“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 Re-search Council (Canada). The authors would like to thank Gary Bolton, Alessandra Casella, Timothy Cason, PedroDal Bo, Eric Dickson, Sanford Gordon, Yoram Halevy, Alessandro Lizzeri, Rebecca Morton, Muriel Niederle, aswell 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 participantsof 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

1 Introduction

Communication is an integral part of bargaining processes. Formal bargaining is typically pre-

ceded 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 regard-

ing 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 out-

comes. 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 re-

sults 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 in-

compatible results. Why does communication impact two-person bargaining games differently

from multilateral bargaining games? Does the effect of communication in multilateral bar-

gaining 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

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previous experimental studies. Indeed, many real-life committees use a unanimity voting rule1

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 de-

gree 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 exclu-

sively 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 commu-

nication 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 pas-

sage 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 com-

municate 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 com-

munication 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 communica-

tion impacts outcomes. This paper clarifies the interaction of communication, voting rules and

group size.

1The Council of the European Union for example has to vote unanimously on any “sensitive” issues, such asthe joining of new members or common security policies. In the United States, many private clubs admit newmembers only if they are accepted by unanimity. Also in the United States, the certificate of incorporation of amajority of companies require action by written consent to be unanimous.

2Voting rules might require a simple majority to pass a bill, or a super-majority (2/3 majority, unanimity etc.).3Our 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 membersof the group.

3

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 communica-

tion: 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 pro-

posals, 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 (ef-

ficiency 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 com-

munication 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 over-

whelmingly private chatting behavior observed under a majority rule setting, as documented

by Agranov and Tergiman (2014). Finally, public and private statements serve opposite pur-

poses. 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 dis-

tribution 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.

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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 doc-

umented 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 exper-

iments we ran in the present paper.4

In a survey chapter on bargaining games published in the Handbook of Experimental Eco-

nomics (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 con-

dition and the unrestricted communication condition.5 These results have been replicated in

many bilateral bargaining studies with variations in communication protocols including com-

puterized 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

4For the analysis of the effects of communication in the more distantly related dictator game see Mohlin andJohannesson (2008), Xiao and Houser (2009), Andreoni and Rao (2011), and the references discussed therein.

5Unfortunately, the conversations were not recorded in these early experiments, and, therefore, the content ofthe conversations was not analyzed. In our experiments we use computerized chats, which allows us to analyzetheir content and investigate the mechanism through which communication affects bargaining.

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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 in-

stitutions 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 com-

parative 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 bar-

gaining 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 fo-

cus 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 com-

munication between group members.

2 Setup and Theoretical Predictions

We consider a classic divide-a-dollar game in which a committee ofN ≥ 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 anN -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 (xi1, ..., xiN) that specifies the share of each group member (xij indicates

the share offered to member j by member i, xij ≥ 0,∀j). Proposals have to satisfy the budget

constraint∑N

j=1 xij ≤ 1. The proposed allocation is observed by all group members and is

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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 bar-

gaining 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 pro-

poser 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 distribu-

tion of resources depends on the voting rule in place, q. Denote by xPq and by xNP

q shares of the

proposer and coalition partners, respectively. Then, in equilibrium

xPq = 1− (q − 1) · xNP

q and xNPq =

δ

N

6The stationarity refinement has been extensively used in the literature in order to overcome the multiplicityof SPEs present in the current environment. By definition, stationary strategies cannot condition on the history ofplay. Therefore, in the bargaining game with communication, the stationary equilibrium concept does not allowbargainers to condition their votes on the conversations that preceded current voting stage. Rather, a vote cast foror 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.

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3 Experimental Design

All the experiments were conducted at the California Social Sciences Experimental Laboratory

(CASSEL) at UCLA between January 2012 and January 2013. 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 xNPq=N = 40 tokens and

proposer appropriates the remaining funds, xPq=N = 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

7This software was developed from the open source Multistage package and is available for download athttp://software.ssel.caltech.edu/

8

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 bargain-

ing 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

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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 de-

scribed 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 con-

sensus 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

4.1.1 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 com-

mon 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

8A two-sided test of proportions at the group level shows efficiency levels are statistically different in Unanim-ity Baseline and Unanimity Chat treatments with p < 0.001. At the session level, a two-sided test supports thesame conclusion with a p-value as good as it can be with three sessions for each treatment (p = 0.0495).

