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Schmeidler?A EE EACEEE4+ 0 0 6 0>?V 4  `jfԔL!?"+ 0S#,$D   0 www.tau.ac.il/~samet$(2g, 0 4  f fԔL!?"6@`NNN?N d  0H 4 0޽h ? ̙33y___PPT10Y+D=' - = @B + 0L0 @r`"(   ^  `3ԔD[Ȝ8c?"+ ,$D 0  S ׿0   ~0Sen s Liberalism Paradox Y H&?"HY ,$ 0 tWho should be allowed to read Lady Chatterley s Lover ?P;( g$g$g$ r C .A0451524985 V,$D 0H  0޽h ? ̙33Z R ___PPT102 +9D ' - = @B D ' = @BA?%,( < +O%,( < +D ' =%(D' =%(D[' =4@BB BB%()))D' =1:Bvisible*o3>+B#style.visibility<*r%(D' =-g6B fade*<3<*rD' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*^%(D' =-6B%slide(fromBottom)*<3<*^D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*Y%(D' =-g6B fade*<3<*Y+8+0+Y0 +P 0L0 (     `3ԔD[Ȝ8c?" ,$D  0   `3ԔD[Ȝ8c?"[0 ,$D  0   `3ԔD[Ȝ8c?" l,$D  0  c $0   ~0Sen s Liberalism Paradox`  H?" ,$ 0 "R s preferences: h eae ae  ZH fԔL!?B,$ 0 " {" {R} {" {B}(2eEEE e EEE`  H ?"p ,$ 0 "B s preferences: h eae ae   Zx  fԔL!?dT9 ,$ 0 0$ {R} {" {B} {" (2EEEeeEEE e E  H8 ?"X x ,$  0 XLiberal social preferences:   e   `3ԔD[Ȝ8c?" 0 ( ,$D   0  Z  fԔL!?  ,$  0 ,{B} {R}(2EEEEEE  HT ?" ] ,$ 0 WPareto social preferences:   e  Z!  fԔL!?,$ 0  {R} {" {B} (2EEEeEEE  # l-  fԔL!? 3 ,$  0 >{" e  # l0  fԔL!? ; ,$ 0 >{" e  # l4 ?3ԔD[Ȝ8c?"0 N,$D 0 Social alternatives are subsets of individuals  the qualified ones. rG(2G G G  G G   Z ԔL!?"d,$@ 0   f ԔL!?"6@ NNN?ND d I,$@  0H  0޽h ? ̙3388___PPT10r8+,"QD5' M = @B D5' = @BA?%,( < +O%,( < +D[' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*DR' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*DR' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*+h+0+0 ++0+0 ++0+0 ++0+ 0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +Q 0L0 P-?(   +  f?3ԔD[Ȝ8c?" t,$D  0  # Tj ԔL!?"%  ,$D  0 D 2E   c $ 0   = The model   Z  fԔL!?"JQ ,$ 0 2N = {1,& ,n} individualsx 2EEEEE EB  Z  fԔL!?"S 6,$ 0 v@A profile  nxn matrix P of 0,1.! 2EEEEfGEfEEfEEfEEfE    `G  oL!?":bx ,$D 0E   fȩ  ԔL!?"Z  ,$  0 m 1 . . . . . 0D(2Ef EEf   f  ԔL!?"F ,$  0 =i (2E    f  ԔL!?" ,$  0 =j (2E !  f  ԔL!?"* * ,$  0 =k (2E( "  fl  ԔL!?" ,$ 0 PP =0 2EfEb % # lG)*HOIoL!?"9  ,$D  0B & Z<  ԔL!?"\|,$  0 vi s vote0 2EEb ' # lGHI=ToL!?"l ,$D  0[ ( Z  ԔL!?"6 V ,$  0  i qualifies jf 2EE EEEb ) # lG<Ha3IoL!?"  ,$D 0 * Z  ԔL!?" ,$ 0 i does not qualify k 2EEEEEEE  - 3 r ?3ԔD[Ȝ8c?"q U,$D 0 )[A rule: f(P) = (f1(P), . . . , fn(P)), a 0,1 vector, designating the socially qualified. \(2EEEEfEG EMEEf EMEEfEG EEfEEf/EQH  0޽h ??`%') ̙33M9E9___PPT10%9.+<ҷD]6'  = @B D6' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-o6Bwipe(up)*<3<*+D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(Du' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =-g6B