Wisdom of Crowds: Galton's Ox — The 1906 Experiment That Proved Crowds Beat Experts

Masanin kimiyya wanda ya so ya tabbatar da cewa taron mutane masu wauta

Mafi kyawun ɓangaren gwaji mafi shahara a cikin hankali na tarayya shine an tsara shi — a ruhin, aƙalla — don tabbatar da akasin abin da ya gano.

A cikin 1906, Francis Galton ya kasance ɗaya daga cikin manyan masana kimiyya a Birtaniya. Dan uwan Charles Darwin ne, ya fara tunanin kididdiga na dangantaka da dawowa zuwa ga matsakaici, ya kirkiro taswirar yanayi, kuma ya sanya tantancewar yatsu a kan tushe na kimiyya. Hakanan yana da — kuma wannan yana da mahimmanci ga labarin — shakku mai zurfi game da hukuncin mutane na yau da kullum. Galton ya yi imanin cewa basira tana taruwa a cikin ƙananan ƙungiyar gado; ya ƙirƙiri kalmar “eugenics” kuma ya shafe shekaru yana inganta ta, wani gado da aka yi wa hukunci daidai a yau kuma ba za a iya raba shi daga yadda ya yi nazari kan wannan tambayar ba. Lokacin da ya juya kayan aikin kididdigarsa kan taron mutane, ya yi tsammanin zai rubuta rashin ƙwarewarsu.

Don haka, lokacin da Galton mai shekaru 84 ya yi yawo a cikin Nunin Dabbobin Nama da Kaji na Yammacin Ingila a Plymouth a lokacin autumn na 1906 kuma ya ci karo da gasar tantance nauyi, ya ga wani tarin bayanai da ba za a iya jurewa ba. Ga taron mutane — wasu kwararru, mafi yawansu ba — suna yin dubban hukunci na lamba masu zaman kansu game da wani abu na gaskiya, tare da ƙaramin kuɗin shiga don tabbatar da gaskiya da kyauta don ƙarfafa su. Kamar yadda ya rubuta daga baya a cikin Nature, mai gasa na matsakaici yana iya zama da kyau don tantance ja-gora kamar yadda mai kada kuri'a na matsakaici yake don tantance fa'idodin mafi yawan batutuwan siyasa da yake kada kuri'a a kansu. Hanyar da ta shafi dimokuradiyya ita ce ma'anar gaba ɗaya. Galton ya yi tsammanin vox populi — muryar mutane — za ta yi kunya.

Taron ƙasa, wani mai kiba, da tikitin shida na 787

Hanyoyin gasar sun kasance masu sauƙi, kuma — kamar yadda muka sani yanzu — a haɗa kusan daidaitaccen ƙira na gwaji. An nuna wani shanu mai rai. Don shilling shida, kowa zai iya sayen kati wanda aka yi masa alama da lamba, ya rubuta sunansa da adireshinsa a kai, kuma ya rubuta hasashen nauyin da shanun zai yi bayan an yanka shi kuma an shirya shi — adadin da ke da ma'ana a kasuwa, kuma tambaya mai wahala fiye da nauyin shanun mai rai. Mafi ingancin hasashe sun lashe kyaututtuka.

Abubuwa uku na wannan tsari suna da muhimmanci, saboda kowanne yana da alaƙa da wani yanayi wanda binciken da zai biyo baya zai nuna cewa yana da mahimmanci ga daidaito na tarayya. Na farko, kudin shigar na shida ya tace masu wasa na gaske - mutane suna da hannu a cikin wasan. Na biyu, kowanne kati an cika shi a sirri: ba a nuna hannu ba, ba a yi kasuwa tare da mai sayarwa yana kira da ra'ayin da ke gudana ba, ba a sami wanda ke gaba da za a kwatanta da shi ba. Hukuncin sun kasance masu zaman kansu. Na uku, taron ya kasance da gaske mai hadewa: masu juyawa da manoma tare da ƙwarewar sana'a suna tsaye tare da ma'aikata da iyalai waɗanda, a cikin kalmomin Galton, suna biye da sha'awar lokacin. Hukuncin sun kasance masu bambanta.

