Bɔ mmɔden hu nkyɛmu no mu 2/3

Paw nɔma bi. Nea ɔpaw nɔma a ɛbɛn obiara nkyɛmu no mu 2/3 a wɔbɛyɛ dapɛn yi no sen biara na odi nkonim. Wontua hwee, na enhia sɛ wokyerɛw wo din.

Helibrain kuw no na ɛkyerɛweeRobert(Borɔfo), biophysics ho PhD suani na ɔhwɛɛ muWɔtintimii Wɔsan hwɛɛ mu koraa wɔ

Sɛnea wobɛte nea wo nyaa ase

  • Wo dodow kyerɛ anammɔn dodow a wodwenee ho. Sɛ wo nɔma a wopaw no bɛn 50 a, ɛyɛ dodow 0: woannwen afoforo no ho. Sɛ ɛbɛn 33 a, ɛyɛ dodow 1: "nnipa bɛpaw bɛyɛ 50". Sɛ ɛbɛn 22 a, ɛyɛ dodow 2: "nnipa bedwene anammɔn biako anim". Anammɔn biara yɛ deɛ ɛbaa n'anim no mu 2/3 [1].
  • Agodie ho nkyerɛkyerɛmu mu mmuae ne 0. Sɛ obiara dwenee ho kosi awiei a, nɔma a obiara bɛpaw no nyinaa bɛkɔ fam akosi 0. Nnipa a wɔbɔ agodie ankasa nyɛ saa da, enti 0 nnii nkonim wɔ baguam akansie biara mu [1][2].
  • Ɛrentumi nni nkonim da: nɔma a ɛboro 66.7 rentumi nni nkonim, efisɛ sɛ obiara paw 100 mpo a, botae no bɛyɛ 66.7.
  • Dapɛn yi nkonimdifo bɛda adi bere a akansi no ba awiei (akansi biara yɛ dapɛn baako, efi Dwoda kosi Kwasida, UTC). Yɛrenkyerɛ nkyɛmu a ɛrekɔ so no ansa na ɛno aba: ɛbɛsɛe agodie no. Sɛ nnipa a wɔbɔ no anyɛ yiye koraa a wɔyɛ 30 a, ɛrennya nea wɔbɛkyerɛ sɛ onii a odi nkonim.

Nɔma bɛn na eye sɛ wobɛpaw?

Nɔma biako pɛ a eye sen biara nni hɔ: egyina nea afoforo nyinaa bɛpaw so. Baguam akansie akɛse mu no, botae no sii bɛyɛ 13 ne 22 ntam. Financial Times akenkanfo nyaa nkyɛmu 18.9, enti botae no yɛɛ 12.6 [2]. Denmark atesɛm krataa bi akansie a akenkanfo 19,196 kɔɔ mu no, wɔn nkyɛmu yɛɛ 32.4, na botae no yɛɛ 21.6 [3].

Poma mfonini: nɔma a wɔpaw no nkyɛmu ne botae wɔ akansie anan a wɔatintim ho. Nhwehwɛmu wɔ adwumayɛbea 1995: nkyɛmu 36.7, botae 24.5. Politiken 2005: nkyɛmu 32.4, botae 21.6. Spektrum 1997: nkyɛmu 22.1, botae 14.7. Financial Times 1997: nkyɛmu 18.9, botae 12.6.
Mfonini 1. Nɔma a wɔpaw no nkyɛmu ne botae a ɛyɛ 2/3 wɔ akansie anan a wɔatintim ho. Nneɛma a wɔde yɛɛ ho adwuma: Nagel 1995, ahyia a edi kan, asuafo 67 [1]; Politiken 2005, akenkanfo 19,196 [3]; Spektrum der Wissenschaft 1997, akenkanfo 2,728, ne Financial Times 1997, akenkanfo 1,476 [2].

Nsɛm tiawa

  • Nea ɛkyerɛ: anammɔn dodow a wodwene ho fa nea afoforo bɛyɛ ho. Aban akenkanfo frɛ eyi level-k adwene [1][4].
  • Sɔhwɛ a agye din: wɔ Rosemarie Nagel nhwehwɛmu a ɔyɛe wɔ 1995 mu no, asuafo no paw 36.7 wɔ nkyɛmu mu wɔ ahyia a edi kan no mu, na nɔma a wɔpaw no dodow no ara yɛ bɛyɛ 33 ne 22 [1].
  • Akansie akɛse: Financial Times akenkanfo 1,476 nyaa nkyɛmu 18.9 (nɔma a edii nkonim yɛ 13), na Politiken akenkanfo 19,196 nyaa nkyɛmu 32.4 [2][3].
  • Nea ɛma wɔpaw 33: wɔ New York Times dwumadi bi a wɔyɛe wɔ 2015 mu, a akenkanfo bɛyɛ 56,000 kɔɔ mu no, nɔma a wɔpaw no dodow no ara yɛɛ 33 [5].
  • Adwene no fibea: sikasɛm ho ɔbenfo John Maynard Keynes de sikakorabea gua no totoo ahoɔfɛ akansie bi ho, a wudi nkonim sɛ wopaw anim a wususuw sɛ afoforo bɛpaw no [6].

