Leadership, cheap talk and really cheap talk - Semantic Scholar

Journal of Economic Behavior & Organization 77 (2011) 40–52

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Journal of Economic Behavior & Organization journal homepage: www.elsevier.com/locate/jebo

Leadership, cheap talk and really cheap talk David M. Levy a , Kail Padgitt a,∗ , Sandra J. Peart b , Daniel Houser a,∗ , Erte Xiao c a b c

Economics Department, George Mason University, United States Jepson School of Leadership Studies, University of Richmond, Richmond, VA 23173, United States Department of Social and Decision Sciences, Carnegie Mellon University, United States

a r t i c l e

i n f o

Article history: Received 1 July 2009 Received in revised form 5 February 2010 Accepted 10 February 2010 Available online 21 September 2010

a b s t r a c t Previous research offers compelling evidence that leaders suffice to effect efficiencyenhancements on cooperation, yet the source of this effect remains unclear. To investigate whether leadership effects can be attributed exclusively to the common information that leaders provide to a group, irrespective of the source of that information, we design a public goods game in which non-binding contribution suggestions originate with either a human or computer leader. We find that group members’ decisions are significantly influenced by human leaders’ non-binding contribution suggestions, both when the leader is elected as well as when the leader is randomly chosen. A leader’s suggestion becomes an upper bound for group member’s contributions. Identical suggestions do not impact the group members’ decisions when they originate with a computer, thus supporting to the view that information provided by human leaders is uniquely able to establish welfare-enhancing norms. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Leadership is a prominent feature of human societies, in part because leaders promote cooperation in non-family groups (see, e.g., Güth et al., 2007; List and Reiley, 2002). Previous research offers compelling evidence that leaders suffice for efficiency-enhancing effects on group cooperation yet, as we discuss below, the source of this effect remains unclear. Can leadership effects be attributed exclusively to the common information that leaders provide, irrespective of the source of that information? To address this we design a public goods game in which non-binding (cheap talk) contribution suggestions originate with either a human or computer leader. We find that group members’ decisions are significantly influenced by human leaders’ non-binding contribution suggestions, both when the leader is elected and when the leader is randomly chosen. In particular, a leader’s suggestion becomes an upper bound for the contributions of her group members. Those same suggestions do not impact the group members’ decisions when they originate with a computer, which we call really cheap talk. This label acknowledges the neurological result that nonreciprocal behavior with machines has less of an impact than it does with humans (McCabe et al., 2001).1 In our study, neither human nor computer leaders have an informational advantage over their group members. As has been previously noted (e.g., Peart and Levy, 2005), a leader with an informational or a first mover advantage can signal the

∗ Corresponding author. E-mail addresses: [email protected] (D.M. Levy), [email protected] (K. Padgitt), [email protected] (S.J. Peart), [email protected] (D. Houser), [email protected] (E. Xiao). 1 If evolved norms constrain human behavior, making deviation from suggestion more costly in one direction than another (Levy, 1992), then a really cheap talk treatment provides a context in which the violation of norms in any direction has small cost. 0167-2681/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jebo.2010.02.018

D.M. Levy et al. / Journal of Economic Behavior & Organization 77 (2011) 40–52

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value of cooperation (or any other action), thus providing an upper bound to her members decisions (Andreoni, 1998, 2006; Hermalin, 1998; Brandts et al., 2007; Güth et al., 2007; Levati et al., 2007; List and Rondeau, 2003; Potters et al., 2005). Even absent information asymmetries, positive leadership effects can stem from social preferences and conditional cooperation (Meidinger and Villeval, 2002; Güth et al., 2007; Moxnes and Heijden, 2003; Gächter and Renner, 2004).2 For example, if a group member believes that others will follow a common signal, then she might reciprocate (Croson, 2000; Fischbacher et al., 2001; Kurzban and Houser, 2005; Camerer, 2003). This effect requires only that all group members know that all receive a common signal. If leadership is just a signal then we have no reason to expect asymmetric response. If leadership depends on reciprocity (e.g., Tyler, 1990, 2002) then we have reason to expect asymmetric response when we know there is a substantial cost of violating reciprocity by contributing less than suggested but not more than suggested. We conduct three treatments of a public goods game: two include human leaders (with the leaders chosen in different ways) and one includes a computer leader. In all cases the leader sends non-binding contribution suggestions to each member of her group. The computer leader treatments were run subsequent to one of our human treatments, and its messages follow the human leaders’ messages exactly. Importantly, participants always know the source of the suggestion they receive. Our key finding is that group members’ decisions are significantly affected by human leaders’ messages, both when a leader encourages cooperation as well as when she does not. In particular, the suggestion of the human leader provides an upper bound to each group member’s contribution while identical suggestions from a computer have no impact. Humans do not hold any informational advantage, so this cannot explain the difference. Rather, this result seems consistent with the view that human leaders are uniquely capable of establishing norms of cooperation or reciprocity. 2. Experiment design 2.1. Overview Our design extends standard linear public goods games, which have been widely used to study social dilemma problems where personal interest conflicts with group interest (see, e.g., Ledyard, 1995). In a standard game, each subject i in each round t is given y experimental dollars (E$, which are exchanged for US dollars at a known exchange rate at the end of the experiment) and chooses, simultaneously with other subjects, the amount to invest in the group account git and the amount to keep in their own individual account. Each E$ kept is worth one E$, and each E$ invested in the group account yields ˛ < 1 E$ to each group member. Thus, in a group of n subjects, the payoff it for each subject i in round t is given by: n