Bayan gasar, Galton ya aro katunan. Daga kusan 800, goma sha uku ba su da karatu ko kuma suna da wasu kurakurai, suna barin 787 ingantattun hasashe. Ya tsara su, ya lissafa su, ya zana rarrabawar su, kuma ya ƙididdige ƙididdiginsu — cikakken aikin kididdiga, wanda aka buga a Nature a ranar 7 ga Maris 1907 a ƙarƙashin taken “Vox Populi” (Galton, F., Nature, 75, 450–451).

Sakamakon da ya ba shi mamaki

Kimar tsakiya — abin da yanzu muke kira median — shine 1,207 fam. Bawon, wanda aka yanka kuma aka shirya, ya nauyi 1,198 fam. Hukuncin taron ya yi kuskure da fam tara: kuskure na kusan 0.8%, wanda ya fi kusa da kimar masana shanu da suka halarta.

Galton — don kyakkyawan yabo a matsayin masanin kimiyya — ya bayar da sakamakon kai tsaye. “Wannan sakamakon, a ra'ayina, yana da karin yabo ga amincin hukuncin dimokiradiyya fiye da yadda aka zata,” ya rubuta. Daga mutum da ya shafe aikinsa yana jayayya cewa kyakkyawan hukunci kyauta ce ta gado mai wuya, wannan jumla tana nuni da yarda ta kimiyya: bayanan sun yi nasara akan na baya.

Labari ya inganta a cikin wasiƙar da ta biyo baya. Masu karatu na Nature sun rubuta, kuma a cikin amsar sa (“The Ballot-Box,” Nature, 75, 509) Galton ya amince cewa matsakaicin lissafi na dukkanin hasashen 787 shine 1,197 fam — fam ɗaya daga nauyin gaskiya. Shekaru ɗari bayan haka, mai nazarin tattalin arziki Kenneth Wallis (“Revisiting Francis Galton’s forecasting competition,” 2014) ya koma kan asalin bayanan da musayar da ke kewaye, yana tabbatar da muhimman abubuwan labarin da James Surowiecki ya shahara da su. Rashin fam ɗaya na matsakaicin shine sigar da aka fi ambata a yau; rashin fam tara na matsakaici shine abin da Galton ya jagoranta da gaske. Duka suna ban mamaki.

Matsakaici ko ma'ana? Zaɓin lissafi na Galton har yanzu yana da mahimmanci

Me ya sa Galton ya fi son kimanta tsakiyar? Dalilinsa yana da alaka da siyasa: tsakiyar shine darajar da yawancin taron zai amince da ita a cikin zaɓe. Kowanne daraja ta daban za ta kasance a ƙasa da wanda ya yi tunanin yana da yawa ko kuma ƙasa. Tsakiyar, a cikin wasu kalmomi, shine hukuncin taron — wanda shine ainihin tambayar game da vox populi da ya sa a gaba don gwadawa.

Amma akwai hujja ta kididdiga da ke ɓoye a cikin ta siyasa, kuma har yanzu ana koyar da ita a yau. Matsakaici shine kididdiga mai ƙarfi: ɗan ƙarin hasashe masu ban dariya — wani yana rubuta fam 10,000 don dariya — ba ya motsa shi sosai, yayin da matsakaicin zai iya ja da nisa ta hanyar wani mai ban mamaki. Matsakaicin, a gefe guda, yana amfani da ƙarin bayanai a cikin bayanan kuma, lokacin da kuskure suka kasance kusan daidaitacce kuma masu zaman kansu, yana soke su da inganci. Taron Galton ya kasance mai kyau sosai har duka biyun suka yi aiki: matsakaicin ya rasa da fam 9, matsakaicin da fam 1. A cikin taron da ya fi rikitarwa — zaɓen kan layi, dandalin da ba a tsara ba — ƙarfin matsakaicin yawanci yana lashe. Zaɓin hanyar haɗin gwiwa yana yanke shawara game da yawan amincewarka da ƙananan ɓangarorin taron ka.

Me yasa haɗawa ke aiki: lissafin sako na soke kuskure

Babu wani abu na sihiri a cikin sakamakon Galton. Kowanne hasashe na iya zama a matsayin ainihin ƙima tare da kuskure. Idan kuskuren suna yanci kuma suna bazuwa a dukkan gefen gaskiya — wasu masu sayar da nama suna ƙimar sama, wasu suna ƙimar ƙasa — to, haɗa hasashen tare yana kawar da yawancin kuskuren yayin da siginar da aka raba ke taruwa. Mafi yawa da bambancin da kuskuren suke, mafi ƙarfi suke kawar da juna.