Sɛnea agodie no kɔ so

  1. Paw nɔma mũ fi 0 kosi 100 na si so dua.
  2. Nnipa nyinaa nɔma a wɔpaw dapɛn yi bɛyɛ nkyɛmu bere a akansi no to mu, na botae no bɛyɛ saa nkyɛmu no mu 2/3.
  3. Nea ɔpaw nɔma a ɛbɛn botae no sen biara na odi nkonim. Sɛ wɔn nɔma yɛ pɛ a, wɔn nyinaa kyɛ nkonim no. Dwoda na krataafa no kyerɛ nnipa a wɔbɔɔ dapɛn a atwam no, wɔn nkyɛmu, botae, nɔma a edii nkonim ne sɛnea wɔpaw nɔma biara.

Wɔkyerɛw obiako pɛ nɔma ma no wɔ akansi biara mu. Yɛkan nɔma baako fi wɛbsaet hwɛfo biara ne nɔma baako fi intanɛt nkitahodi biara mu, enti nnipa a wɔne wɔn a wɔwɔ nkitahodi koro mu (sukuu, adwumayɛbea anaa abusua) no, yɛkan wɔn pɛnkoro dapɛn biara. Nɔma a wobɛpaw nea ɛto so abien no mfa ho. Sɛ wopaw nɔma wie ara pɛ na krataafa no kyerɛ baabi a wo nɔma no wɔ adwene anammɔn so ne sɛnea anka ɛbɛyɛ wɔ akansie akɛse a agye din a ɛwɔ atifi hɔ no mu.

Nea agodie yi kyerɛ ne baabi a efi

Aban akenkanfo frɛ agodie yi p-beauty contest, na ha yi p = 2/3. Rosemarie Nagel maa ɛbɛyɛɛ adwumayɛbea sɔhwɛ a agye din wɔ 1995 mu [1]. Nea ohui ne sɛ: nnipa nnwen ho nkosi 0, na saa ara nso na wɔmpaw nɔma kwa. Dodow no ara gyae bere a wɔadwene ho anammɔn baako anaa abien wɔ "wɔdwene sɛ medwene sɛ" mu.

Saa adwene yi, sɛ nnipa dwene ho anammɔn kakraa bi fa afoforo ho no, bɛyɛɛ level-k ne adwene nhyehyɛe a wɔde kyerɛ ɔkwan a nnipa fa so dwene nhyehyɛe ho [4][7]. Atesɛm krataa akansie a ɛbaa akyiri, a emu biara nyaa akenkanfo mpempem no, daa anammɔn koro no ara adi wɔ 33 ne 22 mu, ne nnipa kuw bi a wɔpaw 0 anaa 1 [2].

Nea agodie yi betumi ne nea ɛrentumi nkyerɛ wo

Wo dodow no kyerɛ nɔma baako a wopaw wɔ agodie baako mu. Ɛnyɛ ɔkwan a wɔfa so susuw nyansa, na dodow a ɛkorɔn kyerɛ sɛ eye kɛse: nea odi nkonim ne nea otumi hu nea nnipa dodow no ara bɛpaw. Nnipa dodow no ara taa dwene ho anammɔn baako anaa abien pɛ. Dodow-4 nɔma paw yɛ adwene a emu dɔ nanso mpɛn pii no ɛma wopaw nɔma a ɛba fam sen botae no.

Nnipa a wɔbɔ agodie yi ne wɔn a wɔba dapɛn no mu, ɛnyɛ nnipa bi a wɔpaw wɔn pɛn na wɔde wɔn ara na ɛyɛ nhwehwɛmu, enti botae no sesa dapɛn biara. Akansie akɛse a agye din no nyaa mmara a ɛsono kakra: Financial Times maa wɔpaw nɔma mũ nko ara, na Politiken ne Spektrum maa wɔpaw nɔma a wɔde decimal kyerɛw [2][3].

Nsɛmmisa a wɔtaa bisa

Mmuae bɛn na ɛwɔ bɔ mmɔden hu nkyɛmu no mu 2/3 mu?

