Appendx for Insttutons and Behavor: Expermental Evdence on the Effects of Democrac 1. Instructons 1.1 Orgnal sessons Welcome You are about to partcpate n a stud on decson-makng, and ou wll be pad for our partcpaton n cash, prvatel at the end of the sesson. What ou earn depends partl on our decsons, partl on the decsons of othe, and partl on chance. Please turn off page and cellular phones now. Please close an program ou ma have opened on the computer. The entre sesson wll take place through computer termnals, and all nteracton between ou wll take place through the compute. Please do not talk or n an wa tr to communcate wth other partcpants durng the sesson. We wll start wth a bref nstructon perod. Durng the nstructon perod ou wll be gven a descrpton of the man features of the sesson and wll be shown how to use the compute. If ou have an questons durng ths perod, rase our hand and our queston wll be answered so everone can hear. General Instructons Please double clck on the con named Expermental Logn and wat for nstructons. In the space marked name please enter the computer number n the whte stcker, as shown on the screen at the front of the room, and clck: SUBMIT. Ths wll log ou on to the sesson. Please do not proceed an further untl ou are told to do so. An questons? Ths experment conssts of two parts. For all parts of ths experment ou wll be dvded nto groups of four people. 1
Part 1 In part 1 ou wll be asked to make decsons n several rounds. You wll be randoml pared wth another peon n our group for each round. Once a round s fnshed, ou wll be randoml pared wth another peon n our group for a new round. There wll be 10 rounds n the ft part of ths experment. In each round ou and the peon ou are matched wth wll smultaneousl and ndependentl choose one of two actons, 1 or. The paoff ou wll earn depends on both our acton and the acton of the peon ou are matched wth as shown at the screen n the front of the classroom. The exchange rate of ponts to dolla s 50 ponts for one dollar. If the peon ou are matched wth chooses 1 and ou choose 1, ou earn 40 ponts. If the peon ou are matched wth chooses 1 and ou choose, ou earn 10 ponts. If the peon ou are matched wth chooses and ou choose 1, ou earn 60 ponts. If the peon ou are matched wth chooses and ou choose, ou earn 50 ponts. Please look at the screen at the front of the room. Ths s what our computer screen wll look lke. Your possble actons are 1 and, denoted n red. The possble actons of the peon ou are matched wth are n blue. As ou can see, the screen gves ou the paoff assocated wth each par of actons. The paoffs are expressed n ponts. You ma choose our acton b clckng on the correspondng acton. The computer screen also shows our past actons, the past actons of the partcpants ou were matched wth and our paoffs at the bottom. You wll be pad the sum of our ponts prvatel at the end of the experment. An questons? We start wth part 1 now. Remember, ou wll now partcpate n 10 rounds, for each round ou wll be randoml match wth another partcpant n our group. Make our decsons. Ths s the end of part 1.
Part In ths part of the experment ou wll partcpate wth the same group n 10 rounds as n part 1 wth the dfference that the paoffs ma be modfed. As shown at the screen n the front of the classroom, f paoffs are modfed the new paoffs wll be as follows: If the peon ou are matched wth chooses 1 and ou choose 1, ou earn 40 ponts. If the peon ou are matched wth chooses 1 and ou choose, ou earn 10 ponts. If the peon ou are matched wth chooses and ou choose 1, ou earn 48 ponts. If the peon ou are matched wth chooses and ou choose, ou earn 50 ponts. The screen also shows the ntal paoffs. Whether the paoffs are modfed s determned as follows. Ft, our group s gong to vote on whether to modf paoffs. Second, the computer wll randoml choose whether to consder the votes or not n our group. If the computer consde the votes then majort wns and n case of a te the computer wll flp a con. If the computer does not consder the votes n our group, t wll randoml choose whether to modf paoffs or not. Your computer screen wll nform ou f the computer randoml choose to consder the votes or not and whether paoffs are modfed or not. Ths slde summarzes the votng stage. Ft the group votes. Then the computer randoml decdes whether to consder the votes or not. If t consdered the votes then majort wns. If the computer does not consder the votes, then t randoml chooses whether to modf the paoffs or not. Your computer screen wll show a screen lke ths f t dd not consder the votes and lke ths f t dd and so on. An questons? Vote now. You wll now partcpate n 10 rounds, for each round ou wll be randoml match wth another partcpant n our group. 3