Scott Page daga baya ya tabbatar da tunanin a matsayin ka'idar hasashen bambance-bambance (Page, The Difference, 2007): don kuskuren murabba'i, kuskuren taron yana daidai da matsakaicin kuskuren mutum rashin bambancin hasashen. Wannan wata alama ce ta lissafi, ba ikirarin kimiyya ba — wanda ya sa ta zama mai amfani sosai. Taron yana wuce mambobinsa na matsakaici daidai gwargwadon yadda mambobinsa ke sabani da juna. Bambanci ba abu ne mai kyau a samu ba; a lissafi, shine dukkan fa'idar. Taron kwafi ba ya samun komai daga taruwa.

An gano wannan tunani iri ɗaya, don tambayoyin eh/aa maimakon adadi, fiye da ƙarni guda kafin Galton. Marquis de Condorcet ya tabbatar a 1785 cewa idan kowanne mai zaɓe yana da ɗan ƙaramin yiwuwar zama daidai fiye da bazuwar, kuma masu zaɓe suna yanke hukunci cikin 'yanci, yiwuwar cewa mafi yawansu suna daidai tana ƙaruwa zuwa tabbaci yayin da ƙungiyar ke ƙaruwa. Muna ba da labarin wannan — da hanyoyin ban mamaki da ka'idar ke fuskanta lokacin da tunaninta ya karye — a cikin ɓangarenmu na haɗin gwiwa akan Ka'idar Juri ta Condorcet.

Daga ƙarin bayani zuwa tsarin: Sharuɗɗan hudu na Surowiecki

A cikin mafi yawan karni na ashirin, saniyar Galton ta kasance wata sha'awa ta kididdiga. Wannan ya canza a 2004, lokacin da James Surowiecki ya bude The Wisdom of Crowds da labarin Plymouth kuma ya tara shaidar karni guda — daga kasuwannin hannayen jari zuwa injunan bincike — cewa taron mutane na iya zama masu hankali a tsarin. Muhimmin abu, Surowiecki bai yi ikirarin cewa taron mutane kullum masu hikima bane. Ya gano sharuɗɗa hudu da adadin Galton ya cika ba tare da niyya ba, kuma duk wani taron mutane mai hikima yana bukatar su da niyya:

Cire kowanne yanayi guda daya kuma taron ba kawai zai rasa fa'idarsa ba — zai iya zama mafi muni fiye da mambobinsa, saboda tarin yana karfafa son zuciya da aka raba maimakon kawar da kurakurai masu zaman kansu. Don cikakken ilimin yanayi hudu da hanyoyin gazawarsu, duba jagorarmu ga hikimar taron.

Rubutun ƙananan: abin da adalci ya yi daidai wanda tarurruka ke yin kuskure

Ga tambayar da ba ta dace ba ga duk wanda ke gudanar da taruka: nawa ne shawarar rukuni a cikin ƙungiyarku ke da tsari kamar na Galton mai adalci — kuma nawa ne ke da tsari kamar akasin haka?

A cikin baje kolin, kowanne hukunci an yi shi a sirrance, a rubuce, kafin kowa ya ga lambar wani. A cikin taron da aka saba, mafi girma ko wanda ya fi kwarin gwiwa yana magana na farko, kuma kowanne “kimantawa” da ya biyo baya yana dogara kan na su. Abin da ke kama da mutane talatin suna yarda yawanci ra'ayin mutum guda ne tare da sauti ashirin da tara. Masana tattalin arziki suna kiran wannan tsarin cascades na bayani: da zarar an ga ra'ayoyi kaɗan daga farko, yana zama mai ma'ana ga kowanne mutum da ya biyo baya ya rage darajar bayanin sa kuma ya kwafi — kuma 'yancin taron, sharuɗɗan da ke ɗaukar nauyin dukkanin wannan al'amari, yana rushewa a hankali (Bikhchandani, Hirshleifer & Welch, 1992). Muna tattauna hanyoyin a cikin jagorar mu na cascades na bayani.

