مخالفت با نابرابری و بهره وری همراه با اولویت های اجتماعی ترتیبی و اصلی؛ یک مطالعه تجربی

In this paper, we report on a series of free-form bargaining experiments in which two players have to distribute four indivisible goods among themselves. In one treatment, players are informed about the monetary payoffs associated with each bundle of goods; in a second treatment only the ordinal ranking of the bundles is given. We find that in both cases, inequality aversion plays a prominent role. In the ordinal treatment, individuals apparently use the ranks in the respective preference orderings over bundles of goods as a substitute for the unknown monetary value. Allocations that distribute the value (money or ranks, respectively) most equally serve as natural “reference points” for the bargaining processes. Frequently, such “equal split” allocations are chosen by our subjects even though they are Pareto dominated. Whether a Pareto optimal allocation is chosen or not depends on whether or not it is a Pareto improvement relative to the “equal split” reference allocation. We find less Pareto-damaging behavior due to inequality aversion in the ordinal than in the cardinal treatment.

Recent research in explaining observed behavior of individuals in laboratory experiments has focused on the question of how to model the agents’ distributional preferences, see, e.g., Fehr and Schmidt (1999), Bolton and Ockenfels (2000), and Charness and Rabin (2002) (henceforth F&S, B&O and C&R, respectively). The common assumption in these models is that agents are motivated not only by their own material payoff but by the entire distribution of monetary rewards. Specifically, F&S and B&O suggest parametric forms of the utility function incorporating different notions of inequality aversion according to which utility decreases with the differences in individual payoffs. By contrast, C&R propose a model of social-welfare preferences according to which agents are concerned with maximizing a combination of the aggregate payoff for the group and the payoff of the worst-off individual. The two approaches have been compared and tested against each other by Engelmann and Strobel (2004).1 By assigning significance to differences and sums of monetary rewards, the proposed models of social preferences use individual utility information in a cardinal and interpersonally comparable way. While this can be justified, e.g., by assuming quasi-linearity of the underlying preferences, it also shows that the applicability of the existing models is restricted to situations in which individual monetary rewards are known to all agents and in which preferences over allocations can be adequately described in terms of the distribution of monetary rewards. The purpose of the present paper is to demonstrate that the basic intuitions behind the distributional preference approach can be fruitfully applied in more general situations. To this end, we conducted a series of free-form bargaining experiments in which two players had to jointly determine an allocation of four indivisible goods. In one treatment both agents were informed about the specific monetary value associated with the bundles of goods for each player (the same bundle usually had different monetary value for the two players). In the other treatment, each player was only informed about her own and the opponent's ordinal ranking of the bundles, i.e. only the ordinal ranking of the monetary payments associated with each bundle was given. Despite the lack of numerical payoff information in the latter treatment, we find that individuals rely on interpersonal comparisons also in this case. Indeed, we find strong evidence that agents use the rank of a bundle in the respective preference ordering as a substitute for its unknown monetary value. Taking these ranks as the basis for interpersonal comparisons, the motives behind the formation of distributional preferences, such as inequality aversion or social concerns in general, are relevant also in the treatment with ordinal information. In fact, the comparison between the two treatments reveals that individual behavior can be accounted for by a simple unifying qualitative theory of distributional preferences. Specifically, the outcomes that we observed in our bargaining experiments suggest that a significant proportion of agents’ behavior is guided by the following rule: Conditional Pareto Improvement from Equal Split (CPIES): First, determine the most equal distribution of rewards. If this allocation is Pareto optimal, then choose it. Otherwise, if there is the possibility to make everyone better off, implement such a Pareto improvement provided that this does not create “too much” inequality. If the monetary rewards are known, the “most equal” distributions are of course the ones with minimal difference of the numerical payoffs for the two agents.2 If, on the other hand, only the ordinal rankings of the bundles of goods are given, then the “most equal” distributions are those with minimal difference of the ranks in the respective preference orderings. Similarly, “too much inequality” is to be understood in terms of differences in monetary payoffs and ranks, respectively. Of course, how much precisely “too much” is depends on individual preferences and varies from subject to subject. The above rule combines elements of the inequality aversion approach of F&S and B&O on the one hand, and the social-welfare preference approach of C&R on the other. With the former it shares the important role played by interpersonal equality, with the latter the demand for Pareto optimality (in the payoff space).3 Interpersonal inequality plays a twofold role here. First, the absence of inequality determines an initial reference point for the bargaining problem. Secondly, it serves as a constraint in the process of achieving a Pareto optimal outcome. In contrast to C&R's results, we systematically find Pareto-damaging behavior in the treatment with known monetary rewards.4 Interestingly, however, such behavior is only very rarely observed in the ordinal treatment. Our conjecture is that this is due to the uncertainty about the differences in final payments associated with differences in ordinal ranks. Indeed, it seems that rank inequality becomes acceptable because it does not necessarily correspond to unequal monetary payoffs. One conclusion from our study is thus that, by making inequality precisely quantifiable, monetary payoff information hinders the realization of Pareto improvements. The CPIES rule allows two different interpretations. The first is purely outcome-oriented: whether or not an allocation is compatible with the CPIES rule can be decided simply by looking at the resulting inequality and by determining whether or not it is a Pareto improvement relative to the most equal allocation. The second interpretation of the CPIES rule is as a proper procedure according to which bargaining partners first determine a “disagreement point” which then serves as the reference distribution for the later bargaining process. In Section 4 below, we look at both interpretations. In terms of statistical analysis, the relevance of the CPIES rule is more easily tested in its outcome-oriented version. On the other hand, an analysis of the communication protocols of the experiments shows that the CPIES rule indeed frequently materializes in the procedural sense: the equal reference distribution is explicitly proposed, or mentioned in the discussion although not necessarily suggested, and then the bargaining partners either settle on a Pareto improvement from there or choose the equal distribution. Our experimental design differs from the literature in several respects. First, while most of the existing studies on distributional preferences have focused on variants of either dictator or ultimatum games, we consider free-form bargaining here. In terms of experimental set-up, we thus follow the literature initiated by Roth and Malouf (1979) who tested the predictive power of the Nash bargaining solution using an unstructured bargaining process (see also the subsequent literature, in particular Roth and Murnighan, 1982, and the review in Kagel and Roth, 1995). The main reason for the departure of our experimental design from the existing literature on social preferences was the conjectured presence of a procedural aspect influencing the outcome. For instance, the role of the equal distribution as a reference point is more easily uncovered in an unstructured bargaining process than in a rigid strategic game. Qualitatively, our results confirm findings of the early study by Kalisch et al. (1953). Using an informal bargaining process, these authors tested solution concepts of cooperative game theory and, in particular, examined how members of a coalition would share the joint surplus. One of their findings was that in the process of coalition formation, the “core” or founding members (mostly two individuals) often split the initial surplus equally. While our context is clearly different, the role of the equal distribution as reference point for the bargaining process emerges here in a pronounced way as well.5 Data generated by free-form bargaining processes are arguably more difficult to interpret than data from more structured bargaining problems such as dictator and ultimatum games, or alternate offer games. But our experimental design also has evident advantages in terms of exploration of the motives underlying bargaining behavior.6 In particular, data from free-form bargaining are much better suited to contribute to our understanding of the procedural and cognitive aspects involved. The growing but still small literature on procedural justice suggests that the way in which final resource allocations are brought about has a significant impact on their acceptability. The role that procedures play in resource allocation problems has been investigated from different perspectives. For instance, Bolton et al. (2005) find that unequal distributions are more easily accepted if they are the outcome of an ex ante fair procedure, say of a fair lottery. Shor (2007), on the other hand, examines the effects of the distribution of decision power among individuals. Our study complements this literature by examining how the bargaining proposals evolve over time and by directly looking at our subjects’ arguments and reasoning during the bargaining process in order to identify regularities and recurring patterns.7 We view the present paper as a first explorative step and hope that it will stimulate further research in this direction. Another distinctive feature of our experimental design is the framing of the decision problem as one of distributing indivisible goods. Hence, the feasible payoff distributions are explicitly derived from an underlying economic allocation.8 In contrast to Kalisch et al. (1953), Roth and Malouf (1979), or Shor (2007) the set of feasible utility distributions is thus restricted.9 More importantly, our design allows us to induce purely ordinal preference information and to compare the corresponding results with those obtained under full (cardinal) payoff information. The remainder of the paper is organized as follows. Section 2 describes the experimental design and Section 3 the division problems that we tested. Section 4 presents the results, treating the outcome-oriented and process-oriented interpretation of the CPIES rule in two separate subsections. Section 5 concludes.

