Communication and Voting Rules in Bargaining Games,

Transcription

1 Communication and Voting Rules in Bargaining Games, Marina Agranov California Institute of Technology Chloe Tergiman The Pennsylvania State University June 2016 Abstract Currently, there is no consensus on the effects communication in bargaining settings. On the one hand, communication has been shown to reduce proposer power in bilateral bargaining games, such as the ultimatum game. On the other, in multilateral bargaining games communication has been shown to have the opposite effect. In this paper we explore how and why these two seemingly opposing effects of communication come about. We focus on the interaction between voting rules and communication channels and show that when determining the effects of communication on bargaining outcomes it is not the size of the bargaining group that matters (bi- versus multi- lateral bargaining), but rather the voting rule used by the group to reach the agreement. This research was made possible thanks to the generous support from the Social Science Humanities and Research Council (Canada). The authors would like to thank Gary Bolton, Alessandra Casella, Timothy Cason, Pedro Dal Bo, Eric Dickson, Sanford Gordon, Yoram Halevy, Alessandro Lizzeri, Rebecca Morton, Muriel Niederle, as well as the seminar participants at Florida State University, London School of Economics, Penn State University, Purdue University, Stanford University, the University of British Columbia, and finally the conference participants of the Economic Science Association (2013), the Public Choice Meetings (2014), the Royal Economic Society (2014) and the Design and Bargaining Workshop in Dallas (2014). 1

2 1 Introduction Communication is an integral part of bargaining processes. Formal bargaining is typically preceded by informal conversations between involved parties who attempt to influence bargaining results. For instance, in legislative policy-making, legislators spend a considerable amount of time and resources communicating with each other before bringing bills to the floor for a vote. Similarly, in arbitration cases and trade agreements, negotiations between conflicting parties are a vital part of the bargaining process. In many of these examples, bargainers communicate with each other despite the fact that they have commonly known unaligned preferences regarding bargaining outcomes and there is no incomplete information embedded in the environment. Great strides have been made in the bargaining literature to better understand the effects of communication on bargaining outcomes and on the bargaining processes underlying these outcomes. Much of the work that analyzes the effects of communication in complete-information bargaining setups comes from experimental studies. By and large, two very different sets of results emerge from this literature (a detailed review is in Section 1.1). In two-person bargaining games, communication decreases inefficient allocations and, more generally, steers allocations towards more egalitarian ones. More recent studies in multilateral bargaining settings show the opposite is true: while communication does not affect the amount of inefficient allocations, it does shift them toward more unequal ones and allows proposers to secure a significantly higher share of resources. The main contribution of this paper is to shed light on these puzzling and seemingly incompatible results. Why does communication impact two-person bargaining games differently from multilateral bargaining games? Does the effect of communication in multilateral bargaining games depend on the institutional rules that govern the bargaining process? To answer these questions, we run a series of laboratory experiments in which a five-member committee is charged with allocating a unit of resources between its members. We use a standard bargaining protocol a la Baron and Ferejohn (1989) with a unanimity voting rule and compare the results with a multilateral game with majority rule as well as what is known about bilateral bargaining settings. In addition, our paper goes beyond reconciling the puzzling results documented in 2

3 previous experimental studies. Indeed, many real-life committees use a unanimity voting rule 1 and as far as we know there has been no work on communication under a unanimous voting rule. Thus this setting is important to study per se. One of the key differences between two-person and multilateral bargaining setups is the degree of consensus required to reach agreements. Generally, in two-person bargaining situations, both bargainers have to agree to pass an allocation, while in multilateral bargaining settings this depends on the voting rule used by the committee. 2 Previous papers that have documented an increase in unequal allocations in multilateral bargaining setups with communication exclusively used a majority voting rule (see Agranov and Tergiman (2014) and Baranski and Kagel (2015)). A majority voting rule means that proposers allocate positive shares only to a subset of committee members (the minimum winning coalition, i.e. those who are expected to support the proposed allocation) and appropriate the remaining funds. The introduction of communication under a majority voting rule allows proposers to create an auction for a place in the coalition among non-proposers, which ultimately drives the shares of coalition partners down via a competition effect. On the contrary, in a two-person bargaining setup in which the passage of a proposal requires the support of both bargainers, such competition effects are not present. By changing the voting rule from majority to unanimity in a multilateral bargaining setting, we remove the competition effect. By varying whether committee members can communicate or not, we can isolate the effect of the unanimity voting rule (versus the majority rule) from that of communication (versus none). 3 While one might expect that the effects of communication in multilateral bargaining with a unanimity rule would be similar to those obtained in two-person bargaining games, it s is not clear ex-ante whether it is the voting rule (majority versus unanimity) or the bargaining (bi- versus multi-lateral) that determines how communication impacts outcomes. This paper clarifies the interaction of communication, voting rules and group size. 1 The Council of the European Union for example has to vote unanimously on any sensitive issues, such as the joining of new members or common security policies. In the United States, many private clubs admit new members only if they are accepted by unanimity. Also in the United States, the certificate of incorporation of a majority of companies require action by written consent to be unanimous. 2 Voting rules might require a simple majority to pass a bill, or a super-majority (2/3 majority, unanimity etc.). 3 Our communication tool allows bargainers to send any kind of text message to any subset of members in their group, including private messages to individual members and public messages that are delivered to all members of the group. 3