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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.

4.1.2 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 propos-

als, 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 bar-

gaining 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,

9Given our parametrization of 250 tokens and 5 committee members, this corresponds to allocations in whicheach member receives exactly 50 tokens.

10Regression analysis using the panel aspect of the data with clustering at the session level shows support forthese conclusions with p-values less than 0.001.

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Table 1: Proposals in the first bargaining stage in the Unanimity treatments.

Unanimity Baseline Unanimity Chatall games last 5 games all games last 5 games

Equilibrium predictionsProposer’s Share 90 tokens 90 tokensFraction of Equal Splits 0% 0%

Submitted ProposalsProposer’s Share, mean 68 tokens 68 tokens 52 tokens 51 tokensFraction of Equal Splits 17.5% 7.5% 84% 88%

Passed ProposalsProposer’s Share, mean 62 tokens 64 tokens 50 tokens 50 tokensFraction of Equal Splits 28.4% 13.3% 95.5% 94.3%

Rejected ProposalsProposer’s Share, mean 77 tokens 74 tokens 62 tokens 59 tokensFraction of Equal Splits 0% 0% 0% 0%

Notes: Equilibrium predictions correspond to the symmetric stationary SPE predictions. We focus on the proposalssubmitted, passed and rejected in the first bargaining stage, in which the budget is 250 tokens. In Equal Splitallocations 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 commu-

nication.

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

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Figure 1: Effect of communication on proposer shares in the Unanimity and Majority treatments

64.6%

Baseline

84.6%

Chat

71%

Baseline

55.8%

Chat

Majority Unanimity

Theory

0.1

.2.3

.4.5

.6.7

.8.9

1

Notes: The mean proposer shares as a fraction of the theoretical prediction for each treatment is reported. Wefocus on the last 5 games and proposals that passed without delay. The 95% confidence intervals for proposershares 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 vot-

ing rules is large but asymmetric. In committees under a majority voting rule, unrestricted com-

munication concentrates the distribution of resources and increases the share held by the pro-

poser. On the contrary, in the committees that use a unanimous voting rule, unrestricted com-

munication 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

11Ranksum tests confirm that the shares of the proposers significantly increase with communication in themajority setting (p < 0.001), while they significantly decrease in the unanimity setting (p < 0.001). The unit ofobservation is, for each subjects when he/she was a proposer, the average number of tokens that they were able tocollect (one observation per subject). This conclusion follows through if instead we use a session as the unit ofobservation.

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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-

12In Roth (1995) communication was face-to-face and not recorded, and, thus, we cannot compare content ofconversations.

13The full transcripts of the chats and their classification are available from the authors upon request.14All 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 eachcategory.

14

Table 2: Frequency and content of messages in the Chat treatments (last 5 games).

Non-Proposers ProposersMajority Unanimity Majority Unanimity

Total subjects 106 75 54 54

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%

aThis represents a single subject.bThis represents a single subject.

Notes: The content analysis pertains to those subjects who have sent at least one relevant message in the firststage of the last 5 bargaining games. Note that some categories have very few observations in them. This is truein particular for private messages under Unanimity as well as among proposers more generally. We report thenumbers here for completeness.

15

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 pro-

posers 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

15These are not disjoint groups, some subjects sent relevant messages both publicly and privately.16These 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 subjectsuse public messages in a relevant way, but not to talk about shares, instead talking about how rejecting an offerleads to a decrease in the number of tokens to distribute. It is also possible that the percentages sum up to morethan 100 as is the case in the Majority treatment, some subjects used private messages to indicate that splittingequal would be “nice” but all they ask in order for them to vote in favor of a proposal is a particular amount.

17The remaining relevant messages have largely to do with timing, wanting the round to end at the first stage tonot “lose tokens,” interpreting the incentives and so on.

16

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 Major-

ity 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.21,22

4.2.1 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 conver-

sations 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 contain18Some 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].”19It 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.20In the Unanimity treatment, there is only a single subject who sent a private message as a proposer and so

cannot perform a meaningful analysis.21Probit regressions using the panel aspect of our data, clustering at the session level, supports these conclusions

with p-values less than 0.001.22For 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

Table 3: Group-level conversations in our Chat treatments (last 5 games).

