THE LOGIC OF COLLECTIVE ACTION: SOME EXPERIMENTAL RESULTS'

zyxwv zyx zyxwvutsrq zyxwvu zyxwvuts zyxwvu THE LOGIC OF COLLECTIVE ACTION: SOME EXPERIMENTAL RESULTS’ by John R. Chamberlin Institute of Public Policy Studies, University of Michigan The results of an experiment to test hypotheses derived from Oleon’s theory of collective action at the group level are reported. Strong evidence in favor of the theory is found with respect to the effects of group size on the amount of the collective good provided and on the degree of suboptimality associated with noncooperative provision of the good. For reasons discussed in the paper, the experimental results do not support the exploitation hypothesis. KEYWORDS:collective goods, free rider. experiment, group decision making,group size. cv7 . ances, but it has not previously been tested in laboratory experiments. Ohon proposed a M not model of the voluntary provision of collective goods. Olson’s work, and subANCUR (1965) COUr- sequent elaborations of it, have provided the following three important hypotheses concerning the effects of group size on the provision of collective goods and the pattern of burden sharing associated with their provision. Hypothesis 1. The larger the group, the greater the amount of the collective good provided. (Chamberlin, 1974; McGuire, 1974). Hypothesis 2. “The larger the group, the farther it will fall short of providing an optimal amount of a collective good” (01son, 1965, p. 35). Hypothesis 3. With respect to the sharing of the burden of providing collective goods, “there is a systematic tendency for ‘exploitation’ of the great by the small” (Olson, 1965, p. 29). Sweeney (1973,1974)has tested versions of the first two hypotheses using experimental data, although the nature of the collective good in each experiment was considerably different from that used in the experiment reported below. The exploitation hypothesis has been studied by several authors (Olson & Zeckhauser, 1965; Pryor, 1968, Russett, 1970; Starr,1974) using data on defense expenditures in military alli- zyx THEEXPERIMENT Subjects for the experiment were undergraduate students at the University of Michigan. They were randomly assigned to groups (rn = 3, 6, 9) and were randomly assigned initial budgets (bi = $1.50, $2.50, $3.50), with one third of the members of each group being assigned each amount of money. Subjects were told that if they took no action, they would each win their initial budgets with probability .2, but that they would first be given the opportunity to purchase increases in the probability of winning. Since any contribution toward increasing the probability of winning would be deducted from the amount of money a subject might potentially win, the subjects were faced with a trade-b€f between the probability of winning and the amount of money which might be won. Each subject was supplied with a table indicating the increase in the probability for all levels of contribution by the group. A portion of this table is shown in Table 1. The probability of winning was made a pure collective good by applying the same probability to all members of a group. Thus an increase in the probability brought about by one member of a group was automatically available to all members of the group. At the end of ’ Research support was provided by a Faculty Re- the experiment, a single collective outcome, search Grant from the Horace H. Rackham School of win or lose, was determined using this probGraduate Studies, the University of Michigan. ability. This property of the probability of 441 oM)5-7940/78/2306-0441~1.00 Behavioral Science. Volume 29, IYPX 0 1978 dames C. Miller, M.D., Ph.D.. Editor 442 zyxwvutsrq zyxw zyxwvu zyxwvu JOHNR. (~ A M B E R L I N zyxwvutsrqpon zyxwvutsrqp zyxwvutsrq zyxwvuts TABLE 1 PROBABILITY TABLE. Total Contnbution 0 50 100 150 200 250 Probability of winning ,200 ,400 ,550 ,650 ,700 ,740 AN EMV MODEL Total Contribu- Probability of tion w w 300 350 ,780 ,810 400 ,340 ,860 ,880 450 500 550 ,895 winning clearly provided the incentives for the type.of free rider behavior on which Olson's work focuses. Two trials of the experiment were run for each group. Following these two trials, a random process was used to determine the payoffs to the subjects. In the first trial, communication among group members was not permitted. Each subject knew only his/her budget and how that compared to the average budget, greater than/equal to/less than. Subjects were offered the opportunity to make contributions to increase the probability of winning, and the group was informed of the total contribution but not the individual contributions. Subjects were then permitted to change their contributions if