An questons? Make our decsons. Ths s the end of the man decson-makng porton of part, before the end of the experment please answer the followng questons. The ft queston s: Could ou please explan our votng decson? Please press submt when ou fnsh. The second queston s: What was the result from the votng stage? You wll receve 100 ponts for a correct answer. The thrd queston s: How dd the result of the votng stage affect our decsons n the second part of the experment? Please press submt when ou fnsh. The fourth queston s: Under the ntal paoffs, what s the paoff n ponts ou receved dependng on our acton (n red) and the acton of the peon ou are matched wth (n blue)? You wll receve 10 ponts for each correct answer. Please fll n the matrx and press submt. The ffth queston s: Under the modfed paoffs, what s the paoff n ponts ou receved or would have receved dependng on our acton (n red) and the acton of the peon ou are matched wth (n blue)? You wll receve 10 ponts for each correct answer. Please fll n the matrx and press submt. Fnall, please answer the next questons that appear n our screen. 1) What s our major? (f ou have not decded please wrte undecded). ) What s our class? (Freshmen, Sophomore, Junor, Senor, f other please explan). 3) What was our SAT score? (f ou took t more than once please report the hghest one) and 4) What s our poltcal phlosoph? Before endng the experment we wll ask ou to make one last decson. Each partcpant wll choose a number between zero and one hundred. The partcpant wth the closest number to two thrds of the average of all numbe n our group wll earn 100 ponts. Please choose our number now 4
You now see our total paoff n a wndow. Please press ok to end the experment. Ths s the end of the experment. Please reman seated to receve our earnngs; we wll round up our total paoff to the hghest quarter and add the show-up fee. Thank ou! 1.. Addtonal sessons Welcome You are about to partcpate n a stud on decson-makng, and ou wll be pad for our partcpaton n cash, prvatel at the end of the sesson. What ou earn depends partl on our decsons, partl on the decsons of othe, and partl on chance. Please turn off page and cellular phones now. Please close an program ou ma have opened on the computer. The entre sesson wll take place through computer termnals, and all nteracton between ou wll take place through the compute. Please do not talk or n an wa tr to communcate wth other partcpants durng the sesson. We wll start wth a bref nstructon perod. Durng the nstructon perod ou wll be gven a descrpton of the man features of the sesson and wll be shown how to use the compute. If ou have an questons durng ths perod, rase our hand and our queston wll be answered so everone can hear. General Instructons Please double clck on the con named Expermental Logn and wat for nstructons. In the space marked name please enter the computer number n the whte stcker, as shown on the screen at the front of the room, and clck: SUBMIT. Ths wll log ou on to the sesson. Please do not proceed an further untl ou are told to do so. An questons? 5
Ths experment conssts of two parts. For all parts of ths experment ou wll be dvded nto groups of four people. Part 1 In part 1 ou wll be asked to make decsons n several rounds. You wll be randoml pared wth another peon n our group for each round. Once a round s fnshed, ou wll be randoml pared wth another peon n our group for a new round. There wll be 10 rounds n the ft part of ths experment. In each round ou and the peon ou are matched wth wll smultaneousl and ndependentl choose one of two actons, 1 or. The paoff ou wll earn depends on both our acton and the acton of the peon ou are matched wth as shown at the screen n the front of the classroom. The exchange rate of ponts to dolla s 50 ponts for one dollar. If the peon ou are matched wth chooses 1 and ou choose 1, ou earn 40 ponts. If the peon ou are matched wth chooses 1 and ou choose, ou earn 10 ponts. If the peon ou are matched wth chooses and ou choose 1, ou earn 60 ponts. If the peon ou are matched wth chooses and ou choose, ou earn 50 ponts. Please look at the screen at the front of the room. Ths s what our computer screen wll look lke. Your possble actons are 1 and, denoted n red. The possble actons of the peon ou are matched wth are n blue. As ou can see, the screen gves ou the paoff assocated wth each par of actons. The paoffs are expressed n ponts. You ma choose our acton b clckng on the correspondng acton. The computer screen also shows our past actons, the past actons of the partcpants ou were matched wth and our paoffs at the bottom. You wll be pad the sum of our ponts prvatel at the end of the experment. An questons? 6