fade*<3<*#D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =-o6Bdissolve*<3<*&D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =-u6Bwipe(right)*<3<*%D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-o6Bdissolve*<3<*(D' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-s6Bwipe(down)*<3<*'D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*!D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*!D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-o6Bdissolve*<3<**D' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =-u6Bwipe(right)*<3<*)D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =-6B%slide(fromBottom)*<3<*-++0+#0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+ 0 ++0+!0 ++0+"0 ++0+&0 ++0+(0 ++0+*0 ++0+-0 + 0L0 p1@(   / # l,2?3ԔD[Ȝ8c?"W,$@ 0 cIndividuals qualify additional persons no one looses social qualification. Jd >g#gc  c $460   V Monotonicity  N ' # l<3ԔD[Ȝ8c?"x w ,$@ 0 p@P e" P f(P) e" f(P )!( g fg c g  g fg c g fc  c  c g fc  0 Z ԔL!?"G,$D 0 1 Z ԔL!?"  ,$D 0H  0޽h ? ̙33  ___PPT10 +3ΛDL ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =-g6B fade*<3<*/D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-g6B fade*<3<*0D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-g6B fade*<3<*'D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =-g6B fade*<3<*1+p+0+/0 ++0+'0 +\ 0L0  |(     `3ԔD[Ȝ8c?"  ,$@ 0   # l 3ԔD[Ȝ8c?"i ,$D 0 @j s qualification depends only on how individuals qualify her. C(2G G G G G G @  c $ 0    < Independence   3 r  ? ԔL!?" cV ,$ 0 dPij = P ij for all i fj(P) e" fj(P )3 2GOfOGOfO GGfGOGOGH  Z ԔL!?"[ 5 ,$D 0H  0޽h ? ̙33  ___PPT10 +׻%DL ' = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* DN' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*+p+0+ 0 ++0+0 +I 0L0  \(    c $7 0    8Symmetry |   C AboyO[i,$D 0~   C "A girlii,$@ 0G    f:  ԔL!?"6@ NNN?N z,$  0 ?Pat (2EH    f|?  ԔL!?"6@ NNN?N6,$ 0 @Dale (2E_   f(C  ԔL!?"6@ NNN?N&  ,$ 0 WDale and are qualified (2ET   fG  ԔL!?"6@ NNN?NC8 ,$ 0 LPat is qualified (2EN  # l(K  ԔL!?"6@`NNN?N ,$D  0 @Dale (2EM  # lN  ԔL!?"6@`NNN?Nk  ,$D  0 ?Pat (2E  # lV 3ԔD[Ȝ8c?";  ,$D 0 0Let p be a permutation of {1, . . . , n} The profile pP is defined by (pP)ij = Pp(i) p(j) The rule pf is defined by (pf)j = fp(j) 0K2EEE EEEEfEEfEMEEf EEEMEPK%  # lq 3ԔD[Ȝ8c?",$D 0 f(pP) = pf(P)(2G  G fG  G G fG $Q  C x{ oL!?"0@NNN?NM ,$ 0 =I (2EH  0޽h ? ̙3355___PPT105+eh`D2'  = @B D2' = @BA?%,( < +O%,( < +DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D\' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D ' =%(D' =%(D' =A@BB%BB0B%()?)?Da' =.)7 BBBBB5M -0.00157 0.01064 L 0.10902 0.05873 C 0.13229 0.06983 0.16701 0.07607 0.20329 0.07607 C 0.24461 0.07607 0.2776 0.06983 0.30086 0.05873 L 0.4118 0.01064 *3>*B ppt_xB ppt_y=F0BB FffFFpBB9S>Bʈ=<* D8' =A@BB,BB0B%()?)?D' =.G7 BBBBBSM 8.33333E-7 0.01063 L -0.11094 -0.0474 C -0.1342 -0.06058 -0.16892 -0.06775 -0.20504 -0.06775 C -0.24635 -0.06775 -0.27934 -0.06058 -0.3026 -0.0474 L -0.41337 0.01063 *3>*B ppt_xB ppt_y=F0BB FffFFpBBSB <* D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D=' =A@BBBB0B%(D' =0l9 CCBB*<3<*D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<**%(D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<**]%(D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*]%(D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 + 0L0 4+,+ &*(    # lp 3ԔD[Ȝ8c?"2 ,$D 0 Fix integers s and t. s  the quota for qualification t  the quota for disqualification The quotas satisfy: s, t 1 s + t n + 2o0P28P2 EEEEEEE EEEEEEEEEEE  c $ئ 0    = Consent rulesB    fDoL!?"0@NNN?N4, ,$D   0B    fDoL!?"0@NNN?N  ,$D  0E    f`  ԔL!?"6@ NNN?NP Sp ,$  0 =s (2EE    f  ԔL!?"6@ NNN?N g,$  0 =t (2E5  Z 3oL!?"0@NNN?N U ,$  0 ?."(2G 5  Z 3oL!?"0@NNN?N4 ,$ 0 ?."(2G 5  Z oL!?"0@NNN?N  ,$   0 ?1"(2G5  Z oL!?"0@NNN?N jd ,$  0 ?1"(2G7  Z oL!?"0@NNN?N+  ,$  0 An+2"(2G7  Z` oL!?"0@NNN?N'  ,$  0 An+1"(2G5  Z  3oL!?"0@NNN?N3E,$ 0 ?."(2G 5  Z 3oL!?"0@NNN?N6,$ 0 ?."(2G 5  Zd 3oL!?"0@NNN?Ne%R ,$ 0 ?."(2G 5  Z 3oL!?"0@NNN?NDR ,$ 0 ?."(2G 7  Z oL!?"0@NNN?N !S,$  0 An+1"(2G7  Z oL!?"0@NNN?N ,$  0 An+2"(2GB  # lD1L!?"0@NNN?Nt Pb ,$D  0B  # lD1L!?"0@NNN?N u  ,$D  0B  # lD1L!?"0@NNN?Nkk ,$D  0B !  fDoL!?"0@NNN?N   #  0e0e    BRCDEF Ao L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| R  @` "0e@      @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abl ,$D 0 $ Z oL!?"0@NNN?N\ ]| ,$ 0 The consent rule f st :l 2EG MMEX % Z ԔL!?"0@NNN?N  ,$D 0 bOne s self qualification wins social consent iff s individuals support it. M(2 E EEEfEEE-^ & Z ԔL!?"0@NNN?N 6,$D 0 hOne s self disqualification wins social consent iff t individuals support it. P(2 EEEEfEEE0H  0޽h ? ̙33#___PPT10+xD' - = @B Db' = @BA?%,( < +O%,( < +D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*8[%(D' =%(D)' =%(D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*[o%(D' =%(D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*o%(D' =-g6B fade*<3<*oD8 ' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<* D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D8 ' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* DK' =%(D' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D#' =+4 8?nCB!#ppt_x-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*DK' =%(D' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DK' =%(D' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D*' =%(D' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =-g6B fade*<3<*#DK' =%(D' =%(Dp' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-6B%slide(fromBottom)*<3<*$D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =-6B%slide(fromBottom)*<3<*%D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =-6B%slide(fromBottom)*<3<*&D?' =%(D.?' =%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*8D' =1:Bhidden*o3>+B#style.visibility<*8%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*8[D' =1:Bhidden*o3>+B#style.visibility<*8[%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*[oD' =1:Bhidden*o3>+B#style.visibility<*[o%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*oD' =1:Bhidden*o3>+B#style.visibility<*o%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(DY' =4@BB BB%()))D' =-g6B fade*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(DY' =4@BB BB%()))D' =-g6B