4 Our experiment shows that the impact of communication on bargaining greatly depends on the voting rule in place. Under a majority rule communication leads to higher proposer power, but introducing unrestricted communication in a unanimity setting decreases proposer shares and leads to more equal allocations. In fact, more than 90% of all passed allocations in the treatment with communication are exact five-way equal splits. This is also very different from the final allocations observed in a treatment with the same voting rule but without communication: in that treatment proposers extract higher shares than coalition partners in more than 85% of final allocations. Our results are similar to those found in bilateral bargaining settings (Roth (1995)). In other words, in settings in which unanimous consensus is required to pass the proposals, the introduction of communication leads to more egalitarian distributions of resources, irrespective of the size of the committee. We then investigate the mechanism through which communication interacts with the voting rule and affects final outcomes. We have three main results in this respect. First, we find that communication has a dramatic effect on efficiency in committees that use a unanimity rule (efficiency is measured by the probability of delays occurring). Without communication, 44% of bargaining games end up with costly delays, while the introduction of communication lowers these disagreements to 7%, a level similar to those achieved under a majority rule. This result speaks to the debate regarding the disadvantages of the unanimity rule (see the discussion in Buchanan and Tullock (1962) and Miller and Vanberg (2013)). Second, the unrestricted communication tool is used very differently in the unanimity and in the majority rule settings. When unanimous support is required to pass proposals, subjects choose to communicate publicly by sending messages that are delivered to the entire committee. This is different from the overwhelmingly private chatting behavior observed under a majority rule setting, as documented by Agranov and Tergiman (2014). Finally, public and private statements serve opposite purposes. When subjects choose to communicate privately via backroom channels, they lobby for themselves, in particular their place in the coalition and their share. When subjects choose to make public statements, these statements serve to promote equality and a more egalitarian distribution of resources between all members. The prevalence of public messages coupled with the content of these messages is the driving force behind the egalitarian allocations observed in committees that use a unanimity rule and permit communication between its members. 4

5 The rest of the paper is structured as follows. We survey related literature in Section 1.1. The bargaining game and theoretical predictions are described in Section 2. The experimental design is presented in Section 3. Our experimental results are in Section 4. Finally, in Section 5 we offer some conclusions. 1.1 Related Literature Our paper contributes to the growing literature that studies the effects of communication in bargaining settings. Starting from the seminal work of Roth (1995), many studies have documented that communication promotes more egalitarian allocations in two-person bargaining settings. This section focuses on the ultimatum game, which is the closest analog to the experiments we ran in the present paper. 4 In a survey chapter on bargaining games published in the Handbook of Experimental Economics (1995), Roth describes an experiment in which ultimatum games are conducted under three conditions: a control condition without communication; an unrestricted communication condition in which bargainers had two minutes to discuss anything they wanted face-to-face; and a restricted communication condition in which bargainers had two minutes to converse but were restricted to social conversations and were not allowed to discuss the game. Two main results emerge from this study. First, communication significantly decreases the frequency of disagreements measured in terms of ultimatum rejections. Second, offers and final allocations are more egalitarian when bargainers can communicate with each other compared to when they cannot. This last effect is especially pronounced when comparing the no communication condition and the unrestricted communication condition. 5 These results have been replicated in many bilateral bargaining studies with variations in communication protocols including computerized chatting or pre-specified messages (see among others Rankin (2003), Schmidt and Zultan (2005), Zultan (2012), and Greiner et al. (2014)). Given that our experiment is about multilateral bargaining, our paper also naturally relates 4 For the analysis of the effects of communication in the more distantly related dictator game see Mohlin and Johannesson (2008), Xiao and Houser (2009), Andreoni and Rao (2011), and the references discussed therein. 5 Unfortunately, the conversations were not recorded in these early experiments, and, therefore, the content of the conversations was not analyzed. In our experiments we use computerized chats, which allows us to analyze their content and investigate the mechanism through which communication affects bargaining. 5