it = y − git + ˛

git ,

0 < ˛ < 1 < n˛

(1)

i=1

Backwards induction in this finite-round game implies that, if individuals are selfish, the subgame-perfect equilibrium git = − 1 + ˛ < 0. However, requires each subject to contribute nzero to the group account each round. This follows from ∂it /∂ n is maximized if the restriction 1 < n˛ ensures ∂ i=1 it /∂git = −1 + n˛ > 0, so that the aggregate group payoff i=1 it every subject contributes everything to the public good. As detailed below, we study three variants of this game. In one, an elected leader sends a non-binding contribution suggestion to all of the group members. Subsequent to this treatment we conduct a signal-only treatment. Each group in the signal-only treatment receives the same suggested contributions in the same order as one arbitrarily determined group from the elected leader treatment. All group members are aware that the message does not originate with a member of their group. In the third variant of the game one group member is randomly selected to be the leader and sends a contribution suggestion to the group. 3. Elected leader treatment The key features of this treatment are as follows. Four subjects (n = 4) know they will play a public goods game for exactly 15 rounds. Each subject receives 10E$ (y = 10) at the beginning of each round and asked to allocate these 10E$ between her individual and group account. The experiment includes two stages. The purpose of the first stage in the elected leader treatment is to accomplish leader selection. Our potential leaders compete on the basis of a proposed platform. First, subjects make decisions in five rounds of a standard public goods game. Before the sixth round, each subject writes a “platform” on carbon paper producing four copies. The platform’s content is unrestricted and the subjects understand that copies will be collected and distributed to each member of the group.3 After each group member has a copy of all four proposed platforms, she votes for one offered by someone else. Subjects are aware that the person who writes the winning platform will have a special role in the remainder of the experiment and

2

Action motivated by reciprocity may stem from an aversion to guilt that results from failing to follow this norm (Vanberg, 2008). Having subjects write platforms on paper makes transparent and credible that the messages are from people and not artificially generated. Subjects were paid $2 to write these messages, in order to help ensure effort on this part of the game. 3

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they have complete information on the nature of this role (described below). Ties did not occur.4 A message was distributed to the winner stating “You wrote the winning platform.” Non-winners were not informed. The subjects were informed regardless of what treatment they were in. The second stage of the experiment, the final ten rounds of the game, proceeds similarly to the first five rounds except that, at the beginning of each round, the person who wrote the winning platform (the “leader”) sends an identical suggestion to each group member, as follows: “Let’s contribute — E$ to the group account.” These message slips were pre-printed, so the leader could only communicate by filling in the number. It was common information to the subjects that (i) each group member received the same message from the leader; (ii) each group member makes his/her decision after observing the leader’s message; (iii) the message was an unenforceable suggestion; and (iv) the leader need not follow her own suggestion. The second stage included exactly ten rounds. At the conclusion of each round subjects’ information included: (1) how much was contributed by each group member (but IDs were not listed, so reputations could not be formed); (2) one’s individual investment and total group investment; (3) the difference between one’s investment in the group account and the average investment amount of the other group members (see Appendix A for details). 4. Signal-only treatment The signal-only treatment enables us to distinguish effects of suggestions made by elected human leaders from effects of those same suggestions sent by an external device. In order to preserve symmetry among treatments, the first stage of the signal-only treatment is identical to the leader treatment; platform writing and voting occurs after the fifth round, and the person who won the vote is so informed. However, the author of the winning platform has no special role in the second stage. At the beginning of each round during the second stage, as in the human treatments, each group member receives a message before she makes her contribution decision. The subjects are informed that messages are generated by a random process. This treatment was conducted subsequent to the elected leader treatments, and the random process involved pairing each signal-only treatment group with a unique (previously run) elected leader treatment group, and then giving the signal-only group exactly the same messages (and in the same order) seen by their paired elected leader treatment group. Subjects were aware that the messages were not from any member in their group, and they understood that the messages were randomly assigned. Just as in the elected leader treatment, subjects understood that they were not required to follow the message. The second stage of this treatment also included ten rounds, after which the experiment concluded. 5. Randomly selected human treatment In addition to an elected human and the signal-only treatment, a randomly selected leader treatment was also conducted. The randomly selected leader treatment was conducted in the same manner as the previous treatments for the first five rounds and the platform writing phase. In this treatment a leader’s selection was unrelated to the outcome of the message writing platform. The experiment then continued with the randomly selected leader sending out messages in the same manner as the elected leader treatment.5 Subjects were seated randomly in the lab, and did not know who was in their group. There are situations where at the group and individual levels the leader’s actual contribution can become known. At the extremes of total donation to the group or individual account, then the group would know that leader had given all ten (or zero) to either account. Additionally if there is only one member of the group who does not donate to the group this member can learn the identity of the leader. Care was taken to insure that the actual leader in the room could not be identified. The leaders simply had to write a number on a piece of paper. The experimenter then looked at this number and distributed the pre-printed messages to the group. The experimenters were careful to pause at every single individual so as to disguise the leader. 6. Procedures Each treatment included two sessions of twelve subjects each. All subjects were recruited from George Mason University’s general undergraduate population, using standard recruiting procedures in place at the Interdisciplinary Center for Economic Science. Subjects earned a US$ 5 bonus for arriving on time. Subjects earned E$ during the experiment and at the end of the experiment E$ were exchanged for dollars at the rate of 15E$ = $1. On average, subjects were in the lab for 90 min and earned US$ 15 in addition to the show-up bonus. Prior to the first round of each session the twelve participants were randomly arranged into three groups of four and told that they would be in the same group for the entire experiment. Subjects read computerized instructions and answered