fade*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(Df' =A@BB BB0B%()))D' =-g6B fade*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(Df' =A@BB BB0B%()))D' =-g6B fade*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(DY' =4@BB BB%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(DY' =4@BB BB%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(DY' =4@BB BB%()))D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(DY' =4@BB BB%()))D' =-g6B fade*<3<*#D' =1:Bhidden*o3>+B#style.visibility<*#%(+8+0+0 ++0+0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+ 0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+$0 ++0+%0 ++0+&0 + 0L0 0 $(    # lY ?3ԔD[Ȝ8c?"<?@@`NNN?N `,$D 0 `Theorem A rule satisfies monotonicity, independence, and symmetry iff it is a consent rule. a(2eee ee eeeeee,   c $0g 0    = Consent rulesA8 \ 6 \ 6  Zj oL!?"0@NNN?N]\ |  The consent rule f st :l 2EG MME,  Zr ԔL!?"0@NNN?N   bOne s self qualification wins social consent iff s individuals support it. M(2 E EEEfEEE-2  Z4| ԔL!?"0@NNN?N 6 hOne s self disqualification wins social consent iff t individuals support it. P(2 EEEEfEEE0  Z oL!?"0@NNN?N ,$D 0 $ZPjj = 1: fj(P) = 1 |{i : Pij = 1}| e" sp.(2EfM EMEEfEEGEEEEfMEGEE6   Z, oL!?"0@NNN?N a ,$D 0 $ZPjj = 0: fj(P) = 0 |{i : Pij = 0}| e" tp.(2EfM EMEEfEEGEEEEfMEGEE6 H  0޽h ? ̙33  ___PPT10 +pn}D '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D/' =4@BB@BB%()?)?D' =.K7 BBBBB]M 1.94444E-6 -2.22222E-6 L -0.00156 -0.49166 *3>*B ppt_xB ppt_y=@0BBAApBB9cB{<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*++0+0 ++0+0 ++0+0 + 0L0 @q(  0z N     N ,$D 0j  3 r 3ԔD[Ȝ8c?"N    f( ) = (P) 8P2G G G fG EG   f  oL!?"6@ NNN?N5  F  =P  2G f   `(  oL!?"6@ NNN?No R ;  =f  2G   c $ 0    7Duality   # l oL!??"6@`NNN?Nm D 2E  l .  T,$D 0t  T  ԔL!?"6@ NNN?N.  Notation: for x " {0,1}, = 1  x For a profile P, = ( ) For a rule f , (P) = ( )i 2EEEfEEfE e  e f e  e f a  e EeEe E  E f E  G  E  G    Z  oL!?"6@ NNN?Nf x & ;x 2E;  Z  oL!?"6@ NNN?NY p  kPij2 2EfM   Z   oL!?"6@ NNN?Ng of  ;P 2Ef   Z0  oL!?"6@ NNN?N_ B   ;f 2Es  Z  oL!?"6@ NNN?N0 K  fi(P)h 2EMEEfEA  # l$ ?3ԔD[Ȝ8c?"<?@@`NNN?Nc VM,$D 0 -yTheorem A rule satisfies monotonicity, independence, symmetry and duality iff it is a consent rule of the form f ss. Rz(2eee ee eeeeeee$egme> %%H  0޽h ? ̙33l d ___PPT10D +qD '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(DE' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*+8+0+0 +7 0L0 ]&U&P(%(    c $ 0    = Special rules  # l oL!??"6@`NNN?Nm D 2E    f\  ԔL!?"6@ NNN?N!   =s (2Ek8 4g  %4g B   fDoL!?"0@NNN?N B   fDoL!?"0@NNN?N L    f   ԔL!?"6@ NNN?N54T =t (2E   Z(% 3oL!?"0@NNN?Nr2  ?."(2G    Z@) 3oL!?"0@NNN?N],  ?."(2G    Z, oL!?"0@NNN?Ni 5[  ?1"(2G   Z0 oL!?"0@NNN?N9  ?1"(2G   Z,4 oL!?"0@NNN?N ]  An+2"(2G   Z7 oL!?"0@NNN?N O  An+1"(2G   Zt; 3oL!?"0@NNN?N\ ?."(2G    Z? 3oL!?"0@NNN?N_2 ?."(2G    ZB 3oL!?"0@NNN?N  ?."(2G    Z`F 3oL!?"0@NNN?N  ?."