they wished, and this process was continued until no one changed his/her contribution, which was taken as an indication that an equilibrium had been reached. This final set of contributions was used as a measure of the amount of the public good provided through Cournot behavior which correspondsto the Nash equilibrium of the noncooperative game. In the discussion below X: will denote the contribution of the ith individual in the noncooperative trial. The total contribution will be denoted by X". For the second trial, each subject was assigned the same initial budget as before, and the group was instructed to arrive at a set of contributions by whatever means it wished. Except for the stipulation that the amounts d'could not be divulged, complete communication was permitted and a binding agreement on a set of contributions was made. For the cooperative trial, x; and X will be used to denote the individual and total contributions, respectively. The total contribution in the cooperative trial, F,is used to define the degree of suboptimality.. (xc_Xn)used to test the second hypothesis. It is possible to solve for noncooperative and cooperative equilibria for this game on the assumption that individuals act to maximize expected monetary value, EMV. As discussed below, the data suggest that such an assumption may be unwarranted, but the equilibrium contributions will nevertheless be useful in interpreting the results of the experiment. The equilibrium amounts are shown in Table 2. It is important to note that the noncooperative Cournot equilibrium is always characterized by the wealthiest members ( bi = $3.50)bearing the entire burden. RESULTS The relationship between group size and the amount of the collective good provided through Cournot behavior is actually more complex than indicated above in Hypothesis 1, since the model makes predictions about both individual and group behavior as size varies. The model predicts that individual contributions will decrease as group size increases, but that the total group contribution will increase, a relationship of considerable subtlety. In addition, the model predicts that budget size will be positively related to individual contributions. The first hypothesis, therefore, has two parts. Hypothesis la. Individual contributions are negatively related to group size and positively related to budget size. Hypothesis 1 b. Group contributions (X") are positively related to size. The second of Olson's hypotheses concerns the degree of suboptimality inherent in Cournot behavior, defined here as the difference (X-X'). Hypothesis 2. The degree of suboptimality, (X-F), is positively related to group size. Tables 3 and 4, which show the mean zyxwvu Behavioral Science. Volume 23, 1978 (a zyxw TABLE 2 EQUILIBRIUM CONTRIBUTIONS UNDER EXPECTED MONETARY VALUEASSUMPTION. Group S i Epuilibrium X" ContributionsX ' 3 6 9 100 150 150 300 210 400 zyxw zyx zy zyxwvut zyxwv zyxwvut zyx THELOGICOF COLLECTIVE ACTION TABLE 3 MEANINDIVIDUAL CONTRIBUTIONS (IN CENTS) (TOP NUMBER Is BOTTOM NUMBER Is x';). XI?, Group Si Budget $1.50 6 9 34.6 15.6 14.4 n=47 48.5 59.6 75.4 24.4 20.6 39.4 46.9 66.9 36.4 n = 47 n = 47 92.3 69.1 44.2 60.8 82.5 33.1 $2.50 $3..50 TABLE 4 MEANGROUPCONTRIBUTIONS GIOUD (IN CENTS). sz ie 6 9 261.4 313.2 51.8 338.4 n=13 n=8 n=fi 423.3 N.9 individual and group contributions for the various treatment groups, provide a brief summary of the results. Inspection of Table 3 shows that the directions of the relationships between individual contributions and budget and group size correspond to those given by Hypothesis la. Similarly, Table 4 shows that total group contribution and degree of suboptimality increase as group size increases, as predicted by hypotheses l b and 2. Analyses of variance for these three hypotheses, shown in Tables 5,6, and 7, establish the statistical significance of these relationships. The final hypothesis to be tested is the exploitation hypothesis, which may be tested in two forms using these experimental data. Hypothesis 3a. Wealthier members of a group allocate a greater proportion of their TABLE 5 ANALYSISOF VARIANCEOF xi". Source Budget Size Interaction Error SS df 43103. 5257. 2 2 236. 4 132 151244. MS F 21551.5 2628.6 59.0 1145.8 18.81 2.29 .05 TABLE 6 ANALYSISOF VARIANCE OF X". Source SS P .ow0 - 7.72 ,0026 2 71818.0 24 9306.0 Behavioral Science, Volume 23,1978 F P 7548.7 3.58 0431 SOH). 