Zabe da Lissafi, ko Rarraba da Nasara
Matsalar zabi ta kasance a gabanmu koyaushe. Mutumin farko kuma ya fuskanci matsala: ta wane yanayi zai rayu? A daya bangaren kuma, zaben shugabannin kabilu ya fi sauki: wanda ya kashe dan takara ya yi mulki. Yau yafi wahala. Hakanan yana da kyau.
Jumlar Latin da aka yi amfani da ita a cikin taken labarin na nufin "raba kuma ku ci". An yi amfani da shi koyaushe. Ka haifar da rigima a cikin al'umma kuma zai yi maka sauƙi ka samu nasara. Masu cin nasara a Spain na ƙarni na 1990 da XNUMX da fasaha sun juya wasu kabilun Indiya gaba da wasu. A ƙarshen karni na XNUMX, jakadan Rasha Repnin ya sami nasara mai yawa: ya yi nasarar haifar da tashin hankali a cikin shekaru na ƙarshe na Poland mai zaman kanta. Haka ma Turawan mulkin mallaka a tsohuwar daularsu, kuma yakin Yugoslavia na XNUMX ya fara da Sabiyawan suna karawa da Croat da akasin haka.
Mun san misalan tada rikici da gangan a cikin ƙasa ɗaya. Abin farin ciki, wannan ba haka yake ba a Poland ta yau. Jam’iyya mai mulki misali ce ta tausasawa, kamewa da hankali, cike da mutunta ‘yan adawa, mutunta doka, kundin tsarin mulki da ra’ayin mutum mai sauki. A taron kasa da kasa muna nasara, sau da yawa tare da sifili (nasara mai tunawa 27: 0). A cikin wasanni, muna da kyau: mun tuna da wasan hockey mai ban mamaki da Kamaru. Babu abin kunya, 'yan siyasa sun fito fili. A ina suke da aljihunsu a cikin kawunansu! Jam’iyyar ce ke kan gaba. Za mu taimaka!
Tsaya, tsaya. Mu ba mujallar jarida ba ce. Bari mu ga yadda za ku iya lankwasa tsarin yanke shawara a cikin girman ilimin lissafi da ... dabaru. Cikakken bayanin zai zama babban aiki, mafi aikin jarida fiye da kimiyya.
Zaɓuɓɓuka masu zuwa suna yiwuwa.
Na farko, sarrafa rarraba kasa zuwa gundumomi.
Na biyu, zabar hanyar sauya kuri’u zuwa kujerun majalisa ko (misali, a batun zaben shugaban kasa) zuwa kujerun zabe.
Na uku: fassara lokacin da muryar take da mahimmanci da kuma lokacin da ba ta ba.
Ba na maganar cin zarafi a bayyane a nan, kamar magudin jahilcin masu jefa ƙuri'a (ga jamhuriyar jama'ar Poland, jefa ƙuri'a mara kyau yana nufin jefa kuri'a ga 'yan takarar da aka jera a saman jerin), zamba a cikin kirga kuri'u da aika bayanan da ke sama.
Zan fara . Menene wannan bakon kalmar? Ina yin bayani ta wata hanya ta zagayawa.
Wataƙila masu karatun ku sun san maki a wasan tennis. Muna samun maki, wasanni da saiti. Don cin nasarar wasan, kuna buƙatar lashe aƙalla kwallaye huɗu (maki), amma aƙalla biyu fiye da abokin hamayyar ku. Banda shi ne wasan da za a yi kunnen doki - ana buga shi har zuwa maki bakwai na nasara (ƙwallaye), kuma tare da ka'idar fa'idar wasan ƙwallon ƙafa biyu. Kwallan da aka ci nasara suna ƙididdige su da ban mamaki: 15, 30, 40, sannan muna amfani da sharuɗɗan "amfani - daidaituwa".
1. Hagu classic gerrymandering. Ma'auni na duniya ya juya zuwa nasara ga blue. Haka ne: a kowace gunduma na gundumar arewa, blues suna da goyon bayan 25% kawai, a cikin sauran har yanzu - amma ba su damu ba.
Ana tattara duwatsu masu daraja a cikin saiti. Don cin nasara saiti, dole ne ku sami aƙalla wasanni shida kuma aƙalla biyu fiye da abokin hamayyar ku. Lokacin da maki ya kai 6:6, ana buga wasan kunnen doki. Ana yin matches tare da nasara sau biyu ko uku. "Har zuwa nasara biyu" yana nufin wanda ya ci nasara biyu ya ci nasara. Don haka, sakamakon zai iya zama 2:0 ko 2:1 (kuma a daidaita 0:2, 1:2). Waɗannan dokokin suna nufin cewa ba kwa buƙatar samun ƙarin ƙwallo (maki) don cin wasan. A taƙaice, dole ne ku ci nasara mafi mahimmanci. Babban misali shine inda mai kunnawa A ya ci nasara a farkon saiti 6-0 yayin da sauran biyun suka yi rashin nasara da ci 4-6. Ya yi rashin nasara a wasa 14 da abokin hamayyarsa 12.