We start wth part 1 now. Remember, ou wll now partcpate n 10 rounds, for each round ou wll be randoml match wth another partcpant n our group. Make our decsons. Ths s the end of part 1. Part In ths part of the experment ou wll partcpate wth the same group n 10 rounds as n part 1 wth the dfference that the paoffs ma be modfed. As shown at the screen n the front of the classroom, f paoffs are modfed the new paoffs wll be as follows: If the peon ou are matched wth chooses 1 and ou choose 1, ou earn 40 ponts. If the peon ou are matched wth chooses 1 and ou choose, ou earn 10 ponts. If the peon ou are matched wth chooses and ou choose 1, ou earn 48 ponts. If the peon ou are matched wth chooses and ou choose, ou earn 50 ponts. The screen also shows the ntal paoffs. Whether the paoffs are modfed s determned as follows. Ft, our group s gong to vote on whether to modf paoffs. Second, the computer wll randoml choose whether to consder the votes or not n our group. If the computer consde the votes then majort wns and n case of a te the computer wll flp a con. If the computer does not consder the votes n our group, t wll randoml choose whether to modf paoffs or not. Your computer screen wll nform ou f the computer randoml choose to consder the votes or not, whether paoffs are modfed or not and wll provde nformaton regardng the votes. Ths slde summarzes the votng stage. Ft the group votes. Then the computer randoml decdes whether to consder the votes or not. If t consdered the votes then majort wns. If the computer does not consder the votes, then t randoml chooses whether to modf the paoffs or not. 7
Your computer screen wll show a screen lke ths f there were at most votes n favor of modfcaton, or lke ths f there were at least votes n favor of modfcaton, and lke ths f the computer randoml choose to consder the votes and so on. An questons? Vote now. You wll now partcpate n 10 rounds, for each round ou wll be randoml match wth another partcpant n our group. An questons? Make our decsons. Ths s the end of the man decson-makng porton of part, before the end of the experment please answer the followng questons. The ft queston s: Could ou please explan our votng decson? Please press submt when ou fnsh. The second queston s: What was the result from the votng stage? You wll receve 100 ponts for a correct answer. The thrd queston s: How dd the result of the votng stage affect our decsons n the second part of the experment? Please press submt when ou fnsh. The fourth queston s: Under the ntal paoffs, what s the paoff n ponts ou receved dependng on our acton (n red) and the acton of the peon ou are matched wth (n blue)? You wll receve 10 ponts for each correct answer. Please fll n the matrx and press submt. The ffth queston s: Under the modfed paoffs, what s the paoff n ponts ou receved or would have receved dependng on our acton (n red) and the acton of the peon ou are matched wth (n blue)? You wll receve 10 ponts for each correct answer. Please fll n the matrx and press submt. 8
Fnall, please answer the next questons that appear n our screen. 1) What s our major? (f ou have not decded please wrte undecded). ) What s our class? (Freshmen, Sophomore, Junor, Senor, f other please explan). 3) What was our SAT score? (f ou took t more than once please report the hghest one) and 4) What s our poltcal phlosoph? Before endng the experment we wll ask ou to make one last decson. Each partcpant wll choose a number between zero and one hundred. The partcpant wth the closest number to two thrds of the average of all numbe n our group wll earn 100 ponts. Please choose our number now You now see our total paoff n a wndow. Please press ok to end the experment. Ths s the end of the experment. Please reman seated to receve our earnngs; we wll round up our total paoff to the hghest quarter and add the show-up fee. Thank ou! 9