Bɔ mmɔden hu nkyɛmu no mu 2/3 no nni mmuae a ɛnsesa. Agodie ho nkyerɛkyerɛmu kyerɛ sɛ ɛyɛ 0, efisɛ obiara wɔ nea enti a ɔbɛpaw nɔma a ɛba fam sen obiara de no. Nanso nnipa ankasa gyae bere a wɔadwene ho anammɔn baako anaa abien, enti wɔ akansie a wɔatintim mu no, nɔma a edii nkonim no yɛɛ 13 ne 21.6 ntam [2][3]. Nɔma a eye sɛ wobɛpaw ne nea ɛyɛ 2/3 wɔ nea wususuw sɛ afoforo bɛpaw no nkyɛmu mu.

Adɛn nti na 0 nni nkonim?

0 bedi nkonim sɛ ɛkame ayɛ sɛ obiara dwenee ho kosi awiei nko ara. Wɔ akansie ankasa mu no, nnipa pii paw bɛyɛ 33 anaa 22, na ebinom paw nɔma akɛse, na eyi ma nkyɛmu no kɔ soro. Financial Times akansie no mu no, nkyɛmu no yɛɛ 18.9 na botae no yɛɛ 12.6, na ɛne 0 ntam yɛ kwan ware [2].

"Onipa a ɔdwene dodow-2" kyerɛ sɛn?

Onipa a ɔdwene dodow-2 susuw sɛ afoforo bedwene anammɔn biako anim (wɔbɛpaw bɛyɛ 33), na ɔno nso dwene anammɔn biako bio: 33 mu 2/3 yɛ bɛyɛ 22. Wɔ Helibrain agodie no mu no, wo dodow yɛ anammɔn a wo nɔma a wopaw no bɛn sen biara wɔ anammɔn a ɛtoatoa so yi mu (50, 33, 22, 15, 10) [1].

Metumi abɔ no mpɛn pii?

Yiw, nanso wo nɔma a wopaw kan dapɛn biara no nko ara na wɔde bɛkan wɔ akansi no mu. Wɔbɛkyerɛ nɔma a wopaw akyiri no wɔ anammɔn no so, nanso wɔrenkan, enti obiara rentumi nni nkonim denam nɔma pii a ɔbɛpaw so. Akansi foforo biara fi ase Dwoda.

Helibrain 2/3 agodie no yɛ kwa ampa?

Yiw. Helibrain 2/3 agodie no ne dapɛn biara nea efi mu ba nyinaa yɛ kwa: enhia sɛ wokyerɛw wo din, email anaa sika tua. Helibrain nya sika fi ne app no mu; ɛwɔ nhyehyɛe a wontua hwee ne nea wɔtua ho ka. Enhia sɛ wode app no di agoru.

Sɔhwɛ a ɛfa ho

Hwɛ adwene ho sɔhwɛ 43 no nyinaa a wontua hwee

Wopɛ sɛ wudi eyi ho dwuma da biara? Helibrain app no (seesei ɛwɔ Borɔfo kasa mu) wɔ nhyehyɛe a wontua hwee ne nea wotua ho ka.

Nwoma ne nsɛm fibea

  1. Nagel R (1995). Unraveling in guessing games: an experimental study. American Economic Review 85(5):1313–1326. www.jstor.org/stable/2950991
  2. Bosch-Domènech A, Montalvo JG, Nagel R, Satorra A (2002). One, two, (three), infinity, …: newspaper and lab beauty-contest experiments. American Economic Review 92(5):1687–1701. doi.org/10.1257/000282802762024737 (nɔma no fi krataa a wɔde yɛɛ adwuma wɔ 1999 mu: econ-papers.upf.edu/papers/438.pdf)
  3. Schou A (2005). Gæt-et-tal konkurrence afslører at vi er irrationelle. Politiken, 22 September 2005. politiken.dk/oekonomi/art5698526
  4. Camerer CF, Ho T-H, Chong J-K (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics 119(3):861–898. doi.org/10.1162/0033553041502225
  5. Quealy K (2015). How readers fared in Upshot's number puzzle. The New York Times, 20 August 2015. www.nytimes.com/2015/08/21/upshot/how-readers-fared-in-upshots-number-puzzle.html
  6. Keynes JM (1936). The General Theory of Employment, Interest and Money, ti 12. London: Macmillan.
  7. Stahl DO, Wilson PW (1995). On players' models of other players: theory and experimental evidence. Games and Economic Behavior 10(1):218–254. doi.org/10.1006/game.1995.1031

Sɛnea yɛyɛɛ krataafa yi: Helibrain kuw no kyerɛw fii nhwehwɛmu a yɛabobɔ din wɔ atifi hɔ no mu, na Robert(Borɔfo) (biophysics ho PhD suani) hwɛɛ mu wɔ 4, Obubuo, 2026. Yɛyɛ nsakrae wɔ mu bere a nneɛma a yɛde gyinaa so no sesa.