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119471954iXip1pnp1++pn=1x1xnx1p1xnpnxp01-pxpX1p1XnpnXiXkXiXkXiXk1a)X5X6X9X10X13X14X15X16X7X8X11X12b)X1X2X3X4c)X9X10X17X181GrahamLoomesandRobertSugden1X5X6X7X81414'X19X20X21X22X13X14X21X22X15X16X7X8abcabc2njPj0Pj1P1+...+Pn=1njixijxijAXC(.)2M(.)mkijcijcij=ckjmkij=cijC(x)xxx-A1A2A1jx1jA2x2jx1jx1jx2jx2jx1jx1jx1j1001001001001951AkAijxijAkxkjC(xij)cijmkij𝑚𝑚𝑖𝑖𝑖𝑖𝑘𝑘=𝑀𝑀(𝑐𝑐𝑖𝑖𝑖𝑖,𝑐𝑐𝑘𝑘𝑖𝑖)12uniqueuptoanincreasinglineartransformationδmkij/δckj0δmkij/δcij0AkAiEki𝐸𝐸𝑖𝑖𝑘𝑘=�𝑝𝑝𝑖𝑖𝑛𝑛𝑖𝑖=1𝑚𝑚𝑖𝑖𝑖𝑖𝑘𝑘(2)AiAkAiAkEkiEik5M(.)M(.)-R(.)𝑚𝑚𝑖𝑖𝑖𝑖𝑘𝑘=𝑐𝑐𝑖𝑖𝑖𝑖+𝑅𝑅(𝑐𝑐𝑖𝑖𝑖𝑖−𝑐𝑐𝑘𝑘𝑖𝑖)3M(.)R(0)=0R(.)R()=0R(.)AiAkAiAk�𝑝𝑝𝑖𝑖𝑛𝑛𝑖𝑖=1[𝑐𝑐𝑖𝑖𝑖𝑖−𝑐𝑐𝑘𝑘𝑖𝑖+𝑅𝑅�𝑐𝑐𝑖𝑖𝑖𝑖−𝑐𝑐𝑘𝑘𝑖𝑖�−𝑅𝑅�𝑐𝑐𝑘𝑘𝑖𝑖−𝑐𝑐𝑖𝑖𝑖𝑖�]≥04Q(.)𝑄𝑄(𝜉𝜉)=𝜉𝜉+𝑅𝑅(𝜉𝜉)−𝑅𝑅(−𝜉𝜉)5AiAk�𝑝𝑝𝑖𝑖𝑛𝑛𝑖𝑖=1[𝑄𝑄�𝑐𝑐𝑖𝑖𝑖𝑖−𝑐𝑐𝑘𝑘𝑖𝑖�]≥06Q(.)Q()=-Q(-)0Q()Q()Q(.)1Q(.)R()=R(-)(6)-2Q(.)0R()R(-)3Q(.)0R()R(-)13123x1x2c1c2C(x1)C(x2)C()C()C()(a)Xi(x1λp)Xk(x2,p)pλ𝑝𝑝̅p𝑝𝑝̅XiXk(i)()x1x2p𝑝𝑝̅XiXkp𝑝𝑝̅XiXk(ii)()x2x1p𝑝𝑝̅XiXkp𝑝𝑝̅XiXkX'=(x1p1)X''=(x2p2)2Xi(x1λp)Xk(x2p)Q(c)c0c1c20[Q(c1)-Q(c1-c2)-Q(c2)]0()0c2c1[Q(c1)-Q(c1-c2)-(c2)]0x1=4000x2=3000λ=0.8p=1.0X5=(x1λp)X6=(x2p)p=0.25X9=(x1λp)X10=(x2p)X5X6X9X10(1.0p0.25)(b)3Xi(x1p1x2α)Xk=(x2p2+α)p2p1p2α𝛼𝛼�α=𝛼𝛼�XiXk(i)()x1x2α𝛼𝛼�XiXkα𝛼𝛼�XiXk(ii)()x2x1α𝛼𝛼�XiXkα𝛼𝛼�XiXkQ(c)c0x1x20[Q(c1)-Q(c1-c2)-Q(c2)]0x2x1[Q(c1)-Q(c1-c2)-Q(c2)]()x1=2500x2=2400p1=0.33p2=0.34α=1-p2X1(x1p1x2α)X2=(x2p2+α)α=0X3(x1p1x2α)X4=(x2p2+α)2X1X2X3X4(0.66𝛼𝛼�0)65%(c)0.750.25X5X6X17=(X5,0.25)(4000,0.20)X9；X18=(X6,0.25)(3000,0.25)X101043104X9X1043aX17和X18b3a3bX17X18X9X103S1…Sn()p1…pn,p1+...+pn=1S1'…Sn+1'()μp1…μpn1-μ0μ1Ai=(X11...X1n)Ak=(X21…X2n)S1…SnAaAbS1'…Sn+1'Aa=(X11...X1ny)Ab=(X21…X2ny)yAa≥AbAi≥AkEkiEikAiAkEba=μEki+(1-μ)C(y)Eab=μEik+(1-μ)C(y)Eki≥EikEba≥EabAi≥AkAa≥AbμAcAdAaAbyzAi≥AkAc≥AdAa≥AbAc≥AdA5A6X5X6A17A18X17X18E1718=μE56+(1-μ)C(0)E1817=μE65+(1-μ)C(0),X5X6X17X18(α)X5X6X9X10X9X10X17X18(d)(a)、(b)(c)C(.)C(.)(d)(e)C(.)xC(x)xXi=(x1，p1)Xk=(x2，p2)Xi'=(-x1，p1)Xk'=(-x2，p2)()Xi≥XkXi'≤Xk'Xi≥XkXi'≤Xk'C(.)C(.)50-50(e)4Xi=(0,1)Xk=(x,p;-px/(1-p),1-p)0p1x0C(.)(7)：Q(x)x0p0.5p0.54C(.)p≥0.5，则XiXkp0.5C(.)Q(.)4C()A1A2A1A2cA2A3S1A2A3A2A3A1A3A3A1C()4564(i)()(ii)(iii)(ii)(iii)SAkEkiAiESiSAiSAkAiESiEkiSAkaSkESi55C(x)xR(ξ)=108ξA2AlA3AlA2A3Al{AlA2A3}()ES1ES2ES3A15()()()()-C()Q()C()C()Q()C()Q()C()(simultaneousgamblingandinsurance)ξQ(ξ)1(i)(ii)(subcertainty)(subproportionality)(subadditivity)(iii)()(sure-thingprinciple)()P1980a1980dC()C()1981(framingeffect)1980b(contexteffect)translationeffect1980(()())198115()()()ABAB(())(P)(PP)12(P)(P)Q(.)Q(.)AiAiAiAkAiAkAiAk(s)(s)AiAkAiAkAiAkAkAiA1A2A3A1A2A2A3A3A1{A1A2A3}((P))AiSS'AiSAiS'A1A2{A1A2}A1{A1A2}A2{A1A2A3}A1{A1A2A3}A2A1A2A2A3A3A1AiAkAiAkAiAkAkAi(AiAkR()R()AkAiR()R())6