«IZA DP No. 1375 Dividing Justly in Bargaining Problems with Claims: Normative Judgments and Actual Negotiations Simon Gächter Arno Riedl October ...»
Recall that CEL implements the most unequal division of the surplus of all four rules, whereas CEA is the most equal ‘musketeer’ (apart from EQUA, of course). When claims are very asymmetric, as in 1980V, people ﬁnd the more equalizing CEA more attractive than the unequal CEL, whereas if claims are more equal, as in 1640V, people appreciate CEL more than CEA. In the experiment CEA is ranked ﬁrst, whereas CEL is ranked last in both claims conditions. However, in the experiments we ﬁnd that PROP and EQUA change ranks across claims (though the change in ranks is not statistically signiﬁcant). When claims are very asymmetric (in 1980E), EQUA is more attractive than PROP, whereas when claims are moderately asymmetric (in 1640E), PROP is better ranked than EQUA. Thus, in both the normative judgments and the actual negotiations, when claims are very asymmetric, people prefer, ceteris paribus, the more egalitarian solutions, whereas they appreciate the more unequal rules when claims are moderately asymmetric.
5 A ‘beauty contest’ of musketeers
So far, our empirical strategy was to investigate which solution comes closest to the normative judgments, or negotiated agreements, by subjects who did not know explicitly about the solutions to claims problems. Thus, subjects could not for themselves evaluate the normative appeal of the various rules. To gain further insights into the perceived attractiveness of the four ‘musketeers’ and to complement our preceding evaluation of rules by direct evidence, we conducted a new survey study with another 59 subjects. These subjects had the same background as the other participants in our study. They had taken part neither in the experiments, nor the vignette studies.
We had the same treatments (i.e., claims points) as above, which we label 1980BC and 1640BC (‘BC’ stands for the ‘beauty contest’ described below). We gave the respondents the same description of the bargaining problem as in our previous vignette study. However, instead of asking them about their opinion how an arbitrator would solve the bankruptcy problem, we described the four rules to them and asked them to rank the rules according to their perceived attractiveness (‘the beauty contest’). After the subjects read the same scenario as documented above, they were told the following (translated from German):8 Before the determination of the objective performance diﬀerence is ﬁnished (i.e., you cannot yet know whether you have the objectively higher or lower performance), you receive several proposals according to which ﬁxed rule the new division of the budget shall be regulated in the future. It is foreseeable that the budget
will change often:
EL: ‘Equal Loss’. The reduction of the budget will be equally shared between the bargaining partners and deducted from their hitherto valid claims. In the above situation this rule would mean the following: The reduction of the budget amounts to 440 money units. This reduction will be borne equally by both, i.e, deducted from the hitherto valid claims. For the bargaining partner with the higher claim this rule would mean that his share now is 1640 − 220 = 1420. The bargaining partner with the lower claim would, according to this rule, earn 850 − 220 = 630 money units.
Here we document the description of rules for 1640BC. In the 1980BC questionnaire, parameters were adapted accordingly.
P: ‘Proportional Division’. The new division is proportional to the hitherto valid division. In the above situation this rule would mean the following: According to the hitherto valid claims the budget would be divided in the proportion of the claims in the old budget (i.e., in the proportions 1640/2490 and 850/2490 resp.). With the new budget this rule would lead to an amount of 1350  money units for the higher claim and to 700  money units for the lower claim [2050 ∗ (1640/2490) = 1350; 2050 ∗ (850/2490) = 700].
E: ‘Equal Split’. The new budget will be split in equal parts. In the above situation this rule would mean the following: Both bargaining partners receive the same amount: 2050/2 = 1025.
N: ‘No Loss for the Lower Claim’. The lower claim will not be cut. In the above situation this rule would mean the following: The bargaining partner with the lower claim would also with the new budget earn 850 money units, i.e., his claim would not be cut. The claim of the bargaining partner with the higher claim would therefore be cut by 440 money units, i.e., by the total reduction of the budget and would therefore amount to 1640 − 440 = 1200 money units.
The rules described for the subjects as ‘EL’, ‘P’, ‘E’, and ‘N’, correspond to CEL, PROP, EQUA, and CEA, respectively. The subjects then received a decision sheet on which they had to rank the four rules from 1st to 4th (i.e., from most preferred to least preferred). Thus, our subjects in this vignette study were in the same impartial situation as our subjects from the previous vignette study. However, they now could compare and judge the rules, which lead to a particular solution of the bankruptcy
problem. This ‘beauty contest’ of rules yielded the following result:
Result 5 When asked to rank the ’musketeers’, subjects overwhelmingly rank PROP ﬁrst (and EQUA last) independent of the claims. When claims are very unequal subjects rank more egalitarian solutions slightly better than when claims are moderately unequal.
In the beauty contest the ranking of rules is stable across claims levels. None of the pairwise comparisons for a given rule returns a signiﬁcant diﬀerence, although for CEL and CEA the p-values are close to being marginally signiﬁcant. That is, the tendency is the same as in the vignettes and the experiments: in 1640BC, CEL is considerably more attractive than CEA (mean ranks are 2.3 and 3.0, respectively); whereas in 1980BC, CEL is only slightly better ranked than CEA.
