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IZA DP No. 1375
Dividing Justly in Bargaining Problems
with Claims: Normative Judgments
and Actual Negotiations
zur Zukunft der Arbeit
Institute for the Study
Dividing Justly in Bargaining Problems
with Claims: Normative Judgments
and Actual Negotiations
University of St. Gallen,
CESifo and IZA Bonn
CREED, University of Amsterdam Tinbergen Institute and IZA Bonn Discussion Paper No. 1375 October 2004 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 Email: email@example.com
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IZA Discussion Paper No. 1375 October 2004
Dividing Justly in Bargaining Problems with Claims:
Normative Judgments and Actual Negotiations∗ Theoretical research on claims problems has concentrated on normative properties and axiomatizations of solution concepts. We complement these analyses by empirical evidence on the predictability of three classical solution concepts in a bankruptcy problem. We examine both people's impartial normative evaluations as well as their actual negotiation behavior in a bargaining with claims environment. We measure people's judgments on the normative attractiveness of solution concepts with the help of a survey and also observe actual agreements in a bargaining experiment with real money at stake. We find that the proportional solution is the normatively most attractive rule, whereas actual negotiation agreements are closest to the 'constrained equal award' solution.
JEL Classification: D63, C78, C92 Keywords: bankruptcy problems with claims, proportional rule, equal-awards rule, equallosses rule, fairness, laboratory experiment, vignette
Simon Gächter FEW-HSG University of St. Gallen Varnbüelstrasse 14 9000 St. Gallen Switzerland Email: firstname.lastname@example.org ∗ This paper is part of the EU-TMR research network ENDEAR (FMRX-CT98-0238) and the research project on “Strategic Bargaining and Coalition Formation" financed by the Österreichische Nationalbank (project number 6933). We are very indebted to Franz Brandel who wrote the experimental software. Caroline Eckhart, Monika Egelwolf, Helmut Elsinger, Markus Knell, Armin Schwienbacher and Jana Vyrastekova provided excellent research assistance. We thank participants of a seminar in Bielefeld for their helpful comments.
1 IntroductionIn this paper we empirically investigate bargaining problems with claims. These are an important class of more general rationing problems where agents have acquired claims on resources that cannot all be satisﬁed. As pointed out by Moulin (2000) rationing problems are among the oldest distribution problems tackled with formal models of distributive justice and encompass a variety of speciﬁc contexts. For instance, problems of taxation (e.g. Young (1988)) and the problem how to share the cost of a public good (e.g. Moulin (1987)) can be interpreted in this way. A prominent interpretation - and one that inspired our paper - is as a (bargaining with) claims problem or bankruptcy problem (e.g. O’Neill (1982), Aumann and Maschler (1985)).1 The prominence and practical relevance of the problem led to a stream of theoretical contributions about the right way to solve the problem. For a recent survey of this literature we refer the reader to Thomson (2003). The game theoretic approach formulates the claims problem as a game and relates the solutions to prominent solution concepts of games without claims (see, for instance, O’Neill (1982), Aumann and Maschler (1985), Curiel et al. (1987), Chun and Thomson (1992), Dagan and Volij (1993)). The axiomatic approach tries to identify rules satisfying a set of intuitively reasonable axioms that can be applied to such claims problems (see among others, Dagan (1996), Moulin (2000), Chun et al. (2001), Herrero and Villar (2001)). 2 The axiomatic approach has derived three prominent rules to solve bankruptcy problems that we will investigate empirically in this paper. These rules, which we describe in detail in the next section are (i) the proportional rule, according to which resources are allocated among claimants in the proportion of their claims; (ii) the constrained equal-losses rule, which distributes the loss equally among claimants; and (iii) the constrained equal-awards rule, which allocates the resource equally among the claimants provided no-one receives more than his or her claims.
Without doubt, the theoretical literature has improved our understanding of the axiomatic and game theoretic underpinnings of various normative rules. Yet, in pracChun and Thomson (1992) distinguish a claims problem from a bankruptcy problem as the former is the non-transferable utility variant of the latter. For convenience we do not distinguish between the two in this paper.