6 to a large experimental literature that studies the divide-a-dollar game with groups that consist of more than two members. Much of this literature has adopted the stylized bargaining protocol of Baron and Ferejohn (1989) and has focused on analyzing the effects of various political institutions on the distribution of resources and bargaining efficiency. This literature is reviewed in Morton (2012) and in Palfrey (2013). Among other things, studies have analyzed the comparative static predictions of the Baron-Ferejohn model (McKelvey (1991) and Diermeir and Morton (2004)), the effects of amendment rules (Frechette, Kagel and Lehrer (2003)), of bargaining protocols (Frechette, Kagel and Morelli (2005)), of voting rules (Miller and Vanberg (2013), and of veto power (Kagel, Sung and Winter (2010)). Most closely related to this paper are the two recent papers that introduced communication in a multilateral bargaining setting: Agranov and Tergiman (2014) and Baranski and Kagel (2015). Both studies exclusively focus on the majority voting rule and document that communication increases proposer power and leads to less egalitarian allocations compared to a treatment without communication. Both studies also find no significant effect of communication on bargaining efficiency: delays are rare with or without communication. The present paper is, to the best of our knowledge, the first to study multilateral bargaining in committees that use a unanimity rule and allows communication between group members. 2 Setup and Theoretical Predictions We consider a classic divide-a-dollar game in which a committee of N 3 players decides how to allocate a fixed budget of $1 among themselves using the q-voting rule, where q N. The parameter q represents the degree of consensus required to reach the agreement with q = N corresponding to the unanimity voting rule. The committee uses the standard bargaining protocol of Baron and Ferejohn (1989), which is an N-person extension of the Rubinstein alternating offers bargaining game. At the beginning of the first bargaining stage, one group member is chosen at random to make a proposal. A proposal is a vector (x i 1,..., x i N ) that specifies the share of each group member (xi j indicates the share offered to member j by member i, x i j 0, j). Proposals have to satisfy the budget constraint N j=1 xi j 1. The proposed allocation is observed by all group members and is 6

7 immediately voted on. If q members support the proposal, then it is implemented and the committee adjourns. If it is rejected (gets fewer than q votes) then the budget shrinks by a factor of (1 δ), the committee moves to the next bargaining stage and the process repeats itself (one group member is chosen at random to make a proposal etc...) until a proposed distribution receives q votes. Committee members have preferences that depend only on their own share. The factor (1 δ) represents the cost of delay in reaching an agreement and allows for efficiency comparisons between different final allocations. Finally, in some treatments, we allow group members to engage in cheap-talk communication after the proposer is chosen and before he/she submits proposed allocation. The general structure of the symmetric stationary subgame perfect equilibrium in this bargaining game (referred to henceforth as the equilibrium ) is independent of the degree of competition q and the availability of communication channels. 6 In this equilibrium, the proposer randomly selects q 1 other committee members (the coalition partners) and offers them an allocation that makes them exactly indifferent between supporting the bill and rejecting it. The proposer appropriates the remainder of the budget. The committee members that are not invited into the coalition (if those exist) get zero shares. Non-proposers support any bill that gives them at least as much as their continuation value and reject any bill that gives them any amount below that. Thus, in the equilibrium, all proposals pass without delay and the distribution of resources depends on the voting rule in place, q. Denote by x P q and by x NP q proposer and coalition partners, respectively. Then, in equilibrium shares of the x P q = 1 (q 1) x NP q and x NP q = δ N 6 The stationarity refinement has been extensively used in the literature in order to overcome the multiplicity of SPEs present in the current environment. By definition, stationary strategies cannot condition on the history of play. Therefore, in the bargaining game with communication, the stationary equilibrium concept does not allow bargainers to condition their votes on the conversations that preceded current voting stage. Rather, a vote cast for or against the proposed allocation may condition only on the proposed distribution of resources, and, in particular, only on member s own share since members care only about their own payoff. 7

8 3 Experimental Design All the experiments were conducted at the California Social Sciences Experimental Laboratory (CASSEL) at UCLA between January 2012 and January The subjects were recruited from the general undergraduate population of UCLA and no subject participated in more than one experimental session. All the interactions between participants were through computer terminals using the MULTISTAGE software. 7 In the experiments we use groups of 5 members who bargain over a budget of 250 tokens using the unanimity rule (q = N = 5). We implemented a discount factor of δ = 0.8, which means that following the rejection of a proposed allocation the budget shrinks by 20%. For this parameterization, the unique symmetric stationary subgame perfect equilibrium predicts that all committee members that were not chosen as a proposer get x NP q=n proposer appropriates the remaining funds, x P q=n = 40 tokens and = 90 tokens. We chose these parameters to facilitate the comparison between bargaining outcomes with unanimity rule and those with majority voting rule, which are reported in Frechette, Kagel and Lehrer (2003) and Agranov and Tergiman (2014). Each experimental session consisted of 15 bargaining games. Before the beginning of each bargaining game, subjects were randomly matched into groups of five and assigned an ID number. Random matching between bargaining games and random assignment of ID numbers was used to minimize repeated bargaining effects. At the end of the experiment, we summed up all the tokens earned by each subject in all bargaining games and converted them to the US dollars using the rate 50 tokens equals $1. Our experimental sessions lasted about an hour and subjects earned on average $20, including the show-up fee of $5. In all our experimental sessions we implemented the Baron-Ferejohn bargaining protocol described in Section 2. At the beginning of each bargaining session, one of the five members was randomly chosen to be the proposer. His/her assigned ID number was revealed to the entire group. The proposer proposed an allocation that was observed by all members of the group, with shares to each member clearly indicated. After that, all members of the group including 7 This software was developed from the open source Multistage package and is available for download at 8