Zan yi nuni ga abin da na rubuta a ɗan lokaci kaɗan. Akwai lokuta da yawa marasa mahimmanci a wasan tennis. Kyakkyawan ɗan wasan tennis yana mai da hankali kan abin da ya fi dacewa.
Makomar miliyoyi a cikin takun salamander
Mu ci gaba zuwa zaben siyasa. Gabaɗaya, zuwa zaɓen da dubbai ko miliyoyi suka yanke shawara.
Dole ne ku fara samun ƙasa don mazaɓa. Domin? Ko yaya? oh ba! Wanda ya fara tunanin yadda zai yi hakan domin kara samun dama ga jam’iyyarsa shi ne Elbridge Jerry, wani dan siyasar Amurka shekaru dari biyu da suka wuce. Daya daga cikin da'irar da ya ba da shawara ita ce siffar ... salamander, kuma hade da sunansa da wannan wutsiya amphibian ya haifar da kalmar. Yana aiki da kyau tare da mazabar memba guda ɗaya, don haka ba a aiwatar da shi kai tsaye ga Poland ba. Tare da ofishin membobi da yawa, lamarin ya bambanta sosai. Kuna iya ƙonewa lokaci zuwa lokaci. Kuma abu mai ban sha'awa.
2. Jagoran damfara. Hagu: 40% na tallafin duniya ya juya zuwa nasara 4-2. Dama: Geometry yana yin babban aiki na juya 32% goyon baya zuwa 4:3 nasara ta duniya.
Don haka, bari mu yi tunanin wata ƙasa, mai yawan jama'a kuma tare da iyakoki na yau da kullun: cikakkiyar fili tare da ƙananan garuruwan filin cikinta. Zaben birni da na magajin gari shine mafi kyawun kwatance, amma a lissafin ba komai. Jam'iyya mai mulki a blue tana da goyon baya a sassan da aka yiwa alama fig. 1. Ganye gubar a cikin murabba'i kore. Tun da yake muna magana ne game da gundumomi masu zaman kansu, ba kome ba ne mene ne amfanin. Muna da haɗin kai a cikin ƙasa, yawancin murabba'in shuɗi kamar yadda akwai kore. Amma shuwagabanni suna mulki sun raba kasar zuwa yankuna. Akwai mazabu takwas (XNUMX)1). Menene sakamakon zaben? Ba zato ba! 'Yan wasan blue suna nasara a A, C, E, F, G, wato a cikin biyar cikin takwas. Dangane da mazabar mambobi daya, suna da damar 5:3 a duk fadin kasar (watakila garuruwan idan zaben magajin gari ne).
labarin kasa na zabe wannan yana da muhimmiyar fa'ida ga jam'iyyar da ake yawan samun badakala. A yi tunanin wata badakala ta kunno kai a mazabar B - shugaban karamar hukumar ya wawure kudin kasafin kudi ya ce komai ya daidaita. Masu zabe da dama sun juya masa baya. Idan a baya an raba kuri'u kusan daidai (51:49 na goyon bayan daya ko wata jam'iyya), yanzu a gundumomi B a kowace karamar gundumomi, kore ya sami kashi 75%, blue kawai 25. Duk da haka, a ma'auni na kasa, wannan bai yi nasara ba. ciwo ko kadan (Table 1). Don amfani da kwatankwacin wasan tennis, sun rasa maki mara komai.
| mazabar | Dark Blue | Zeloni | Wanene yake cin nasara |
| A | 251 | 249 | Dark Blue |
| B | 100 | 300 | Zeloni |
| C | 251 | 249 | Dark Blue |
| D | 198 | 202 | Zeloni |
| E | 251 | 249 | Dark Blue |
| F | 251 | 249 | Dark Blue |
| G | 251 | 249 | Dark Blue |
| H | 149 | 151 | Zeloni |
| Jimlar kuri'u | 1702 | 1898 | 5 zu3 za shuɗi |
Table 1. Yawan kuri'un 1898: 1702 na goyon bayan 'yan kore, amma 5: kujeru 3 a majalisa don blue! A zaben shugaban kasar Amurka, yakan faru cewa wanda ya yi nasara ya samu karancin kuri'u.