4

It did occur that the winner received two votes with one vote each to the other platforms. Thus ours is a system of plurality voting. It has long been understood that behavior can differ depending on whether a role is earned or randomly assigned (Hoffman and Spitzer, 1985; Hoffman et al., 1994). 5


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embedded questions. Answers to questions were monitored and the experiment did not begin until all subjects demonstrated that they understood the instructions. At the beginning of each of the first five rounds group members received their endowment and made simultaneous investment decisions via the software’s user interface. At the end of the fifth round each subject created and wrote a message, effectively their platform, on four-layer xenographic paper. These platforms were collected, stapled and redistributed to the entire group along with a ballot. Group members read the platforms and voted for one. To avoid ties resulting from all voting for self, subjects were asked not to vote for their own platform. Voting ballots and platforms were collected and the results tabulated. The experimenters then informed each subject about whether s/he wrote the winning message. Only the winner knew the identity of the winner. This procedure was carried out identically in each of the three treatments. There was not a measurable difference when consensus differed as to the choice of the leader. This could in part be due to the fact that lack of consensus happened most often when messages where similar in content. During both the elected and random leader treatments the experimenter collected messages from leaders and distributed them to their corresponding group members at the beginning of each round of the second stage. During the signal-only treatment’s second stage the experimenter distributed messages to each group member in exactly the same way, but the message was based on the outcome of a previously conducted leader treatment. Our specific procedures are detailed in the experiment’s instructions (see Appendix A). 6.1. Hypotheses Our design provides the contrast necessary to distinguish the importance of human leaders and the selection mechanism for leaders in generating leadership effects. We organize our examination of this issue around three closely related hypotheses, each of which is tested in Section 3.2 below. The key hypotheses consistent with the specification that violations of reciprocity and legitimacy are costly are as follows. Hypothesis 1.1. Contribution suggestions made by elected leaders are followed more closely by group members than are identical contribution suggestions that do not originate from a human leader. Hypothesis 1.2. Contribution suggestions made by elected leaders are followed more closely by group members than contribution suggestions made by randomly selected leaders. Hypothesis 2. Followers of human leaders who advocate cooperation will exhibit more cooperation than (i) followers of human leaders who advocate non-cooperative decisions, and (ii) followers without a human leader. Hypothesis 3. Elected leaders will more closely follow their own contribution suggestion than randomly selected leaders. Hypothesis 4. Members of groups with elected leaders who advocate cooperation will earn more than (i) members of groups with elected leaders who advocate non-cooperative decisions, and (ii) members of groups without a human leader. 7. Results 7.1. Data overview 7.1.1. Candidate platforms Tables 1–3 list all of the platforms that were written in the elected leader treatment, signal-only treatment and randomselection treatment, respectively. The winning platform throughout is denoted in bold. Two aspects of the platforms deserve attention. First, the platforms are meaningful and thoughtful: our subjects took this task seriously. Second, note that the winning platforms tend to suggest and defend, often through example, reasonable strategies for achieving efficient outcomes. For instance, one winning platform argues for a trigger strategy, where everybody contributes everything until one person does not, after which everybody is free to make any decision they like. 7.1.2. Contribution decisions Fig. 1 displays the average contribution in each round by treatment. Average contributions between treatments during the first five periods are statistically identical at about 4.6 E$. In round six, the first round after the voting procedure, contributions increase to 8.4 E$, 7.1 E$, and 6.7 E$ of endowment in the elected-leader, signal-only, and randomly selected treatments, respectively. Contributions remain higher on average in the elected-leader than signal-only and randomly selected treatment for the remainder of the experiment, and end at 4.3E$ for the elected-leader, 3.5 E$ for signal-only and 2.5 E$ for the randomly selected treatment. Table 4 reports the results of a simple censored regression of the percent of endowment contributed by each group on an intercept and the round. This reveals statistically significant between treatment differences (the test of the null hypothesis that the intercept and round coefficients are jointly identical between both the elected leader and signal-only treatment and the elected leader and the randomly selected leader treatments is rejected, p < 0.01). We next investigate whether these differences might be traced to differences among messages received by subjects.