9 the proposer voted to accept or reject the proposed allocation. If the allocation was approved by all 5 members then it passed and the bargaining session was over. Otherwise, the budget shrank by 20% and the bargaining continued with a random selection of a (possibly) new proposer from the same group. This process repeated itself until a proposer s allocation received 5 votes and passes. We ran two different treatments. In one treatment, Unanimity Baseline, no communication between committee members was allowed. In the other treatment, Unanimity Chat, committee members could communicate with each other using a chat tool. In this treatment after the proposer was determined and his/her ID number revealed to the group members, but before the proposer submitted his proposal, members of the group could communicate with each other using a chat tool. This chat tool allowed subjects to send any message they wanted to any subset of members in their group. For instance, members could send private messages that would be delivered only to a particular member or to a subset of members, and they could also send public messages that would be observed by all members of the group. Subjects could only see the messages that were sent to them. If a message is sent to two or more individuals at the same time, those individuals know who the other recipients are. The duration of the communication was in the hands of the proposer: the chat tool was disabled when the proposer submitted his proposal for a vote. Our software recorded all the messages sent by subjects during the communication stage. We conducted three sessions of the Unanimity Baseline treatment with total of 80 subjects, and another three sessions of the Unanimity Chat treatment with total of 75 subjects. Complete instructions for the Unanimity Chat treatment are presented in Appendix A. 4 Results We present our experimental results in the following order. We start by documenting how unrestricted communication affects bargaining outcomes. Specifically, we evaluate bargaining outcomes through two lenses: (1) the frequency of delays and inefficient agreements, and (2) the distribution of resources among committee members. We then proceed to analyze the 9

10 content of the communication between bargaininers and investigate the dynamics that underly these bargaining outcomes. Throughout this section, we will compare the results of our unanimity experiments described in Section 3 with the the results from Roth (1995) as well as those from Agranov and Tergiman (2014). The comparison with the experiments reported in Agranov and Tergiman (2014) is made possible by the fact that the two experiments differ only in the degree of consensus required to reach agreements: in the current experiment, we use a unanimity rule where all five members have to support the proposal, while in our previous experiment, in order to pass, proposals only needed the support of a simple majority of members. All the other details of the experimental procedures are exactly the same in the two experiments. 4.1 Bargaining Outcomes Efficiency Efficiency in this setup is measured by the probability of delays occurring. If a proposer is unable to gather the required number of votes, delays in implementing a budget occur. Because the budget shrinks by 20% before a new round of voting can take place, an inefficiency is created. Previous experimental studies have documented higher delays in bargaining situations in which unanimity (as opposed to a simple majority) is required to pass a proposal (see Miller and Vanberg (2013)). This has served as support for the theoretical argument by Buchanan and Tullock (1962) that less-than-unanimity decision rules are more efficient. Consistent with the argument above, we find that disagreements and delays are very common under a unanimity rule when communication between committee members is not allowed. Indeed, in our Unanimity Baseline treatment, the fraction of delays is staggeringly high at 43.8%. However, the introduction of communication in our Unanimity Chat treatment reduces the amount of delays to only 6.7%. Thus, introducing communication under a unanimity rule dramatically improves efficiency. 8 8 A two-sided test of proportions at the group level shows efficiency levels are statistically different in Unanimity Baseline and Unanimity Chat treatments with p < At the session level, a two-sided test supports the same conclusion with a p-value as good as it can be with three sessions for each treatment (p = ). 10

11 Two points are worth noting. First, our finding that communication reduces the frequency of delays echoes the results observed in two-person ultimatum games, in which the agreement of both bargainers is required to make a deal. In Roth (1995), without communication, 33% of groups fail to reach an agreement. After the introduction of communication, the percentage of groups that fail to reach an agreement drops to 4-6% depending on the communication protocol. The order of magnitude of these numbers is similar to our findings here despite very different experimental protocols. Second, this effect is specific to environments in which unanimous support is required to pass a proposal: Agranov and Tergiman (2014) who focus on a majority voting rule find that communication does not impact the frequency of inefficient agreements, which is quite low with and without communication Final Allocations Table 1 presents the predicted and observed shares of proposers in our two treatments as well as the fraction of final allocations in which all committee members get the exact same share. We refer to this allocation as Equal Split. 9 The data reported in Table 1 focus on the first bargaining stage in which the budget is 250 tokens and shows all submitted proposals, all passed proposals as well as all rejected proposals. Without communication under a unanimity voting rule, in a large majority of passed proposals, proposers appropriate higher shares of resources than coalition partners, but under-exploit their power relative to the equilibrium prediction. 10 Indeed, in the last 5 games the average share of the proposer constitutes just 71% of the one predicted by the theory, and 13.3% of passed proposals are exact equal splits. This echoes a well-known and robust finding in bargaining games with a majority voting rule, which establishes the failure of the proposers to extract equilibrium rents absent communication (see Frechette et al. (2003, 2005a, 2005b), Battaglini et al. (2012), Agranov and Tergiman (2014) and Baranski and Kagel (2015)). The introduction of unrestricted communication steers final allocations in the direction of more egalitarian ones. In fact, it removes proposer power all together: In the Unanimity Chat, 9 Given our parametrization of 250 tokens and 5 committee members, this corresponds to allocations in which each member receives exactly 50 tokens. 10 Regression analysis using the panel aspect of the data with clustering at the session level shows support for these conclusions with p-values less than