2106.7 budgets to the provision of collective goods than less wealthy members ($/bi is positively related to bi). Hypothesis 3b. Wealthier members of a group bear a greater proportion of the burden of providing collective goods through noncooperative behavior than they would bear if the goods were cooperatively provided through some cost sharing arrangement (xP/xf is positively related to bi). The first form of the hypothesis is the one suggested by Olson and has been tested using data on defense expenditures in military alliances (Olson & Zeckhauser, 1965; F'ryor, 1968,Russett, 1970; Starr, 1974).The second form of the exploitation hypothesis suggests an alternative baseline for evaluating burden sharing arising from Cournot behavior, the pattern of burden sharing arising from cooperative behavior. Difficulties arise with this second statement of the hypothesis, however. There exists an infinite number of cooperative Pareto optimal solutions to the problem of providing collective goods and the hypothesis as stated would be true in only a fraction of these. In particular, if members of a group should choose to carry out some degree of redistribution of wealth in the process of cooperatively providing the collective good, the hypothesis is not likely to be descriptive of group behavior. Tables 8 and 9 summarize the relationships stated in the two forms of the exploitation hypothesis. An analysis of variance corresponding to Table 8 shows no significant effect ( p = .50) of budget size on the percentage of budget contributed. An analTABLE 8 MEANPERCENTAGE OF BUDGET CONTRIBUTED IN NONCOOPERATION TRIAL. Group Size P 143640. MS 2 24 Budget F 223340. df ,1049 MS Error SS 15097. zyxwvuts zyxw df S k Source zyxwvut 3 158.5 185.0 26.5 x X X -x" TABLE 7 ANALYSIS OF VARIANCE OF (X - X"). Size Error 3 443 $1.50 $2.50 $3.50 3 6 9 23.1 16.3 15.8 19.1 10.4 14.6 17.4 19.4 21.5 444 zyxwvutsrq zyx zyxwvutsr zyxwvutsr JOHNR. CHAMBERLIN ___~ zyxwvutsrqponmlkj zyxwvutsrq zyxwvut TABLE 9 MEAN RATIOOF xI)I TO x;. Group Size Hdget I $1.50 $LW 1.39 .79 1- 5.50 .H1 6 9 zyxw zyxw .87 .78 .73 1.25 .84 .73 ysis of variance corresponding to Table 9 shows a significant ( p = .04)negative relationship between budget and the ratio of X: to xF.Thus both of these forms of Olson’s exploitation hypotheses receive no support whatsoever from the data. A likely explanation for the failure of the data to c o n f i i the first version of the hypothesis is that subjects felt an obligation to be unselfish, to sacrifice personal gain for the benefit of the group by contributing, so long as others reciprocated. An indication that this may have been the case can be seen from a comparison of the pattern of burden sharing, indicated by the values of d i n in Table 3, with the pattern of burden sharing under the EMV assumption. Even though the pattern under this assumption may be extreme, it can be expected to be generally representative of patterns of burden sharing in the absence of altruistic behavior. The contrast between the two patterns of burden sharing suggests that less wealthy members may have contributed beyond what was in their own interest because they felt their unselfishness was being reciprocated. Changes in contributions prior to an equilibrium being reached in the noncooperative trial were frequently consistent with such a model of reciprocal altruism. Small declines in the total contribution often led to further declines, as members responded tit-for-tat to the decreases in others’ contributions. Such behavior is inconsistent with a model of self-interested behavior. Relative t o the pattern of burden sharing expected under self-interested behavior, altruistic behavior in this case worked to the benefit of the wealthiest members of the group. In the case of the second version of the exploitation hypothesis, altruistic behavior in the noncooperative trial appears to have been accompanied by redistributive behavior in the cooperative trial. This resulted in Behavioral Scienw. Volume 23, 1978 the relationship having the opposite sign from that predicted by the hypothesis. In 18 of the 27 groups the discussions during the cooperative trial resulted in the application of a progressive tax to determine the shares of the burden. In only 11groups, five of which had three members, was the amount contributed by the least wealthy members greater than the amount these individuals had contributed in the noncooperative trial. Table 10 shows the ratio of mean contribution to mean expected gain. These ratios suggest that ability to pay rather than benefits received was a more important determinant of the pattern of burden sharing. In this experiment, it appears that a subject’s willingness to pay, as evidenced by his/her consent to the cost sharing arrangement, was not greatly different from the subject’s ability to pay. The exploitation hypothesis thus seems to have fallen victim in this case to norms concerning appropriate behavior in a group decision making situation. These norms