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Table 1 Proposed platform from elected leader treatment.a Group

Platforms

1

→ Contribute at least a little bit to the group account; we would all be better off with a mutual donation to the group account. → It would be optimal to each contribute all $10 to group. We’d all get $20 in return for each round. → PUT EVERYTHING INTO THE GROUP SO WE ALL GET MORE MONEY $40 × .5 = 20 every round if we put all in → LETS DEPOSIT 10E$ EACH INTO THE GROUP ACCOUNT

2

→ I+(0.5 × TG) 1st ex: 9 + (0.5 × 4) = 11$ everyone invests 9$ into “I” everyone invests 1$ into “G” 2nd ex: 1 + (.5 × 36) = 19$ 18$ per person The more the entire group contributes to the group, the greater the total earnings. → Dump all your money into group account so we all make big profit! → I think that we are doing fine. → Keep putting high amounts in the Group Account. More beneficial for all of us.

3

→ For the next round we should all invest 10E$ giving us the highest rate of return collectively. We can do this for one trial run, and if after one round there is not 40 E$ then we can go back to individual Investments → Put at least 6 E$ into group account. It would be better all is put in group account. → We should try putting in 4 E$ into the group account. → EVERYONE PUTS IN $10 THEN WE ALL GET $20 BACK

4

→ I know everyone is trying to figure out how to make the most amount of money as possible, so here’s what I’ve figured out: If everyone contributes $10 into the group account then we will make as much money as possible $10 × 4 group members = $40 × 2 = 80/4 members = $20 each × 10 rounds = 200 15$E = $ 1 200/15 = 13.3 at the end of the experiment → Put more money into group account than individual account. → WOW, I’m really hungry for french toast & fresh OJ. → Hi all, Good Contribution guys. But one of us is not contributing well (3,0,0,0,2). Come On Now! Let be team players and contribute generously. Hope to see higher group investment next rounds. By the way, nice easy way to earn money, huh. . . Enjoy AND CONTRIBUTE WELL

5

→We should invest all $10E, we would all receive more earnings that way! → Hey all what’s wrong with half? → Let’s all make a lot of money by putting more into the group account and less into the IA. I will follow through with my messages! → Hey, we are not getting any thing. It is better we spend everything and share the profit. Good Luck → Group, When we play stingey(in a selfish way) we make money But! Not more than the equivilant of one U.S. dollar. Lets trust our group and put in the same amount each time. That’s the only way to have steady earnings coming back. I.e. everyone bets 6 that’s 24 × 2 = 48/4 = $12 plus your 4 in savings = $16 The higher we go as a group the more solid cash we get. → Group I think we all should invest 4 in the group and 6 in our own. That way there’s 16 in the group and you still have money in your account. We might make more money this way. Or we all can stay with 7(I) and 3(G), 8(I) and 2(G). One of these 3 combinations will make us money. → Let’s contribute 6E$ to I and 4E$ to G total I = 6 E$ G = (4 × 4)1/2 = 8 earnings round = 14E$ → If we all put in 10 or close to it, we all walk away with more cash.

a

Bolded messages are winning platforms.

10

Mean Contribution

6

8 6 4 2 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Round Elected

Random

Signal-Only

Fig. 1. Mean contribution by treatment.


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Table 2 Proposed platform from signal-only treatment.a Group

Platforms

1

→ If we all contribute largely to the group account then its better for all of us really in the end but it won’t work unless we ALL do it. → Invest more on the group account. It can bring a lot of earnings → Everyone invest 10E$ to group account & each person will earn 20E$ → All investing in group will create better profits.

2

→ No more $0 Group investments. If all $10s. . . we’re guaranteed $20E. C’mon Guys!! → I’m not really sure what I’m doing. Hopefully, we’ll all get a good amount of money! → If everyone puts all 10 in group, we each get 20. That’s a damn good profit for this exp and is better then other people fending for themselves. And by the looks of how things are going 20 E$ is a whole lot more than what we are all getting right now. → Stop being greedy – 10 × 4 = 40/2 = 20 each round to everyone Help me make money I’m broke PUT ALL 10 in group

3

→ If everyone puts all 10 E$’s in the Group account – Everyone will earn 20 E$’s after each round. (Instead of keeping your own $10E.) 10 × 4 = 40 in Group 40 × .5 = 20 E dollars per person * this is the most you can make → I think we should evenly split each of our endownments 50/50. → The entire group makes more money if we all contribute to the group account. When one person stops, the entire group will stop and we all make less money 0 Individual = > 10 Group → Everyone invest 10E$ into the group account.

4

→ The more we invest into the group account the more we’ll make, so let’s invest as much as we can each round. → I $. and need lots of it! P.S. Bush sucks! → If we all put more in we all get more. → Invest $7 into group account. The will pay the highest dividend to all of us.

5

→ If we give to the group investment $40 we will individually receive $20 i.e. E = I+.5 × TG = 0+.5 × 40 E = $20 each lets try it this is more than the ten dollars we would get to ourselves → This is confusing! → I suggest for round 6 that we all put 1$ individual +9 in group account, so that there is 36$ in the group account, and if all goes well, we will each earn 18$ (+ the one (I) dollar) for 19$ a piece. → Lets invest all money and make 20 dollars each time.

6

→ Invest all your 5 E$ into the group account ex. 0 + 0.5 × 10 = $5 × 4 = $20 your group earning ex. 5 + .5 × 5 = 7.5 group earning → Fellow group members, let do first 5 rounds, everybody put all 10 E$ into the group account And own decision for the last 5 rounds. → Let’s invest 2 E$ to individual account then 8 E$ to the group account to increase earnings, = $18 → Lets all put 10 in the group account please. As long as we put the same amount in then everyone wins. The higher that amount, the better.

a

Bolded messages are winning platforms.