12 Table 1: Proposals in the first bargaining stage in the Unanimity treatments. Unanimity Baseline Unanimity Chat all games last 5 games all games last 5 games Equilibrium predictions Proposer s Share 90 tokens 90 tokens Fraction of Equal Splits 0% 0% Submitted Proposals Proposer s Share, mean 68 tokens 68 tokens 52 tokens 51 tokens Fraction of Equal Splits 17.5% 7.5% 84% 88% Passed Proposals Proposer s Share, mean 62 tokens 64 tokens 50 tokens 50 tokens Fraction of Equal Splits 28.4% 13.3% 95.5% 94.3% Rejected Proposals Proposer s Share, mean 77 tokens 74 tokens 62 tokens 59 tokens Fraction of Equal Splits 0% 0% 0% 0% Notes: Equilibrium predictions correspond to the symmetric stationary SPE predictions. We focus on the proposals submitted, passed and rejected in the first bargaining stage, in which the budget is 250 tokens. In Equal Split allocations all members of the committee receive exactly 50 tokens. 94.3% of final allocations in the last 5 games are exact equal splits with all members earning 50 tokens. Focusing on all submitted proposals in the first stage regardless of whether they passed shows the same pattern: in the last 5 games 88% are equal splits when communication is allowed and only 7.5% when communication is not allowed. The rejected proposals, on the contrary, feature higher shares for proposers and are never equal splits, regardless of whether communication is allowed. The distribution of resources between committee members observed in our two unanimity treatments is aligned with results from bilateral bargaining reported in Roth (1995) where the percentage of equal split offers goes from 31% without communication to 75% with communication. Figure 1 compares the effect of communication under unanimity and majority voting rule. The introduction of unrestricted communication has opposite effects on proposer power in the two voting treatments. In this figure we used proposals that passed without delay in the last 5 bargaining games. While the average share of the proposer increases from 110 tokens to 144 tokens in the Majority treatment when communication is available, it decreases in the 12

13 Figure 1: Effect of communication on proposer shares in the Unanimity and Majority treatments Theory % Baseline Chat 84.6% 71% Baseline Chat 55.8% Majority Unanimity Notes: The mean proposer shares as a fraction of the theoretical prediction for each treatment is reported. We focus on the last 5 games and proposals that passed without delay. The 95% confidence intervals for proposer shares as a fraction of what is theoretically predicted are represented for each treatment. Unanimity treatment from 64 tokens to 50 tokens. 11 In summary, the effect of unrestricted communication in committees that use different voting rules is large but asymmetric. In committees under a majority voting rule, unrestricted communication concentrates the distribution of resources and increases the share held by the proposer. On the contrary, in the committees that use a unanimous voting rule, unrestricted communication promotes equal splits, decreases proposer power and improves efficiency. These effects seem to be robust across group sizes. 4.2 Communication Protocols Our next step is to analyze the content of the communication between subjects in order to understand how subjects reach the final outcomes described in the previous section. There are different ways one can perform content analysis. We start by classifying individual messages 11 Ranksum tests confirm that the shares of the proposers significantly increase with communication in the majority setting (p < 0.001), while they significantly decrease in the unanimity setting (p < 0.001). The unit of observation is, for each subjects when he/she was a proposer, the average number of tokens that they were able to collect (one observation per subject). This conclusion follows through if instead we use a session as the unit of observation. 13

14 sent by different subjects in our communication treatments. We then corroborate these results by considering the whole conversation that each group engaged in as the unit of observation. Both techniques lead to the same conclusions. In both cases, we separate the analysis between communication that was public, that is sent to the entire bargaining group, or private. Table 2 summarizes the frequency of different types of messages (public and private) as well as their content, treating messages from proposers and non-proposers separately. We focus on the last 5 games in each experimental session and present data from both our Unanimity Chat treatment as well as from our past Majority Chat treatment. 12 The content is broken down only for the subsample of subjects whose messages were classified as relevant. Relevancy was broadly defined so that messages that were in any way related to the game were counted as relevant. Examples of relevant messages include those that pertain to the structure of the game, proposals, consequences of rejecting a proposal and strategies. 13 In the Majority treatment, 84 out of the 110 subjects at one point or another in the last five bargaining games when they were non-proposers used the chat messages in a way that was directly relevant to the game. So did 62 of the 75 subjects in the Unanimity treatment. In both cases this represents about 80% of our subjects. 14 As Table 2 shows, proposers talk much less than non-proposers: only about 40% (30%) of proposers sent relevant messages at some point in the last 5 games in the Unanimity (Majority) treatment. We will largely focus on non-proposer messages, as the number of observations related to proposer communication are relatively small. We include include the latter in Table 2 for completeness. In the Public Messages section of Table 2, we look at those subjects who communicated a relevant message publicly at least once. This represents 15.5% and 29.4% of subjects in the Majority treatment and 98.4% and 95.7% in the Unanimity treatment for non-proposers and proposers, respectively. In the Private Messages section of the table, we look at those subjects that communicated a relevant message privately at least once. This fraction is 94% and 82.4% in the Majority treatment and 8.1% and 4.3% in the Unanimity treatment for non- 12 In Roth (1995) communication was face-to-face and not recorded, and, thus, we cannot compare content of conversations. 13 The full transcripts of the chats and their classification are available from the authors upon request. 14 All the chat messages were analyzed by two undergraduate students at UBC as well as a masters student at UBC. The students were given the categorizations and were asked to determine which chat messages fell into each category. 14

