democracy, dan arxivlangan asl nusxasi 2004-10-30 kunlari, olingan 2004-11-02.
• McKinnon, Ron, Condorcet Canada Initiative, CA, olingan 2019-01-08. Multipage description of Condorcet method and Ranked Pairs from a Canadian perspective.
• Moulin, Hervé, Voting and Social Choice (PDF), NL: UVA, olingan 2015-06-27. Demonstration and commentary on Condorcet method.
• Perez, Joaquin, A strong No Show Paradox is a common flaw in Condorcet voting correspondences (PDF), ES: UAH, archived from asl nusxasi (PDF) 2016-03-03 da, olingan 2015-06-27.
• Prabhakar, Ernest (2010-06-28), Maximum Majority Voting (a Condorcet method), Radical centrism, olingan 2015-06-27.
• Schulze, Markus, A New Monotonic, Clone-Independent, Reversal Symmetric, and Condorcet-Consistent Single-Winner Election Method (PDF).

Dasturiy ta'minot

• CIVS, a free web poll service using the Condorcet method, Cornell.
• Condorcet PHP (Open-source command line application and PHP kutubxona for computing multiple Condorcet methods and others).
• Condorcet.Vote (A free web poll application using the original Condorcet method and many others like Schulze method.).
• Gorr, Eric, Condorcet Voting Calculator.
• STV (software for computing Condorcet methods and STV), Sourceforge.
• VoteFair surveys (Free ranking service that calculates Condorcet–Kemeny results), VoteFair
• VoteFair Ranking (Open-source C++ election software that calculates Condorcet–Kemeny results.), VoteFair
• Voteer (free web pool service using a Condorcet algorythme), Arpinum
• w.c.s. (A free web poll application using OpenSTV for voting algorithms), Entr'ouvert