7.1.3. Messages Fig. 2 shows the mean suggested contribution messages for the two treatments with human leaders. The electedleader treatment message had a range of 9.5E$ to 7.2E$. The randomly selected leader treatment had a range of 9.6E$ to 6.5E$. Table 5 reports the results of a simple, censored regression of the suggested contribution message by each group on an intercept and round. The results are statistically identical (the test of null hypothesis that the

Mean Message

12 10 8 6 4 2 0

6

7

8

9

10

11

12

Round Elected

Random

Fig. 2. Mean message.

13

14

15

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Table 3 Proposed platform from randomly selected treatmenta . Group

Messages

1

If we all invest $10, we make $20 per round – the optimal gain. Why is it optimal? Because I’, not going to keep contributing $10 if you don’t reciprocate. If I see another $0, I’m at 0 for the next round. Otherwise, I’m at average for you three. We can get $20 per round, or we can get $10 – the choice is yours. BTW, I’ll assume we’re going to play nice now, and stater with $10. Don’t disappoint, please. Let’s contribute $10.00 to the Group Account so that everybody’s earning is guranteed to be $20.00/each person. If you contribute more to the Individual Account and less to the group account, you probably can earn more than $20.00 in the best situation, (e.g. IA = $5, GA = 5, Total GA = 35, then you earn 5 + 35/2 = $22.5) But it’s not guranteed and other group members may contribute less and less to the Group Account. Later if they feel unfair. I think 7 individual, 3 Group works Best. We have the most to gain from total investment but that can hardly be expected either. 5-5 even split get more, risk less. (Picture: Stick figure flying kite on sunny day)

2

Hey yall It seems were being Rats again but this time its serius so I say lets get the hang of this and make some Money. . .. Oh and help the cause. Right. Put 8 E in the group account. 2 $ into Group Account Plz invest All 10 E into the group account in round 6,7,8, and 5E for round 9,10.

3

Guys, it’s only logical that everyone puts in $10 each time to the group account, this way everyone will get $20 out each time. It is guaranteed that you will make the most money this way. Heres how to make the most money: Everyone invest all ten in the group account that way everyone will get 20e$ back after the round. If you don’t believe me then look at this chart. Individual Acct Group account E$ *0 10 = 40:5 = 20 1 9 = 36:5 = 19 2 8 = 32:5 = 18 3 7 = 28:5 = 17 4 6 = 24 = 16 5 5 = 20 = 15 6 4 = 16 = 14 This way to get 20E$ every round is to invest everything in group act. There is no other way to make more than 20. Let’s contribute 10E$ to the group account.

4

Please listen. If everyone puts all 10E$ into the group fund, we can all share the same profit (20.00 E$) if everyone enters 10.00 E$. Thats 40.00 E$ for the group, x 2 (40.00 E$ X 2) equals 80.00 E$’s, then divide by group member (80.00E$’s/4) = 20.00. We could all make over a dollar per round! Do it! Enter all your Endowment E$’s into Group Account. Iof all the group members enter 10 E$ in group account your earnings will be 20 E$. ((10x4)x0.5 = 20) Let’s put at least E$ 4 in the group account so that everybody get something. Good luck everybody! Lets all invest $10 to the group. Or I will stop investing to the group and soon we will only make $10 E$ per round. Just because you can screw other people over now won’t mean we will return the favor for the next 10 rounds.

5

Let us put 7 E$ each round towards the group account. Investing more in our Individual accounts gives us more earnings and it everyone else goes between 6-8 for the group. We might make more in the end. Each person, one time bids a high amount while others do middle or low. Let’s Invest 8 E$ into the group’s account. Everyone do a 5/5 split everytime!

6

Give all 10 E dollars to group account I am here to make money as are you. If we all put E$ in the group account we all walk out with more real dollars than if we try to do this on our own. Make money, that’s all. If we can be smart about it and make more, why not? Put more into individual account. . . thats what seems to be the pattern so far. Everyone should invest all $10 into the group account. If everyone does this, we will all make more money.

7

We should all throw in all 10 fro the next 10 rounds. We would make $20 per round and maximize w/o getting screwed over. Please contribute all of us money to the group account. because we can earn double (20 each round). Every round, I contribute more than 5 to our group however some guy only contribute 2! Stop contribute only 2! Because you never earn more than $20 each round. In order to get max money. Please contribute all money to group account!! Let’s invest 7$ in round 6 and increase it by 1 until in the next round then start investing ½ for the rest of the rounds. If we all invest a good amount of money into the group, the avg. group investment goes up, and we could make more money. That’s what I’ve noticed so far. Let’s work together!

a

Bolded messages are winning messages.