. Estmaton of democrac effects usng ndvdual data after round 11 In ths appendx we descrbe n detal the methodolog used to estmate the effect of democrac n all rounds after the votng stage dscussed n secton 4.. We focus on the effect of democrac under modfed paoffs. The methodolog we present here allows us to estmate the effect of democrac on behavor after controllng for the fact that subjects under endogenous modfcaton are more lkel to meet subjects that voted for modfcaton than subjects under exogenous modfcaton are. In addton, ths methodolog consde the fact that a subject s behavor ma be correlated wth her prevous behavor and be affected b the behavor of prevous partne. Consder the followng model of behavor after the votng stage: (A1)... 1 3 x u 1 1 x u x u 3 1 1 u 3 1, u 1, 3, u 3, r x r r1 s1 u s r1 s1 s, u r where r denotes the round number n part (for smplct we start countng from 1), denotes the subject and - denotes prevous partner of. The varable r denotes cooperaton n round r b subject, r,- denotes cooperaton n round r b subject s partner n that round, and x s a vector of ndcator varables for the four combnatons of ndvdual vote (es or no) and whether votes where consdered (Endo or Exo). The erro u r are assumed to follow these propertes: 0 E, E 0 u r u r u sj, and Eu r x j 0 for an rounds r or s and subjects or j. Note that (A1) s a lnear approxmatons to decson rules and that our nference wll be vald to the extent that ths lnear approxmaton s reasonable. To estmate the paramete n (A1) we start b estmatng the sstem n (A) whch dffe from (A1) n that we nclude the prevous behavor of the subject as a control nstead of prevous erro: 10
(A)... 1 3 x b x b x b 1 3 1 r r 1 1 f r 3 1, f 1, f 3, 3, r x b r r1 s1 r s r1 s1 f s, r ur It can be easl shown that the erro n (A) concde wth the erro n (A1):. Gven our prevous assumptons about the erro n (A1) t follows that the rj erro n (A) satsf all the requrements for an OLS regresson: 0 E, E 0, 0 u r u r u sj fnall 0 E u r x j for an subjects and j and rounds r and s, and E u r sj for an subjects and j and rounds r and s such that s<r. From the vector of estmated coeffcents b ˆ, rˆ, fˆ ) for (A) we can construct the estmates of the coeffcents n (A1) as follows: ( r (A3) ˆ bˆ ˆ ˆ r r rˆ fˆ r1 s1 ˆ bˆ r1 ts1 r1 ts1 ˆ rˆ rt ˆ fˆ rt s ts ts. Ths s straghtforward for r=1, as the ft equaton n (A1) concdes wth the ft equaton n (A) and ˆ ˆ 1 b1. For r=, we can use the ft equaton n (A) to substtute for u 1 n the second equaton n (A1) and then: b1 1 1, u x. Whch mples that bˆ ˆ ˆ ˆ b1, r ˆ ˆ and f ˆ ˆ. Rearrangng, we fnd the equaltes n (A3) for r=. For r=3, we can use the ft two equaton n (A) to substtute for u 1 n the thrd equaton n (A1) and then 3 b1 3b 3r 1 3 3 f 1, 3, u 3 x Whch mples that bˆ 3 ˆ ˆ ˆ ˆ ˆ b1 3b, rˆ ˆ ˆ ˆ 3r, r ˆ ˆ 3 3, 11
fˆ ˆ ˆ 3 f and f ˆ 3 3 ˆ. Rearrangng, we fnd the equaltes n (A3) for r=3. In smlar wa we can verf (A3) for r>3. Wth the vector of estmates ˆ, ˆ, ˆ ) we can calculate the effect of ( r democrac b round. As sad before, we focus on groups wth paoff modfcaton. Ft, we calculate the drect effect of democrac b ndvdual vote and round: DED rv, where r denotes the round and v the ndvdual vote (es or no). The drect effect of democrac can be thought as the dfference n cooperaton under endogenous and exogenous modfcaton once we control for the behavor of prevous partne. Ths dfference can be calculated as DED ˆ ˆ, rv rv, Endo rv Exo, where rv, Endo ˆ s the estmated coeffcent for those n round r, wth ndvdual vote v and whose vote was counted (endogenous ˆ rv, modfcaton) and s the coeffcent for those whose vote was not counted Exo (exogenous modfcaton). The effect of democrac s not onl the drect effect as a subject s behavor s modfed b the behavor of other subjects whch n turn depends on whether paoffs are modfed endogenousl or exogenousl. We calculate the effect of democrac round r for subjects wth vote v, as follows: ED rv on ED ED 1v rv DED DED 1v rv r 1 s1 ˆ p v ED r p vn ED rn, where ˆ s the estmated coeffcent measurng how subjects cooperaton n round r responds to cooperaton b ther partne n round s, and p v and p vn denotes the probabltes that a subject wth vote v meets a es and no subject respectvel under endogenous modfcaton. The estmates of the effect of democrac under modfcaton are presented n Table 6. 1