Tsarin guda ɗaya yana da fa'ida da rashin amfani. Ya fito ne daga al'adar majalisar dokokin Ingila. An gabatar da dabaru iri-iri na lissafin lissafi don ɗan rage ƙa'idar "mai nasara ya ɗauki duka". Dokar da aka fi sani ita ce "mafi girman juzu'i". Bari mu ɗauka cewa jam'iyyu huɗu A, B, C da D sun fafata a yankin Grodzisko Nadmorsky. Akwai wurare bakwai don cin nasara. A zaben, wadannan jam’iyyu sun samu kuri’u 9934 5765, 4031 1999, 21 729 da XNUMX XNUMX; jimlar XNUMX XNUMX. Muna sa ran:
7 ∙9934/21729= 3,20
7 ∙5765/21729= 1,86
7 ∙4031/21729= 1,30
7 ∙1999/21729= 0,64
Bayyana; idan Commonwealth ta kasance, kamar yadda Yarima Radziwiłł ya ce a cikin Ruwan Tsufana, jajayen zane, jam’iyyun za su wargaje shi daidai da 320:186:130:64. Amma akwai wurare bakwai kacal don raba. Kuri'a A sun cancanci wurare uku (saboda adadin ya fi 3), kuri'a B, C sun cancanci wuri ɗaya kowanne. Ta yaya zan iya zaɓar sauran biyun? Ana ba da shawarar mafita mai zuwa: don ba da ita ga jam'iyyun da "ƙananan ba su da cikakken kuri'a", watau, waɗanda ke da kashi mafi girma. Saboda haka, sun fada cikin sassan B, D. Bari mu wakilci sakamakon a cikin madaidaicin jadawali akan fig. 3.
fig.3 Hanyar "mafi girman juzu'i". Hadakar B+C+D ta doke jam'iyyar A
Menene abin da ake kira. mulkin d'Onda? Na tattauna wannan kadan kadan. Ina ba da shawarar shi azaman motsa jiki. Sakamako akan fig. 4.
fig.4 Sakamakon hanyar d'Hondt. Jam'iyyar A tana mulki da kanta.
Don motsa jiki mai sauƙi na gaba, ina ba da shawarar cewa masu karatu su yi wani abu kamar haka: yi tunanin jam'iyyun B, C, da D sun yarda kuma su tafi rumfunan zabe a cikin rukuni guda - kira shi E. Sannan, kamar yadda tsarin mulkin d'Hondt ya nuna, sun cire guda ɗaya. jam'iyyar A tana da umarni, watau. sakamakon A:E shine 3:4. An san ƙarshen shekaru da yawa a matsayin karin magana: Yarda yana haifar da rashin jituwa.
Abin farin ciki, misalan da na bayar a nan na tatsuniyoyi ne kuma duk wani kamanni da sanannun ƙasashen da aka sani kawai ya zo daidai.
D'Ond
Ta yaya hanyar d'Hondt da aka ambata ke aiki? Misali ya fi dacewa da wannan. A ce wata mazaba ta kada kuri'a a zaben bishop, kamar yadda aka nuna. Table 2.
| Sunan jam'iyya | Sauti, N. | H/2 | H/3 | H/4 | H/5 |
| Jam'iyyar Cikakkun Cigaba | 10 000 | 5000 | 3333 | 2500 | 2000 |
| jam'iyyar wadata | 6600 | 3300 | 2200 | 1650 | 1320 |
| Locomotive na ci gaba | 4800 | 2400 | 1600 | 1200 | 960 |
| Masu zamba da zamba | 3600 | 1800 | 1200 | 900 | 720 |
Tebura 2. Sakamakon jefa kuri'a a mazabar Klapucko Male a zaben a Klapadocsy.
Ya bayyana cewa jam'iyyar masu zamba da gochstaplers sun yi nasara sosai kawai a Klaputsky Maly. A duk duniya, ba su sami maki 5% ba, don haka ba a la'akari da sakamakonsu. Mukan sanya sauran bi da bi, ba mu manta da jam’iyyar da suka fito ba:
10 (PTD), 000 (SO), 6600 (PTD), 5000 (LP), 4800 (PTD), 3333 (SO), 3300 (PTD), 2500 (LP), 2400 (SO), da dai sauransu Muna ba da tikiti. a cikin ƙayyadadden tsari. Sakamakon ya dogara ne akan adadin tikitin da ake samu.
| 3 wurare | PTD 2, SO 1, LP 0 |
| 4 wurare | PTD 2, SO 1, LP 1 |
| 5 kujeru | PTD 3, SO 1, LP 1 |
| 6 kujeru | PTD 3, SO 2, LP 1 |
| 7 kujeru | PTD 4, SO 2, LP 1 |
| 8 kujeru | PTD 4, SO 2, LP 2 |
| 9 kujeru | PTD 4, SO 3, LP 2 |
Tebur 3. Rarraba kujeru dangane da adadin su.