15 Table 2: Frequency and content of messages in the Chat treatments (last 5 games). Non-Proposers Proposers Majority Unanimity Majority Unanimity Total subjects Nb subjects who send relevant chats 84 (79.2%) 62 (82.7%) 17 (31.5%) 23 (42.6%) Public Messages % who send public messages at least once 15.5% 98.4% 29.4% 95.7% % who lobby for fairness 76.9% 91.8% 20% 68.2% % who lobby for themselves 23.1% 6.6% 0% 0% % who exclusively send public messages 5.6% 91.9% 17.6% 95.7% Private Messages % who send private messages at least once 94% 8.1% 82.4% 4.3% a % subjects who lobby for fairness 5.1% 40% 0% 100% % subjects who lobby for themselves 97.5% 80% 7% 100% % who exclusively send private messages 84.5% 1.6% b 70.6% 4.3% a This represents a single subject. b This represents a single subject. Notes: The content analysis pertains to those subjects who have sent at least one relevant message in the first stage of the last 5 bargaining games. Note that some categories have very few observations in them. This is true in particular for private messages under Unanimity as well as among proposers more generally. We report the numbers here for completeness. 15

16 proposers and proposers, respectively. 15 The last row of the Public Messages section shows that the fraction of subjects who sent all their messages publicly: this is quite a rare event in the Majority treatment (5.6% for non-proposers and 17.6% for proposers), while this is very common in the Unanimity treatment (91.9% for non-proposers and 95.7% for proposers). On the contrary, the vast majority of both proposers and non-proposers exclusively send private messages in the Majority treatment (84.5% and 70.6%, respectively), while only a very small fraction of subjects do so in the Unanimity treatment (1.6% and 4.3%, respectively). In a large fraction of cases, non-proposers who use public messages use them to ask proposers for an equal distribution of resources or use them to express concern for the welfare of all members of the group (though not necessarily equal). Most of the messages that were classified as lobby for fairness are similar to: Equal is nice, Let s just do 50 each, and Just play fair. Among non-proposers, these fractions are 76.9% and 91.8% in the Majority and Unanimity treatments, respectively. The fraction of non-proposers who have used relevant public messages at least once to lobby for themselves is much smaller. Among non-proposers these fractions are 23.1% and 6.6% in the two treatments, respectively. 16 It is worth pointing out that while these fractions vary across treatments, under both voting rules, the fraction of subjects who use the public messages to lobby for themselves is significantly lower than the fraction of subjects who use the public messages to lobby for equality or fairness. 17 Messages from proposers exhibit a similar pattern despite the small number of observations. Thus, public messages in both voting treatments and across both proposers and non-proposers tend to focus on statements about equality and fairness. Among non-proposers, when subjects choose to send private messages, a significantly smaller fraction of subjects use these types of messages to pressure the proposer to offer a more equal split of the budget. This is true in both treatments. Indeed, among non-proposers, only 5.1% of those who send relevant private messages in the Majority treatment use them to 15 These are not disjoint groups, some subjects sent relevant messages both publicly and privately. 16 These percentages do not need to add up to 100. Indeed, any given subject can use the public messages for both fairness motives as well as selfish ones, or may use these messages for neither. For example, some subjects use public messages in a relevant way, but not to talk about shares, instead talking about how rejecting an offer leads to a decrease in the number of tokens to distribute. It is also possible that the percentages sum up to more than 100 as is the case in the Majority treatment, some subjects used private messages to indicate that splitting equal would be nice but all they ask in order for them to vote in favor of a proposal is a particular amount. 17 The remaining relevant messages have largely to do with timing, wanting the round to end at the first stage to not lose tokens, interpreting the incentives and so on. 16