(2G    ZJ oL!?"0@NNN?NJ( An+1"(2G   ZM oL!?"0@NNN?N=X}, An+2"(2GB   # lD1L!?"0@NNN?NB B ! # lD1L!?"0@NNN?Ng B " # lD1L!?"0@NNN?N9  #  0e0e    BNCDEF o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| N @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab) $ ZLQ  oL!?"6@ NNN?N ,$ 0  The size of the quotas s,t reflects the power of society The difference |s-t| reflects the asymmetry of qualification and disqualification. % 2EEEE1EEEEE EEEE,1A & Z^  oL!?"6@ NNN?Ns Y0 ,$ 0 ;The size and the difference are the smallest for s = t = 1.f< 21EEEEE2 '  ` oL!?"6@ NNN?No ,$D  0 ( # lj ?3ԔD[Ȝ8c?"<?@@`NNN?N `,$D 0 SThe liberal rule f 11 : fj11(P) = Pjj  T 2eeeegm0emmemoOH  0޽h ? ̙33___PPT10+93ID' v = @B D' = @BA?%,( < +O%,( < +DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$;%(DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$;%(D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =-g6B fade*<3<*&DR' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*'D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*'D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-6B%slide(fromBottom)*<3<*(++0+$0 ++0+&0 ++0+(0 +Q 0L0 --`3g-(  yF 4g    4g B !  fDoL!?"0@NNN?N B "  fDoL!?"0@NNN?N L  #  f  ԔL!?"6@ NNN?N54T =t (2E  $ Z8 3oL!?"0@NNN?Nr2  ?."(2G   % Z̃ 3oL!?"0@NNN?N],  ?."(2G   & Z oL!?"0@NNN?Ni 5[  ?1"(2G  ' Z oL!?"0@NNN?N9  ?1"(2G  ( ZH oL!?"0@NNN?N ]  An+2"(2G  ) Z oL!?"0@NNN?N O  An+1"(2G  * Z 3oL!?"0@NNN?N\ ?."(2G   + Z4 3oL!?"0@NNN?N_2 ?."(2G   , Zء 3oL!?"0@NNN?N  ?."(2G   - Z| 3oL!?"0@NNN?N  ?."(2G   . Z  oL!?"0@NNN?NJ( An+1"(2G  / ZĬ oL!?"0@NNN?N=X}, An+2"(2GB 0 # lD1L!?"0@NNN?NB B 1 # lD1L!?"0@NNN?Ng B 2 # lD1L!?"0@NNN?N9  3  0e0e    BNCDEF o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| N @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab)  c $@ 0    = Special rules  # l oL!??"6@`NNN?Nm D 2E    fP  ԔL!?"6@ NNN?N!   =s (2E  ZĴ  oL!?"6@ NNN?N   The size of the quotas s,t reflects the power of society The difference |s-t| reflects the asymmetry of qualification and disqualification. % 2EEEE1EEEEE EEEE,1Ae  Z  oL!?"6@ NNN?N b9( ,$ 0 i/Maximal societal influence for equal quotas ...0 20E2   ` oL!?"6@ NNN?N<,$D  0x  # l, ?3ԔD[Ȝ8c?"<?@@`NNN?N `,$D 0 dThe majoritarian rule f ss for odd n and s = (n+1)/2. fjss(P) = x |{i : Pij = x}| e" (n+1)/2 (d(2 2e eeegmeefeeemm eGEEEEfMEG EoP  (   `< GH oL!?"6@ NNN?N ,$D  0 &8The choice between qualification and disqualification of j is determined by simple majority where j s vote for herself counts like all other votes for her. (2E EEEEE(EE:Eb8B  ZDjJL!?"0@NNN?N7,$D  0   `l GHoL!?"6@ NNN?NH  ,$D  0 UThese are the rules that bridge between liberalism and democracy (majoritarian rule)hV(2)E EE EEC H  0޽h ?/  ̙33""___PPT10k"+mV rD '  = @B D ' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(down)*<3<*D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(+P+0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 += 0L0 N*F*p2)(  yF 4g   4g B    fDoL!?"0@NNN?N B !  fDoL!?"0@NNN?N L  "  fh  ԔL!?"6@ NNN?N54T =t (2E  # Z  3oL!?"0@NNN?Nr2  ?."