6 Concluding discussion
In this paper we have taken an empirical approach to study bargaining problems with claims. We see our paper as complementary to the axiomatic characterization and game-theoretic analyses that are prevalent in most of the literature. The results from this literature are important because they make the normative and strategic underpinnings of solution concepts transparent. However, for practical ends also sound empirical knowledge about the predictive power and practical sustainability of various derived rules is necessary.
We have argued that an empirical investigation of solution concepts involves two dimensions: the normative views people hold, and the actual negotiation behavior when real money is at stake. To study the normative views we have developed two separate survey studies that use a vignette technique. For studying negotiation behavior we have designed a bargaining with claims experiment. To investigate the robustness of the solution concepts we also varied the claims points. To our knowledge no other study has combined these diﬀerent research methods and variations in claims points in the empirical investigation of bargaining problems with claims.
We ﬁnd that the proportional rule (PROP) does very well in people’s normative judgments. In particular, PROP is the clear ‘winner’ in a ‘beauty contest’ of diﬀerent rules. This holds irrespective of the asymmetry of claims. This popularity of PROP is also consistent with ‘equity theory’ (e.g., Selten, 1978) or the ‘accountability principle (Konow, 2000), which is related to equity theory. Equity theory argues with the relative value of ‘inputs’ (performance in our case) and ‘outputs’ (claims). Since the reduced pie does not aﬀect this relative value, equity theory in this case predicts the proportional solution. According to the accountability principle, entitlements vary “in direct proportion to the value of the subject’s relevant discretionary variables, ignoring other variables, but does not hold a subject accountable for the diﬀerences in the values of exogenous variables” (Konow, 2000, p. 1075). In our case the discretionary variables is the performance, and the exogenous variable the pie reduction.
The appeal of CEL and CEA in the normative judgments depends to some extent on the asymmetry of claims. When claims are very asymmetric, people prefer the ‘more egalitarian’ CEA rule whereas when claims are moderately asymmetric people prefer the - in terms of outcomes - more inequitable CEL rule.
We ﬁnd a strong diﬀerence between the outcomes in actual negotiations and the normative judgments. While claims strongly matter for the normative judgments of how the surplus should be divided, actual negotiations moderate the eﬀect of the diﬀerence in asymmetries in claims considerably. Additionally, compared to the normative judgments there is a strong level eﬀect in so far that the actually agreed outcomes are closer to the equal split than the normative judgments would indicate. In the experiments, CEA predicts the actual agreements best for both claim levels.
How can we square the observation that PROP is the preferred rule in the normative judgments and CEA in the actual negotiations? We oﬀer the following explanation.
The impartial normative judgments show that the proportional solution is the most attractive focal point when there is no actual negotiation. Yet, when negotiations actually have to take place, the claims are infeasible and, hence materially irrelevant.
Given the symmetric disagreement payoﬀ of (0, 0), the equal split becomes another focal point. Moreover, when viewing (the last few seconds of) the free-form bargaining as a Nash demand game even every eﬃcient allocation of the surplus can be sustained by a non-cooperative Nash equilibrium. Focal points are helpful in coordinating on one of the many equilibria. However, in the negotiations there is a tension between several reasonable focal points. This tension is the bigger the more asymmetric the claims are.
This tension between the asymmetric outcome provided by PROP and the symmetric outcome of the equal split can explain why the variance in agreements is much larger in 1980E than in 1640E. Since CEA lies between EQUA and PROP, it apparently is an attractive compromise for many actual bargainers.
The diﬀerence between normative judgments and actual negotiation behavior underscores the importance of studying both normative judgments and actual behavior.
In our view, learning about impartial normative views and actual behavior when one is a stakeholder are complements, not substitutes. Learning about normative judgments tells us about likely focal points in the negotiations. The fact that we get diﬀerent results in the experiment than in the normative judgments just illustrates that being a stakeholder matters strongly. This makes perfect sense for the following reasons. First, actual negotiations are strategic interactions with a threat point, where the disagreement results in a zero payoﬀ for both, which may make the equal split another focal point. Second, in actual negotiations the opponents do not necessarily hold the same normative views. As we have shown elsewhere (G¨chter and Riedl, 2004), diﬀerences a in normative attitudes indeed strongly shape the whole negotiation process. Third, it is a well-known tendency of people to subconsciously mix their normative views with what beneﬁts them. This ‘self-serving bias’ can sometimes strongly inﬂuence negotiations (Babcock et al., 1995; G¨chter and Riedl, 2004). Fourth, negotiators diﬀer in a their degree of selﬁshness, toughness and willingness to compromise. Fifth, psychological research has shown that in many decisions there is a ‘hot-cold’ empathy gap (Loewenstein, 2000). Being in the ‘hot state’ of an actual negotiation is psychologically a diﬀerent matter than making a normative judgment while being in an impartial ‘cold state’. All these factors can already be observed in a well-controlled and ‘cool’ laboratory environment. It is therefore very likely that they matter even more in outside-lab negotiations. The ﬂip-side of these observations is that the study of normative views really requires impartiality.
References Aumann, R. J. and Maschler, M. (1985). Game theoretic analysis of a bankruptcy problem from the Talmud. Journal of Economic Theory, 36:195–213.
Babcock, L., Camerer, C., Issacharoﬀ, S., and Camerer, C. F. (1995). Biased judgments of fairness in bargaining. American Economic Review, 85:1337–1343.