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Table 4 Group-level censored regression contribution analysis. Independent variables

Dependent variable: Percent of endowment contributed by each group in each round (Coefficient)

Elected Leader (=1 if in elected leader treatment; =0, o.w.) Signal-Only (=1 if in Signal-Only treatment; =0, o.w.) Random Leader (=1 if in random leader treatment; =0, o.w.) Round • Elected Leader Round • Signal-only Round • Random Leader

41.214** (4.294) 32.153** (4.041) −1.821** (0.676) −2.144** (0.649)

41.214** (4.294) 25.896** (3.008) −1.821** (0.676) −1.292 (0.508)

2

R = 0.8413

R2 = 0.7733

Note: numbers in parenthesis are standard errors. ** p < 0.01, two-tailed test.

Table 5 Message regression analysis. Independent variables

Dependent variable: Message (Coefficient)

Elected Leader (=1 if in elected leader treatment; =0, o.w.) Random Leader (=1 if in random leader treatment; =0, o.w.) Round • Elected Leader Round • Random Leader R2 = 0.8946

9.122** (0.496) 9.085** (0.645) −0.095 (0.102) −0.202 (0.118)


intercept and round coefficient are jointly identical between the elected and random leader treatment is accepted at p < 0.444).

7.1.4. Message effects Fig. 3, panels A–F, details the average contribution of each paired elected leader and signal-only group, along with the suggested contribution observed by that group’s members. Three features of this figure are noteworthy. First, the elected-leader and signal-only groups behaved differently when faced with the same suggestion, with the human leader groups evidently following the suggestion more closely. Differences are especially stark in groups 4–6, where the suggested contribution was almost always 10. The elected leader groups generally followed the message, while the message did not have an obvious visual impact on decisions in the signal-only group. To further assess differences between these treatments, Table 6 reports the results of a simple censored regression of the absolute deviation of each group’s contribution from the suggested contribution on an intercept and the round. A random effects model without clustering was used. This reveals statistically significant between treatment differences (again, a test of the hypothesis that the intercept and round coefficients are jointly identical between treatments is rejected, p < 0.01). The second aspect of Fig. 3 worth noting is that groups seem to follow an elected leader more closely when the leader’s advice is consistent and “good.” In our experimental setting, we can suppose that there is no difference between maximizing group income and “good.” In groups 4–6 the leader consistently suggested a high contribution and group members followed this suggestion. On the other hand, in the first three groups the leader’s suggested contribution was lower on average and less consistent and the group members followed less closely. Third, the average of the elected leader groups never exceeds the suggested contribution amount, while this occurs frequently in the signal-only treatment. In fact, we will see below that the result is much stronger: there are only two instances where a participant in the human leader treatment contributed more than the suggestion.

Table 6 Group-level censored regression analysis of absolute deviation of contribution from message for elected and signal-only treatment. Independent variables

Dependent variable: Absolute deviation of group’s average contribution from message (Coefficient)

Elected Leader (=1 if in elected leader treatment; =0, o.w.) Signal-Only (=1 if in signal-only treatment; =0, o.w.) Round • Elected Leader Round • Signal-Only R2 = 0.9727

−3.896 (3.330) 9.681** (2.958) 1.265** (0.516) 1.815** (0.476)


48


Mean Contribution

(A)

(B)

Group 1

10

10

8

8

6

6

4

4

2

2

Group 2

0

0 6

7

8

9

10

11

12

13

14

15

6

7

8

9

10

Round

Mean contribution

(C)

(D)

Group 3

10

10

8

8

6

6

4

4

2

2

12

13

14

15

Group 4

0

0 6

7

8

9

10

11

12

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14

15

6

7

8

9

Round (E)

Mean Contribution

11

Round

(F)

Group 5

10

10

8

8

6

6

4

4

2

2

0

6

7

8

9

10 11 12 13 14 15

Signal Only

11

12

13

14

15

0

6

Group 6

7

8

9

Round Elected

10

Round

10

11

12

13

14

15

Round Message

Elected

Signal Only

Message

Fig. 3. Mean contribution by group and treatment.

7.2. Hypothesis tests We next provide evidence on each of the key hypotheses stated in Section 2.5. Messages are held constant only between the elected leader and the computer treatment. Random leaders will send different messages. Result 1.1. Contribution suggestions made by elected leaders are followed more closely by group members than are identical contribution suggestions that do not originate from a human leader. Evidence for this result can be found in Fig. 4, which shows mean absolute deviation from the advice in the elected leader and signal-only treatments for rounds 6 through 15. (Recall that there were no messages in the first five rounds.) Mean absolute deviations are uniformly higher in the signal-only than in the elected leader treatment, averaging 4.94 E$ and 2.06 E$, respectively. A Mann–Whitney test (with one degree of freedom per subject) easily rejects the null hypothesis that the medians are the same (Z = 3.206, p < 0.01).6

6 For the non-parametric tests the data was at the group level. There were six observations in the computer and the elected leader treatments and seven for the random leader.

Absolute Deviation from Message


49

8 6 4 2 0

6

7

8

9

10

11

12

13

14

15

Round Elected

Random

Signal-Only

Fig. 4. Mean absolute deviation from suggested contribution by treatment.