An ce irin wannan tsarin yana daidaita sakamakon - yana rage yiwuwar rinjaye na wata ƙungiya. Duk da haka, lamarin ya fi rikitarwa. Duk ya dogara da takamaiman bayanai. Ba ni da wurin da zan ƙara tattaunawa, zan lura da abubuwa biyu masu ban sha'awa kawai:
1. Da ’yan damfara da masu damfara sun kai matakin zaben kasa, da sakamakon zai bambanta. Ba za su canza ba idan aka sami kujeru uku ko hudu don samun nasara, amma idan mutane biyar daga mazabar sun shiga majalisar, sakamakon zai kasance: PTD 2, SO 1, PL 1, JG 1. Jam’iyyar PTD za ta rasa cikakken ‘yancinta. . rinjaye. Yana aiki akasin haka: idan ƙaramin yanki ya balle daga jam’iyyar, kowa ya yi hasara, har da waɗanda ba su yarda ba.
2. Idan SO da LP suka hadu suka tafi rumfunan zabe tare, to ba za su kasance mafi muni ba a kowane hali, amma yawanci sun fi kyau.
Bari mu kuma ga yadda hanyar d'Hondt ke bi da halin da ake ciki fig. 2lokacin da babu kujeru biyu ko uku a cikin unguwa. Bari in tunatar da ku cewa a cikin yanayin gundumomi guda ɗaya, wannan ya ba da nasara mai ƙarfi ga Blues. A wajen ninka biyu kuwa, an yi rashin nasara gaba daya, amma a wajen sau uku, ya sake yin nasara.
| mazabar | Dark Blue | Zeloni | Hanyar d'Hondt |
| A | 251 | 249 | Matsakaicin Gear: 251/249; tsarin 1-1 |
| B | 100 | 300 | 300/100; 0-2 |
| C | 251 | 249 | 251/249; 1-1 |
| D | 198 | 202 | 202/198; 1-1 |
| E | 251 | 249 | 251/249; 1-1 |
| F | 251 | 249 | 251/249; 1-1 |
| G | 251 | 249 | 251/249; 1-1 |
| H | 149 | 151 | 151/149; 1-1 |
| Jimlar kuri'u | 1702 | 1898 | Blue 7 - Kore 9 |
Tebur 4. Halin da ake ciki tare da fig. 2, amma tare da mazabu mai wakilai biyu. Kasawar shuɗi 7:9.
| mazabar | Dark Blue | Zeloni | Hanyar d'Hondt |
| A | 251 | 249 | Matsakaicin Gear: 251/249/125,5; hoto 2-1 |
| B | 100 | 300 | 300/150/100; 0,5-2,5 |
| C | 251 | 249 | 251/249/125,5; 2-1 |
| D | 198 | 202 | 202/198/101; 1-2 |
| E | 251 | 249 | 251/249/125,5; 2-1 |
| F | 251 | 249 | 251/249/125,5; 2-1 |
| G | 251 | 249 | 251/249/125,5; 2-1 |
| H | 149 | 151 | 151/149/75,5; 1-2 |
| Jimlar kuri'u | 1702 | 1898 | Blue 12,5 - Kore 11,5 |
Tebur 5. Halin da ake ciki tare da fig. 2, amma tare da mazabar mutum uku.
Daga cikin wasu fasalulluka, na haɗa da "geometry" a cikin cancantar ƙuri'u mai mahimmanci ko maras muhimmanci. A cikin ƙasashe da yawa, alamar amincewa ita ce "kaska", wato, v, da kuma wani lokacin Y. Muna da x, wanda ya fi dacewa da ƙaddamarwa (sabili da haka ƙi). Dan majalisar ya so ya fayyace hakan kuma ya ba da ma’anar kimiyance-lissafi – “Layuka masu tsaka-tsaki guda biyu”, yana fassara cewa layukan biyu na harafin v ba sa haduwa.
Na farko, a cikin ilimin lissafi, "intersecting" yana nufin "samun ma'ana guda ɗaya" - wannan ya kamata a danganta shi da matasa (masu kasa da hamsin), saboda haka makaranta take a yanzu. Duk da haka, idan wani bai yi imani da ilimin lissafi ba, to yana iya tunawa cewa juyawa a kan hanya ma marar iyaka ne.
Zai fi kyau a bar ma'anar da ba daidai ba: duk wata alamar da ke nuna alamar zaɓen dan takara zuwa matsayi wanda ya kasance mai daraja, amma yanzu yana da ƙungiya mai ƙima.