(2G   $ Z 3oL!?"0@NNN?N],  ?."(2G   % Z| oL!?"0@NNN?Ni 5[  ?1"(2G  & Z oL!?"0@NNN?N9  ?1"(2G  ' Z0" oL!?"0@NNN?N ]  An+2"(2G  ( Z% oL!?"0@NNN?N O  An+1"(2G  ) Zx) 3oL!?"0@NNN?N\ ?."(2G   * Z- 3oL!?"0@NNN?N_2 ?."(2G   + Z0 3oL!?"0@NNN?N  ?."(2G   , Zd4 3oL!?"0@NNN?N  ?."(2G   - Z8 oL!?"0@NNN?NJ( An+1"(2G  . Z; oL!?"0@NNN?N=X}, An+2"(2GB / # lD1L!?"0@NNN?NB B 0 # lD1L!?"0@NNN?Ng B 1 # lD1L!?"0@NNN?N9  2  0e0e    BNCDEF o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| N @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab)  c $(? 0    = Special rules  # ldB oL!??"6@`NNN?Nm D 2E    fD  ԔL!?"6@ NNN?N!   =s (2E  ZH  oL!?"6@ NNN?N   The size of the quotas s,t reflects the power of society The difference |s-t| reflects the asymmetry of qualification and disqualification. % 2EEEE1EEEEE EEEE,1A1  Z`X  oL!?"6@ NNN?N b9(  i/Maximal societal influence for equal quotas ...0 20E2   ` oL!?"6@ NNN?N\,$D  0  # l` ?3ԔD[Ȝ8c?"<?@@`NNN?N `,$D  0 The majoritarian rule f ss for even n and s = n/2 + 1. fjss(P) = x |{i j : Pij = x}| e" n/2 + 1 fi(2 2e eeegm eefeeemm eGEEE E  E f M  E  G   E oP !n   `z GHoL!?"6@ NNN?NA ,$D  0 l|The choice between qualification and disqualification of j is determined by simple majority of all the voters other than j. }(2E EEEEE4EEEEEH  0޽h ? ̙33___PPT10+!ЦD'  = @B D' = @BA?%,( < +O%,( < +DR' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D0' =%(D' =%(D' =A@BB5BB0B%()))D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(++0+0 ++0+0 ++0+0 +58 0L0 ''3e'(  yF 4g    4g B !  fDoL!?"0@NNN?N B "  fDoL!?"0@NNN?N L  #  f,  ԔL!?"6@ NNN?N54T =t (2E  $ Z 3oL!?"0@NNN?Nr2  ?."(2G   % Zx 3oL!?"0@NNN?N],  ?."(2G   & Z@ oL!?"0@NNN?Ni 5[  ?1"(2G  ' ZP oL!?"0@NNN?N9  ?1"(2G  ( Z oL!?"0@NNN?N ]  An+2"(2G  ) Z oL!?"0@NNN?N O  An+1"(2G  * Z< 3oL!?"0@NNN?N\ ?."(2G   + Z 3oL!?"0@NNN?N_2 ?."(2G   , Z 3oL!?"0@NNN?N  ?."(2G   - Z( 3oL!?"0@NNN?N  ?."(2G   . Z̺ oL!?"0@NNN?NJ( An+1"(2G  / Zp oL!?"0@NNN?N=X}, An+2"(2GB 0 # lD1L!?"0@NNN?NB B 1 # lD1L!?"0@NNN?Ng B 2 # lD1L!?"0@NNN?N9  3  0e0e    BNCDEF o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| N @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab)  c $ 0    = Special rules  # l oL!??"6@`NNN?Nm D 2E    f  ԔL!?"6@ NNN?N!   =s (2E  Zp  oL!?"6@ NNN?N   The size of the quotas s,t reflects the power of society The difference |s-t| reflects the asymmetry of qualification and disqualification. % 2EEEE1EEEEE EEEE,1A  ZH  oL!?"6@ NNN?N b9 ,$ 0 rThe most extreme case of asymmetry between qualification and disqualification is attained at (n+1,1) and (1,n+1). s 2+EEEEEEEEEEEEE2   ` oL!?"6@ NNN?Nm,$@  0  ZD  oL!?"6@ NNN?Nx oS,$D 0 vAt (n+1,1) players are disqualified no matter how they vote. At (1,n+1) players are qualified no matter how they vote.w 2EEEEE EEEEEE EE2   ` oL!?"6@ NNN?ND,$D  0H  0޽h ? ̙33___PPT10+?DD4'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D2' =%(D' =%(D' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*+p+0+0 ++0+0 +#" 0L0   7 (    c $h 0    BSelf determination  Tp  3ԔL!?"6@ NNN?N$S,$D  0 | Let Hobbits determine who is a Hobbit. J.R.R. Tolkien0? 