Most of the literature applies cooperative game theory. For an important exception using a noncooperative approach, see Dagan et al. (1997).
tice, many people who have to deal with claims problems will use arguments on the perceived attractiveness of the rules. Hence, a normative solution should not only be theoretically appealing but also prove to be tenable and sustainable in the sense that all parties involved in the claims problem can accept it. This is even more so if several diﬀerent theoretical concepts correspond to diﬀerent attractive solutions of games or satisfy diﬀerent attractive sets of axioms. Therefore, as a complementary approach it is useful to have positive evidence on solutions to claims problems.
In this paper we assess the three rules to claims problems empirically. There are two dimensions to this empirical assessment. The ﬁrst dimension is the moral or normative intuition people have on what they think a fair solution is. If we devise rules they should hold for a broad class of problems and have to be normatively acceptable for many people who are potentially subjected to the rule. The second dimension is actual behavior that may or may not be inﬂuenced by justice arguments. If we want to understand how people will behave if they negotiate on their behalf in a bankruptcy problem we need to know how the claims inﬂuence the bargaining outcome. This paper provides empirical evidence on both dimensions.
Diﬀerent tools are needed for appropriately covering both dimensions. Assessing normative views requires impartiality. In contrast, when people actually negotiate over the division of a surplus that they will enjoy after an agreement has been reached, people are certainly not impartial. To assess impartial normative views we employ a vignette technique. Vignettes describe the bargaining with claims problem and then the respondents are asked to make a judgment about a fair division of the available pie. Our second tool is laboratory experiments where subjects actually negotiate in a bargaining with claims environment.
Vignettes have the advantage that they measure the unbiased responses of impartial participants. Exactly because the question is hypothetical, responses cannot be confounded by self-interest, but reﬂect the normative judgments of the respondents.
This is why vignettes are very popular in empirical research on ethical rules of theories of justice (e.g., Yaari and Bar-Hillel (1984), Kahneman et al. (1986), Schokkaert and Overlaet (1989), Schokkaert and Capeau (1991), Gaertner et al. (2001), Gaertner and Jungeilges (2002); see Konow (2002) for an extensive survey).
Our second instrument measures people’s actual behavioral responses in a laboratory bargaining experiment, where ﬁnancially motivated subjects have to negotiate in a free-form bargaining with claims environment and where the agreements determine the bargainers’ compensation. Thus we can examine which normative solution concept corresponds best to the agreements in real, not hypothetical, negotiations. Previous experiments in the area of fairness and justice research that is related to our experiments comprise Frohlich et al. (1987), Frohlich and Oppenheimer (1990), Gaertner and Klemisch-Ahlert (1992); Klemisch-Ahlert (1996) and Beckman et al. (2002). In the experiment we may observe a conﬂuence of motivations, like envy, egoism and toughness.
The comparison of surveys and experiments will allow us to assess the diﬀerence of moral judgments and actual behavior.
Our research design also varies the claims. We look at two diﬀerent claims points because theoretically the normative attractiveness of bankruptcy rules is independent of the speciﬁc claims. Empirically, however, diﬀerent distributions of claims may make particular solutions more or less attractive. One claims point is very asymmetric in that one claimant has a much higher claim than the other one. The second claims point is more balanced. This oﬀers us the possibility to observe if and how the asymmetry of the claims point inﬂuences the normative judgments and actual behavior.
In our research design the normative solutions make diﬀerent point predictions about how the resource should be allocated. Our empirical strategy is to observe the normative judgments in the vignette study and the negotiated agreements in the experiment and then to investigate which of the normative rules comes closest to the observed outcome. In the vignettes we ﬁnd that for both claims levels the subjects’ answers come closest to the proportional rule. By contrast, in the experiments, the agreements are for both claims points closest to the solution proposed by the ‘constraint equal-awards’ rule.
One may argue that with our questionnaires and the experiments we can only indirectly assess the attractiveness of the diﬀerent bankruptcy rules, because we ‘only’ judge the vicinity of a judgment or agreement to a proposed solution. To gain direct evidence on the attractiveness of the normative rules, we investigate in the last part of our study the bargaining problem with claims from a diﬀerent viewpoint. In a further survey study we confronted respondents with the description of the rules and asked them to rank the proposed rules according to their perceived attractiveness. Thus, in this ‘beauty contest’ of rules subjects can explicitly compare the rules. Again, we ﬁnd that the proportional rule receives the strongest support.