perhaps are particularly strong in groups of college students participating in experiments involving small amounts of money. EVALUATING THE EMV MODEL A comparison of Tables 2 and 4 shows that in all cases the average contributions exceed those derived under the EMV assumption. The differences are significant at the .05 level for groups of three and nine in the noncooperative case. For groups of six in the noncooperative case and for groups of three in the cooperative case, the differences are significant at the .10 level. These results suggest that the subjects’ behavior was inconsistent with the EMV assumption. In addition, the strong partial correlation (-88)between x” and F,controlling for group size, attests to the fact that there are factors operating within groups that lead to zyx TABLE 10 RATIOOF MEANCONTRIBUTION (x:) TO MEAN EXPECTED GAIN IN COOPERATIVE TRIAL. Group Size Budget $1.50 $2.50 $3.50 3 6 9 ,453 ,451 ,196 ,124 ,245 ,533 ,285 ,436 ,367 zyxw zyxwvut zyxwvut zyxwvu zyxwv zyxwvu zyx zyxwv zyxwv THELOGICOF COLLECTIVE ACTION differences in group behavior that are inconsistent with the EMV model. For these reasons it was deemed judicious to avoid using the equilibrium amounts of the EMV model to test the suboptimality hypothesis, and the quantity ( X c- x")was used instead of the difference between x" and the contribution which maximizes expected group gain. Inspection of Tables 2 and 4 will show that under the latter measure of suboptimality, the degree of suboptimality increases with group size, although the differences are not significant ( p = .45). The discussion of altruistic behavior in the previous section raises the possibility of another interpretation of the consistency of the experimental results with the EMV model. With the exception of groups of three, the contributions in the cooperative trial were on average quite close to those predicted by the EMV model. In addition, if behavior in the noncooperative trial was to a certain extent altruistic, then the equilibrium contributions (d) of the less wealthy members might be consistent with the EMV model. In the absence of a specific model of altruistic behavior, it is impossible to determine whether the subjects' behavior was consistent with an EMV assumption as a part of such a model, but it is certainly possible. If this is the case, the contributions (d) of the wealthiest members are below those associated with the EMV model, suggesting that these members took advantage of the anonymity aftforded them by the experimental design to shift some of the burden of providing the collective good onto the other members of the group. SUMMARY The experimental results offer strong confirmation of the fist two of the three hypotheses derived from Olson's model. In the case of the exploitation hypothesis, for which the data offer no support, it appears Behavioral Science, Volume 23,1978 445 most likely that behavior in the noncooperative trial was characterized by a measure of altruism and that behavior in the cooperative trial was accompanied by some redistribution of wealth. The effects of redistribution were sufficient to mask the exploitation relationship predicted by Olson's model. The data were also used to test predictions based on the assumption that individuals act self-interestedly to maximize expected monetary value. While the experimental results cast doubt on the validity of this model, the likelihood that behavior in the noncooperative trials was somewhat altruistic raises the possibility that behavior might have been consistent with the EMV assumption if it were a part of a more complicated model of individual decision making. REFERENCES Chamberlin, J. Provision of collective goods as a function of group size. Amer. pol. sci. Rev., 1974,68, 707-716. McGuire, M. Group size, group homogeneity and the aggregate provision of a pure public good under Cournot behavior. Pub. Choice, 1974, 18, 107-126. Olson, M., Jr. The logic of collective action: Public goods and the theory of groups. Cambridge: Hmard Univ. Press, 1965. Olson, M., Jr., & Zeckhauser, R. An economic theory of alliances. Rev. econ. Stut., 1965, 48, 266-279. Pryor, F. Public expenditures in communist and capitalist nations. Homewood, Ill.: Irwin, 1968. Russett, B. What price vigilance? The burdens of national defense. New Haven: Yale Univ. Press, 1970. Starr, H. A collective goods analysis of the Warsaw pact after Czechoslovakia. Znt. Organ., 1974.28, 521-532. Sweeney, J. An experimental investigation of the freerider problem. Soc. sci. Res.. 1973, 2, 277-292. Sweeney, J. Altruism, the free rider problem and group size. Theor. Dec., 1974,4,259-276. (Manuscript received December 20,1976 revised June 6, 1978)