20EE7  # l0  ?3ԔD[Ȝ8c?"<?@@`NNN?NwR ,$D 0 mSelf determination If non-Hobbits change their votes about Hobbits, then the set of Hobbits does not change. 6n(2e[e  # l ?3ԔD[Ȝ8c?"<?@@`NNN?N~ c=,$D  0 ZNon-degeneracy For each j there are profiles P and Q such that fj(P) = 1 and fj(Q) = 0. VZ(2 2e aeaefaef amaef amaefao,@    RAxIȜ@@?hobbitsg ,$D 0   `$ )L!?"6@ NNN?N( ,$D  0  Theorem: The only rule that satisfies monotonicity, independence, non-degeneracy, and self-determination is the liberal rule.   2GEE EE EEEEEEG' NH  0޽h ? ̙33 ___PPT10+@FD' 9 = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D ' =%(D' =%(Dp' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D&' =%(D' =%(Dv' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-u6Bwipe(right)*<3<*D$' =%(D' =%(Dt' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*Du' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*++0+0 ++0+0 ++0+0 ++0+0 +Z 0 |(  |X | C P<    | S xPH .*    H | 0re"f ? ̙33r| #G)u. .5ӔPDFW7PVDu;sZwOh+'0 `h  דילמת האסיר Samet Dovs324Microsoft PowerPoint@@ov@t~n!@@g#Gg   %  y---$x x ----$ xx ----$x!x!----$!!x)x)!----$))x.x.)----$..x3x3.----$33x6x63----$66x:x:6----$::x?x?:----$??xBxB?----$BBxExEB----$EExIxIE----$IIxLxLI----$LLxOxOL----$OOxSxSO----$SSxVxVS----$VVxYxYV----$YYx]x]Y----$]]x`x`]----$``xcxc`----$ccxgxgc----$ggxjxjg----$jjxnxnj----$nnxqxqn----$qqxvxvq----$vvx{x{v----${{xx{----$xx----$xx----$xx----$xx---'@Times New Roman-. 2 #<Betweenr."Systemh9-@Times New Roman-. 2 / Liberalism .-@Times New Roman-.  2 /Fand.-@Times New Roman-. 2 /X Democracym.-@Times New Roman-. 2 KD. Samet.-@Times New Roman-.  2 K?,.-@Times New Roman-.  2 KGD. .-@Times New Roman-.  2 KSSc.-@Times New Roman-. 2 K\hmeidler.---$VV---- $VV----$TT--f-- $TT--'@Times New Roman-. 2 "?Betweenr.. 2 !>Betweenr.-@Times New Roman-. 2 . Liberalism .. 2 - Liberalism .-@Times New Roman-.  2 -Hand.-@Times New Roman-. 2 .[ Democracym.. 2 -Z Democracym.-@Times New Roman-. 332 ID. Samet.-@Times New Roman-.  2 IA,.-@Times New Roman-. 33 2 IID. .-@Times New Roman-. 33 2 IUSc.-@Times New Roman-. 332 I^hmeidler.-@Times New Roman-. %2 k!www.tau.ac.il/~samet.---$`nn``---- $`nn`----$]kk]]--f-- $]kk]--'@Times New Roman-. 33%2 i#www.tau.ac.il/~samet.-՜.+,D՜.+,`    On-screen ShowSametW DavidArialTimes New RomanSymbolArial Unicode MSDefault Design?Between Liberalism and Democracy D. Samet, D. SchmeidlerSens Liberalism ParadoxSens Liberalism Paradox The model Monotonicity Independence SymmetryConsent rulesConsent rulesDualitySpecial rulesSpecial rulesSpecial rulesSpecial rulesSelf determination  Fonts UsedDesign Template Slide Titles 8@ _PID_HLINKSA 458,47,Ordinal solutions458,47,Ordinal solutions_dss  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFHIJKLMNOPQRSTVWXYZ[\^_`abcdkRoot EntrydO)PicturesCurrent User]SummaryInformation(G8PowerPoint Document(zDocumentSummaryInformation8U