Result 1.2. Contribution suggestions made by elected leaders are followed more closely by group members than contribution suggestions made by randomly selected leaders. Evidence for this result can be found in Fig. 4, which shows mean absolute deviation from the message by the followers (excluding the leaders) in the elected leader and random leader treatments from rounds 6 to 15. (Recall that there were no messages in the first five rounds.) Mean absolute deviations are uniformly higher in the random leader than in the elected leader treatment, averaging 2.98E$ and 1.62E$, respectively. A Mann–Whitney test (with one degree of freedom per subject) rejects the null hypothesis at the 10% level that the medians are the same (Z = 1.919, p = 0.0550). Though the deviations from the elected leaders’ messages are less than those for the randomly selected leader treatment, this does not mean that the random leaders had no effect on follower contributions. See the results below. Result 1.3. A human leader’s contribution suggestion becomes an upper bound for contributions by other group members. Absent a human leader, in the signal-only treatment that same suggestion does not serve as an upper bound. This provides a partial explanation for Results 1.1 and 1.2. Evidence for this result is provided by Fig. 5, which describes the distribution of differences between actual and suggested contribution amounts. Out of 520 observed decisions (including the leader), there were only five instances in the human leader treatment where a contribution exceeded the suggested contribution. None of the positive deviations came from the leader. In the signal-only treatment, there were 41 occurrences (17.1%) from 11 distinct subjects (45.8%) of a contribution exceeding the suggestion. One can easily reject the null hypothesis that the frequency of subjects who contribute more than the suggested amount is the same in the elected leader and the signal-only treatments (p < 0.01, two-sided Mann–Whitney test). Finally, it is strikingly apparent from Fig. 5 that the frequency with which the message was exactly followed (deviation of zero) is much greater in the human leader treatments than in the signal-only treatment. Result 2. Contribution suggestions made by elected leaders are followed, so high suggested contributions lead to efficient group outcomes and low suggested contributions lead to inefficient group outcomes. Contribution suggestions do not affect contribution decisions if they do not originate with a human leader. Thus, our data supports Hypothesis 2. To provide evidence for this we divide our six groups into two sets of three each. One set includes groups that received “bad” suggestions (groups 1, 2 and 3) and the other set includes “good” suggestions (to groups 4, 5, and 6). There is no ambiguity in this classification. Because the efficient outcome (which we identify with the social good) occurs when everybody

Fig. 5. Distribution of contribution deviations from messages.

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D.M. Levy et al. / Journal of Economic Behavior & Organization 77 (2011) 40–52 No messages

Messages

Mean Contribution

10 8 6 4 2 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Round Elected Leader/Good

Elected Leader/Bad Signal-Only/Bad

Signal-Only/Good

Fig. 6. Mean contribution by treatment and type of suggestion.

contributes everything to the public account, it is reasonable to view a suggestion of “10” as a “good” suggestion and to argue that suggestions are less good as they fall further from 10. Three of the leaders (groups 4, 5 and 6 in Fig. 2) suggested 10 in nearly every round, while leaders in the other groups almost always suggested contributions that were less than 10. Fig. 6 shows the path of mean contributions among the four cases. Note that there are exactly three groups underlying each path. Cooperation is sustained only in the case where a human leader gives good advice. Cooperation in other cases decays, and the paths are visually quite similar. We proceed with formal analyses by conducting a random (individual-level) effects censored regression of individual contribution decisions on the suggestion, a subject’s previous contributions, the previous contributions by other group members and a constant. We do this separately for each treatment, and include dummy variables to indicate whether each person was a member of a group who received “good” or “bad” suggestions. Table 7 reports the results. The control variables are the standard ones for such experiments. Contribution suggestions are not statistically significant predictors of decisions in the absence of a human leader, while suggestions are significant when they originate with a human leader, even when the suggestion advocates a non-cooperative decision. The coefficients on the suggestion are individually significant in the human leader treatment at the p < .001 level, even for groups that are receiving messages that advocate non-cooperation. Thus, our evidence is that contribution decisions vary with the suggestion when there is a human leader, and that this is true regardless of whether the suggestion is to cooperate or not. On the other hand, the suggestion does not have a statistically significant effect in the signal-only treatment. Result 3.

Elected leaders will more closely follow their own contribution suggestion than randomly selected leaders.

Elected leaders are more likely to follow their own suggestions than randomly selected leaders. Evidence for this is given in Fig. 7, which plots mean absolute deviation of leaders’ contributions from their suggestions. The mean absolute difference is less than 1E$ to the final round, when the deviation increases to about 2E$ for the elected leader treatment. In fact, elected leaders followed their own suggestions somewhat more closely than this result suggests. Excluding one group for the elected leader treatment, leaders exactly followed their own advice 96% of the time (48 out of 50 opportunities), with the exceptional

Table 7 Individual-level random effect censored regression analysis of determinants of contributions. Dependent variable: individual i’s contribution at round t: git Elected Leader treatment Lagged own contribution (gi,t-1 ) Lagged mean contribution of other group members (gj,t−1 ) Round t Round t suggestion if a member of a group that receives “bad” suggestions, and zero o.w. Round t suggestion if a member of a group that receives “good” suggestions, and zero o.w. Constant Note: numbers in parenthesis are standard errors. ** p < 0.01, two-tailed test.