17 ask for equal or fair distributions. This fraction is 40% in the Unanimity treatment. Instead of being used to lobby for equality, relevant private messages are used to lobby for one s own fate. Most of the messages that were classified as lobby for themselves are similar to I ll vote yes for [amount here], or Give me [amount here] for an automatic yes. 18 About 97.5% of private messages in the Majority treatment are used to lobby for one s self. In the Unanimity treatment, this fraction represents 80% of private messages. 19 Among proposers, in the Majority treatment, none of the 82.4% of subjects who send private messages do so to pressure the proposer for equality. 20 Finally, statistical tests confirm that among non-proposers, in both treatments lobbying for one s own self is more likely to be done privately, while lobbying for fairness is more likely to be done publicly. 21, Group-level Conversations In Table 3 we no longer separate our data between proposers and non-proposers. Instead we take a group as our unit of observation. We focus on groups who have sent at least one relevant message in the first stage of the last 5 bargaining games. We document the fraction of conversations where at least one message was relevant to the game being played as well as the topic of these conversations. The data presented in Table 3 show the same patterns as the ones documented in Table 2. First, a large majority of the conversations under both voting rules contain relevant messages regarding the bargaining game: 97.4% in the Majority treatment and 93.7% in the Unanimity treatment. Moreover, while 100% of conversations in the Majority treatment contain at least one message in which a bargainer lobbies for himself, this percentage is only 11.9% in the Unanimity treatment. On the other hand, 81.7% of conversations in the latter treatment contain 18 Some messages were classified as both, for example, statements similar to: Equal is nice but I ll vote yes as long as I get [amount here]. 19 It is worth stressing that in the Unanimity treatment, the fraction of subjects who use private messages is low at 8.1%, which represents only 5 subjects out of the 62 who use the chat messages in a relevant way. 20 In the Unanimity treatment, there is only a single subject who sent a private message as a proposer and so cannot perform a meaningful analysis. 21 Probit regressions using the panel aspect of our data, clustering at the session level, supports these conclusions with p-values less than For proposers we do not have enough data or variation in data to conduct those tests, though qualitatively the data seem to be along the same lines as for non-proposers. 17

18 Table 3: Group-level conversations in our Chat treatments (last 5 games). Majority Unanimity Total number of conversations Fraction of conversations with at least one relevant message 97.4% 93.7% Fraction of relevant conversations where at least once message relates to fairness 17.1% 81.7% Fraction of relevant conversations where at least once message relates to self interest 100% 11.9% Notes: The maximum number of conversations in the last 5 games given the number of subjects in the two treatments are 80 and 75 for the Majority and Unanimity treatments, respectively. The number of observed conversations is smaller than the maximum number because in some groups the proposer submitted a proposal right away before any conversations could take place. However, most groups did engage in conversations before proposals were submitted. at least one message about fairness, while this percentage is only 17.1% in the former treatment. To summarize our results, the differences in usage of the communication tool explain the differences in how communication impacts bargaining, and help understand why the results of Roth (1995) and Agranov and Tergiman (2014) differ. How the communication tool is used depends on the voting rule used by the committee. When a simple majority is required to pass proposals, communication is primarily bilateral, and deals are established in backroom conversations. On the other hand, when unanimous support is required to reach agreements, communication is public. This difference is important as different types of communication channels are used to transmit different types of information. Public messages contain requests for fairness and in general express pro-social behavior, while private messages are used to lobby for one s own interest. 5 Conclusion Communication is an integral part of bargaining processes. However, as we show in this paper, even within the class of divide-a-dollar bargaining games, communication does not necessarily have a uniform impact on observed outcomes. Indeed, in this paper we reconcile puzzling results that exist in the experimental literature regarding the differential effects that communication has on bargaining outcomes. In two-person ultimatum games the introduction 18

19 of communication has been shown to decrease the frequency of disagreements and promote more egalitarian allocations. On the contrary, in multilateral bargaining games that use a majority voting rule to reach agreements, the introduction of communication has been shown to promote higher proposer power and fewer egalitarian allocations, without any effect on the frequency of disagreements. We conduct a new series of multilateral bargaining games with a unanimity voting rule and show that the interaction between communication protocols and voting rules explain the opposing effects of communication documented in the previous studies. In our experiments, just like in two-person ultimatum games, the introduction of communication significantly decreases the frequency of inefficient allocations and promotes more egalitarian allocations. In fact, more than 90% of all final allocations are exact equal splits of resources between group members; that is, proposer power is completely eliminated. Taken together with Roth (1995), our results strongly suggest that group size does not impact the effects of communication on bargaining outcomes. Rather, it is the voting rule in place. An analysis of the chat messages sent by our subjects reveal that communication is used very differently depending on the voting rule used by the group: when unanimous support is required to pass proposals, a large majority of the conversations are conducted in public chats, while when majority support is required to pass proposals, a large majority of conversations are bilateral and private. Further, private and public conversations are used very differently: subjects use public statements to promote equality and express desire for egalitarian allocations, while they lobby for their own interests in private chats. Our results suggest that design of bargaining protocols should consider different types of communication channels as an additional available instrument. References [1] Agranov M. and C. Tergiman, Communication in Multilateral Bargaining, Journal of Public Economics 118: [2] Andreoni J. and J. M. Rao, The power of asking: how communication affects self- 19