Wannan kuma shine dalilin da yasa maimaitawar gwajin Galton wani lokaci ke ba da mamaki: gudanar da wasan hasashen sa, tare da matsakaicin gudu mai bayyana, ko barin mahalarta su yi ihu da hasashen su, kuma inganci yana raguwa. Sihrin ba ya cikin taron — yana cikin protocol. Sixpence, kati na kashin kai, da akwatin kuri'a mai kulle suna zama mafi kyawun tsarin yanke shawara fiye da yawancin dakunan taro.

Zamanin zuriyar shanu

Ka'idar tarin da Galton ya rubuta yanzu tana gudana ta cikin wani babban tsarin zamani:

Kowane jini yana tara wani abu daban — kasuwanni suna tara imani cikin farashi, kungiyoyi suna tara fitar da samfurori cikin hasashe, tsarin kada kuri'a suna tara zaɓuɓɓuka cikin sakamako — kuma kowanne yana gaji da wannan dogaro: taron yana da kyau kamar yadda 'yancin kai da bambancin abin da ke ciyar da shi. Wannan kamanceceniya ta iyali ita ce hanyar da ta shafi dukkan al'adar bincike, daga ka'idar Condorcet ta 1785 zuwa binciken basirar tarayya na Cibiyar Basirar Tarayya ta MIT a yau — wani zango na shekaru 240 da muke bin diddigi a Basirar Tarayya: Shekaru 240 na Bincike.

Abin da ox na Galton ke nufi ga ƙungiyarku

Fassarar aikace-aikace na gwajin 1906 shine jerin abubuwa masu sauƙi, kuma yana aiki a wani takamaiman lokaci a rayuwar hukunci — lokacin da kake tattara da haɗa ra'ayoyi, kafin kungiyar ta fara tattaunawa:

• Tattara kimantawa a kan kai, a rubuce, da farko. Kafin taron, kafin babban mutum ya yi magana. Lokacin da hukunci suka bayyana, 'yancin kai — da kuma fa'idar kididdigar taron — suna fara raguwa.
• Yi ƙoƙarin ɗaukar ra'ayoyi masu bambanci. Ka'idar hasashen bambanci tana bayyana: fa'idar ku a matsayin ƙungiya akan mambobin ku na yau da kullum ita ce bambancin ku. Kwamitin mutane masu irin wannan asali da irin wannan bayani na ɗaya daga cikin hasashe da ke da sunayen da yawa.
• Zaɓi hanyar haɗa bayananka da kyau. Matsakaici don taron da ba su da tsari, matsakaici don waɗanda ke da kyau, kimantawa mai tsari lokacin da hukuncin ke da manyan sassa. “Mun tattauna kuma mun cimma yarjejeniya” ba hanyar haɗa bayanai ba ce — yawanci hanya ce ta tsayawa.
• Ka kiyaye dalilan, ba kawai lambobi ba. Katunan Galton sun gaya masa abin da taron ke tunani, ba dalilin ba. Ga saniya, hakan yana da kyau. Ga shawarar dabaru, tunani shine ɓangaren da za ka buƙaci lokacin da yanayi ya canza.

Wannan maki na ƙarshe shine inda yanke shawara tare na zamani ya wuce Galton. Argumentree an gina shi don ba wa ƙungiya tsarin taron adalci tare da dalilin da aka haɗa: mahalarta suna bayar da hujjoji da kansu da ba tare da jinkiri ba — kafin dakin ya haɗu — cikin itacen pro/con mai tsari; ƙungiyar sannan tana kimanta kowace hujja bisa ga ma'auni na fili (amfani, bayyana, daidaito, cikakkun bayanai), kuma kimantawa suna taruwa cikin maki na yarda kamar yadda katunan 787 suka taru cikin fam 1,207. Zaɓuɓɓukan bayar da gudummawa na ɓoye suna kare 'yancin kai daga tsarin mulki, kuma dukkanin hanyar bincike tana adana abin da gasa ox ba ta taɓa iya yi ba: dalilin da ke bayan lambar.

Galton ya tafi kasuwa don tabbatar da cewa hukuncin yau da kullum ba za a iya dogara da shi ba. Ya tafi da shaidar da ta fi karfi wanda kowa ya taɓa samarwa cewa — idan an haɗa shi daidai — za a iya dogara da shi. Na'urar ta canza daga akwatin kuri'a zuwa software. Darasin bai canza ba.