**

Signal-Only treatment

0.300 (0.058) −0.030 (0.026)

0.273** (0.089) 0.043 (0.034)

−0.302** (0.058) 0.531** (0.073)

−0.359** (0.080) −0.039 (0.100)

0.782** (0.078) 2.950** (.948) R2 = 0.5859

−0.216 (0.112) 8.551** (1.649) R2 = 0.2440

Absolute Deviation from Message


51

8 6 4 2 0 6

7

8

9

10

11

12

13

14

15

Round Elected

Random

Fig. 7. Mean absolute deviation from suggested contribution by leader. Table 8 Earnings (US$) by treatment and type of suggestion. Treatment

Suggestion

Elected Leader

Good Bad Good Bad

Signal-Only

Earnings Min

Median

Max

18.57 14.4 13.73 12.98

19.53 15.38 14.15 15.23

20.00 16.13 15.88 18.95

cases occurring in round 15. The leader of the excluded group exactly followed her own suggestion only one time over ten rounds, and otherwise contributed a few E$ less than the amount she suggested. The random leader treatment, however, was significantly different. Excluding one group where the leader always followed her advice, the leaders exactly followed their own advice 53% of the time (32 out of 50 opportunities). The leader of the excluded group lowered the suggested amount to an average of 2E$ for rounds 7 to 15. This allowed the leaders to follow their advice. A Mann–Whitney test (with one degree of freedom per subject) rejects the null hypothesis that the medians are the same (Z = 2.245, p < 0.0247) Result 4. Members of groups with elected leaders who advocate cooperation will earn more than (i) members of groups with elected leaders who advocate non-cooperative decisions, and (ii) members of groups without a human leader. To assess the effects of leadership on earnings, we calculated the earnings for each of the (non-leader) subjects in all of the treatments. We then compared earnings among the four groups: elected leader with good suggestions, elected leader with bad suggestions, signal-only with good suggestions and signal-only with bad suggestions. Table 8 details our results. Earnings are higher on average in the elected leader, good suggestion groups than in any of the others. Earnings are nearly identical on average among the low earning groups. Consequently, we pooled all of the earnings in the randomly selected and elected leader/bad suggestion cases, and compared earnings among those nine groups to earnings in the three leader/good suggestion groups. Even with this small sample, we find that the leader/good suggestion groups earn significantly more (p < 0.01, two-tailed Mann–Whitney). 8. Conclusion We designed a novel public goods game to compare whether suggestions made by democratically elected leaders are followed to the same extent as the identical suggestions in the absence of human leaders. In both treatments the suggestions were non-binding for the leader and his/her group members. We find statistically and economically significant differences between treatments. People follow leaders’ suggestions, but when the same suggestion does not originate with a human leader it is not followed. Our results suggest that communication is really cheap, that it is without consequence, when it comes from a machine but not when it comes from another human. As a result, elected leaders who give good advice can obtain high levels of cooperation and achieve nearly efficient outcomes in groups. Our results also suggest that bad leaders can have a significant detrimental impact of group effectiveness. The reason is that group members treat a human leader’s cooperation signal as an upper bound for their own cooperation decision. Our data suggests that being chosen by the group is important for a group’s effectiveness. In particular, group members continue to treat a randomly selected leader’s suggestion as an upper bound on their own decision, but the suggestions tend to be for relatively lower contribution amounts. It follows that groups with randomly selected leaders are relatively less productive than groups with elected leaders. A potential explanation is that elected leaders feel a greater obligation to encourage good policy.

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Our research opens the door to further investigations on why signals from human leaders are followed while those from non-humans are not. One possibility is that non-human signals are eventually irrelevant because they are less-connected to the group’s path of play. While this might be a partial explanation for their ineffectiveness, it does not explain their ineffectiveness in early rounds, nor does it explain why messages from human leaders that are not connected to group decisions (e.g., Fig. 3 panel C) nevertheless serve as upper bounds for group member’s decisions. Future research might profitably address this issue. Several research paths are suggested by our findings. It would be useful in future research to explore connections between our results and the advice effects (e.g., Schotter and Sopher, 2007) as well as the importance of having the leader of a group also be a member of the group (e.g., Chen and Li, 2009). Also interesting is to understand the extent to which elected leaders reflect group members’ preferences and the corresponding implications this has for how we understand leading and following in groups. It also seems important to know how different “types”, especially cooperators and free-riders, respond to leadership (e.g., Cason and Mui, 1998). Finally, it would be good to discover how different types of institutions, and in particular transparency in which the leader’s actions can be observed, can help to create a sense of obligation among leaders to promote decisions consistent with high social welfare. Acknowledgements Jonathan Baron offered helpful insights. We appreciate comments from seminar participants at George Mason University, the University of Pennsylvania, the Jepson School of Leadership Studies and the NPRST, as well as participants at the Summer Institute for the Preservation of Economic History of Thought and the International Leadership Association annual meeting (2005). Xiaorong Zhou provided excellent assistance with programming. Jane Perry helped with the proofreading. The authors gratefully acknowledge that support for this research was provided by the International Foundation for Research in Experimental Economics (Houser), Center for the Study of Public Choice (Levy), the American Council on Education (Peart) and the Searle Freedom Trust (Xiao). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jebo.2010.02.018. References Andreoni, J., 1998. Toward a theory of charitable fundraising. Journal of Political Economy 106, 1186–1213. 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