20 ishness, empathy, and altruism, Journal of Public Economics 95: [3] Baranski A. and J. Kagel, Communication in Legislative Bargaining, mimeo. [4] Baron D.P. and J.A. Ferejohn, Bargaining in legislatures, American Political Science Review 83(4): [5] Battaglini M., Nunnari, S. and T.R. Palfrey, Legislative Bargaining and the Dynamics of Public Investment, American Political Science Review 106(2): [6] Buchanan J.M. and G. Tullock, The calculus of consent: logical foundations of constitutional democracy. Ann Arbor: University of Michigan Press. [7] Diermeier D. and R. Morton, Proportionality versus Perfectness: Experiments in Majoritarian Bargaining, in Social Choice and Strategic Behavior: Essays in the Honor of Jeffrey S. Banks, ed. by David Austen-Smith and John Duggan. Berlin: Springer. [8] Frechette G.R., Kagel, J. H. and S. F. Lehrer, Bargaining in legislatures: An experimental investigation of open versus closed amendment rules, American Political Science Review 97(2): [9] Frechette G.R., Kagel, J. H. and M. Morelli, 2005a. Behavioral identification in coalitional bargaining: An experimental analysis of demand bargaining and alternating offers, Econometrica 73(6): [10] Frechette G.R., Kagel, J. H. and M. Morelli, 2005b. Nominal bargaining power, selection protocol and discounting in legislative bargaining, Journal of Public Economics 89(8): [11] Greiner, B., Caravella, M. and A. E. Roth, Is avatar-to-avatar communication as effective as face-to-face communication? An Ultimatum Game experiment in First and Second Life, Journal of Economic Behavior and Organization 108: [12] Kagel J. H., Sung H. and E. Winter, Veto power in committees: an experimental study, Experimental Economics 13 (2),

21 [13] McKelvey R., An Experimental Test of a Stochastic Game Model of Committee Bargaining, in Contemporary Laboratory Research in Political Economy, Ann Arbor: University of Michigan Press. [14] Miller L. and C. Vanberg, Decision costs in legislative bargaining: an experimental analysis, Public Choice 155(3): [15] Mohlin, E. and M. Johannesson, Communication: Content or relationship? Journal of Economic Behavior and Organization, 65(3-4): [16] Morton R., Experimental Political Science: Principles and Practices, co-edited with Bernhard Kittell and Wolfgang Luhan, Palgrave. [17] Palfrey T., Experiments in Political Economy, in Kagel, J. H. and Roth, A. E. The Handbook of Experimental Economics, Vol. II, forthcoming. [18] Rankin F., Communication in ultimatum games, Economics Letters 81: [19] Roth, A. E., Bargaining experiments. in Kagel, J. H. and Roth, A. E. The Handbook of Experimental Economics published by Princeton University Press: [20] Schmidt, C. and R. Zultan, The uncontrolled social utility hypothesis revisited, Economics Bulletin 3(33): 1-7. [21] Xiao, E. and D. Houser, Avoiding the sharp tongue: anticipated written messages promote fair economic exchange, Journal of Economic Psychology 30(3): [22] Zultan R., Strategic and social pre-play communication in the ultimatum game, Journal of Economic Psychology 33(3):

22 A Instruction for the Unanimity Chat This is an experiment in the economics of decision making. The instructions are simple, and if you follow them carefully and make good decisions you may earn a CONSIDERABLE AMOUNT OF MONEY which will be PAID TO YOU IN CASH at the end of the experiment. The currency in this experiment is called tokens. All payoffs are denominated in this currency. The total amount of tokens you earn in the experiment will be converted into US dollars using the rate 50 Tokens = $1. In addition, you will get a $5 participation fee if you complete the experiment. In this experiment you will act as voters. You will distribute funds between yourself and others in a series of Periods. In each Period you will be randomly divided into groups of 5 members each. Each group will decide how to split a sum of money. Proposals will be voted up or down (accepted or rejected) by unanimity rule. That is, if 5 out 5 voters approve a proposal, it passes. In any Period you will not know the identity of the subjects you are matched with and your group-members will not know your identity. In each Period you will have to decide how to divide 250 tokens among the 5 voters in your group. One of the 5 voters in your group will be randomly chosen to make a proposal of how to split 250 tokens among the 5 voters (provisional budget proposal). Each voter has the same chance of being selected to make a proposal. Allocations to each member must be between 0 and 250 tokens. All allocations must add up to 250 tokens. After the selected proposer has made his/her allocation, this proposal will be posted on your computer screens with the proposed allocation to you and the other voters clearly indicated. You will then have to decide whether to accept or reject the proposed allocation. If the proposal passes (gets all 5 votes), the proposed allocation is implemented and we will move on to the next Period. If the proposal is defeated (gets fewer than 5 votes), there will be a call for new proposals and the process will repeat itself. However, the amount of money to be divided will be reduced by 20% of the amount of money in the preceding Round and rounded to the nearest integer. Thus, if the proposal in Round 1 is rejected, the new proposal in Round 2 will involve splitting 200 tokens among the 5 voters. And if this new proposal is rejected in Round 2, then in round 3 you will be splitting 160 tokens. If the proposal in rejected in Round 22