Our experimental results suggest a particular qualitative description of how agents reach agreements in bargaining problems with indivisibilities, the CPIES procedure. The key element is the role of “equal split” as the reference point for the bargaining procedure. Pareto improvements are implemented provided that they do not create too much inequality. Indeed, our most striking finding is that a majority of 51 percent of bargaining partners reject the payoff distribution (46,75) in favor of the Pareto inferior equal split distribution (45,45) (aggregated data from EXP I, R3 and EXP II, R3). This is in contrast to the results of C&R, who “find a strong degree of respect for social efficiency” (p. 849). It also conflicts with Kritikos and Bolle's (2001) experiments in which the majority of participants were efficiency- rather than equity-oriented. However, the experiments in these studies consisted of simple dictator games and not of dynamic bargaining games as in our present study. Inspecting the communication protocols we find strong evidence that procedural aspects play a decisive role in our experiments. For instance, in R3 of EXP I five of the seven pairs who settled on the Pareto optimal distribution (46,75) considered the equal payoff distribution (45,45) at an earlier stage, confirming the explicit reference status of the latter. In this example, it also seems to matter who is the first to propose the Pareto improvement. A detailed analysis of this issue of path dependence is beyond the scope of the present paper, but generally partners seem to agree more easily on the payoff distribution (46,75) if the first individual suggests it to the second individual than vice versa. It seems to matter whether the individual suggesting the Pareto improvement benefits more or less than the other person – an issue we plan to investigate further. The failure of Pareto optimality due to equity concerns is much less pronounced in the ordinal treatment, even though we do find evidence that the ranks of bundles in the preference orderings serve as substitutes for the unknown monetary payoff. In some cases of the ordinal treatment there is no longer one clear equal split reference distribution because the inequality associated with any rank difference is unknown. Despite this difficulty, most participants try to establish an “equal split” reference allocation during the bargaining process confirming the key role this reference allocation plays.