ʻO ka Simpson paradox kekahi o ka maʻalahi e hoʻomaopopo a ma ka manawa like pūʻiwa nā phenomena i nā helu helu. Kū i kēlā me kēia manawa ke hōʻike nā hui o ka ʻikepili i kekahi ʻano, akā huli ʻia kēlā ʻano ke hoʻohui ʻia nā hui. Me ke kōkua o kahi laʻana maʻalahi, hiki ke hoʻomaopopo koke ʻia ka paradox.

Nānā mākou i nā ʻāpana hoʻokaʻawale ʻelua $$\#1$$ a me $$\#2$$ a me $$G = \#1 \cup \#2$$ a hoʻāʻo i ka helu holomua o $$A$$ a ma loko o kēia mau set $$B$$:

 $$A$$ $$B$$ $$win$$ $$\#1$$ $$\frac{1}{1}=100\%$$ $$\frac{3}{4}=75\%$$ $$A$$ $$\#2$$ $$\frac{2}{5}=40\%$$ $$\frac{1}{3}=33\%$$ $$A$$ $$\#1 \cup \#2$$ $$\frac{3}{6}=50\%$$ $$\frac{4}{7}=57\%$$ $$B$$

ʻIke ʻia ʻo $$A$$ ʻoi aku ka holomua ma mua o $$B$$ i loko o $$\#1$$ a ʻo $$\#2$$ $$B$$ , akā ʻo ka mea kupanaha ma $$G$$ $$B$$ ʻoi aku ka holomua ma mua o $$A$$ . ʻO kēia laʻana kekahi o nā mea me ka hoʻonohonoho liʻiliʻi $$G$$ me $$|G|=13$$ . ʻAʻohe $$G$$ me $$|G|<13$$ (hōʻoia e ka ikaika ikaika).

Hoʻokaʻawale mākou i ka hoʻonohonoho $$G$$ ma kahi o $$2$$ i loko o $$3$$ pūʻulu $$\#1, \, \#2, \, \#3$$ me $$\#1 \cup \#2 \cup \#3 = G$$ . A laila kūkulu mākou i ka hihia $$e_k \neq \emptyset$$ no kēlā me kēia mehana $$e_k \neq \emptyset$$ ka mana hoʻonohonoho $$P(G)$$ o $$G$$ e pili ana kēia: $$\forall e_1, e_2 \in P(G): |e_1| \neq |e_2| \Rightarrow win(e_1) \neq win(e_2) \land |e_1| = |e_2| \Rightarrow win(e_1) = win(e_2)$$ $$\forall e_1, e_2 \in P(G): |e_1| \neq |e_2| \Rightarrow win(e_1) \neq win(e_2) \land |e_1| = |e_2| \Rightarrow win(e_1) = win(e_2)$$

Ma hope o kekahi mau hola o ka ikaika ikaika ma ka Core i7 maʻamau, hiki ke loaʻa i kahi hiʻohiʻona aʻe:

 $$A$$ $$B$$ $$C$$ $$win$$ $$\#1$$ $$\frac{6}{7}=85,71\%$$ $$\frac{12}{15}=80,00\%$$ $$\frac{22}{37}=59,46\%$$ $$A$$ $$\#2$$ $$\frac{95}{167}=56,89\%$$ $$\frac{48}{88}=54,55\%$$ $$\frac{38}{67}=56,72\%$$ $$A$$ $$\#3$$ $$\frac{48}{144}=33,33\%$$ $$\frac{16}{50}=32,00\%$$ $$\frac{2}{20}=10,00\%$$ $$A$$ $$\#1 \cup \#2$$ $$\frac{101}{174}=58,05\%$$ $$\frac{60}{103}=58,25\%$$ $$\frac{60}{104}=57,69\%$$ $$B$$ $$\#1 \cup \#3$$ $$\frac{54}{151}=35,76\%$$ $$\frac{28}{65}=43,08\%$$ $$\frac{24}{57}=42,11\%$$ $$B$$ $$\#2 \cup \#3$$ $$\frac{143}{311}=45,98\%$$ $$\frac{64}{138}=46,38\%$$ $$\frac{40}{87}=45,98\%$$ $$B$$ $$\#1 \cup \#2\cup \#3$$ $$\frac{149}{318}=46,86\%$$ $$\frac{76}{153}=49,67\%$$ $$\frac{62}{124}=50,00\%$$ $$C$$

Ma laila (e noʻonoʻo ana i ka manawa loiloi lōʻihi ʻana) e ʻike ʻia nā laʻana o $$n$$ me nā ʻano like. Ke kū maoli kēia mau hihia, ʻo nā hopena i hoʻokumu ʻia ma ka ʻōlelo aʻoaʻo no ka kūleʻa ʻana o kahi hui a maʻalahi ʻole hoʻi.

I kēia manawa, paipai mākou i ka heluhelu hoihoi Causality: Models, Reasoning and Inferensi na ʻOria Pearl .

Hope