Majority Unanimity

Total number of conversations 76 59Fraction 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 treat-ments are 80 and 75 for the Majority and Unanimity treatments, respectively. The number of observed conversa-tions is smaller than the maximum number because in some groups the proposer submitted a proposal right awaybefore any conversations could take place. However, most groups did engage in conversations before proposalswere 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 pa-

per, even within the class of divide-a-dollar bargaining games, communication does not nec-

essarily 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

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 ma-

jority 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 oppos-

ing 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 pub-

lic 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.

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[4] Baron D.P. and J.A. Ferejohn, 1989. “Bargaining in legislatures”, American Political Sci-

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study,” Experimental Economics 13 (2), 167-188.

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[19] Roth, A. E., 1995. “Bargaining experiments.” in Kagel, J. H. and Roth, A. E. The Hand-

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21

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

3, then in Round 4 you will be splitting 128 tokens, etc? This process will repeat itself until a

proposed allocation is passed (gets all 5 votes).

To summarize, the steps of the process will work as follows:

1. One voter is randomly selected to make a proposal of how to split 250 tokens.

2. A vote is held (each member of the group votes to accept or reject the proposal of the

selected voter).

3. If all 5 voters accept it, then the proposal passes and the Period is over. If the proposal is

rejected, then the money shrinks by 20%, we move on to the next Round of this Period

and a new voter is chosen to propose the split (each of the 5 voters in a group has equal

chance of being chosen). The process repeats itself until the proposal of the selected

voter for that Round passes.

At the start of each Period, you will be randomly re-matched into groups of 5 voters each. Each

member of the group is assigned an ID number (from 1 to 5), which is displayed on the top of

the screen. Once the Period is over, you will be randomly re-matched to form new groups of 5

voters each and you will be assigned a (potentially) NEW ID. Please make sure you know your

ID number when making your decisions. Since ID numbers will be randomly assigned prior

to the start of each Period, all voters are likely to have their ID numbers vary between Periods,

and, thus, it is impossible to identify subjects using their ID numbers.

In each round, after one voter is selected to propose a split but before he/she submits his/her

proposal, members of a group will have the opportunity to communicate with each other using

the chat box. The communication is structured as follows. On the top of the screen, each

member of the group will be told her ID number. You will also know the ID number of the

voter who is currently selected to make a proposal. Below you will see a box, in which you

will see all messages sent to either all members of your group or to you personally. You will

not see the chat messages that are sent privately to other members. In the box below that one,

you can type your own message and send it either to the entire group or to particular members

of the group. To select subjects that will receive your message, simply click on the buttons that

23

correspond to the ID numbers of the subjects you wish to send this message to and hit SEND.

You can send a message to all members of your group by clicking the SELECT ALL button.

The chat option will be available until the voter selected to make a proposal submits her pro-

posal. At this moment the chat option will be disabled.

Remember that in each Period subjects are randomly matched into groups and ID numbers

of the group-members are randomly assigned. Thus, your ID number is likely to vary from

Period to Period, and, therefore, it is impossible to identify your group-members using your ID

number.

At the conclusion of the experiment we will sum up all the tokens you earned in the experiment

and convert this amount into US dollars using the conversion rate 50 tokens = $1. In addition,

you will receive a $5 participation fee for completing the experiment.

You are not to reveal your (potential) earnings, nor are you to speak or communicate in any

other way with any other subject while the experiment is in progress. This is important to the

validity of the study and will be not tolerated.

We will now go slowly through one practice Period to familiarize you with the screen. After

the practice Period is over, we will start the experiment, in which you will play 15 Periods for

cash.

Review. Let’s summarize the main points:

1. The experiment will consist of 15 Periods. There may be several Rounds in each Period.

2. Prior to each Period, you will be randomly divided into groups of 5 voters each. Each

subject in a group will be assigned an ID number.

3. At the start of each Period, one subject in your group will be randomly selected to propose

a split of 250 tokens between the five of you. Before he/she submits his/her proposal,

members of the group can use the chat box to communicate with each other. You may

send public messages that will be delivered to all members of your group as well private

messages that will be delivered to members that you specify explicitly.

4. Proposals to each voter must be greater than or equal to 0 tokens.

24

5. If all 5 voters accept the proposal, the Period ends.

6. If one or more voters reject the proposal then a (potentially) new voter will be randomly

selected to make a proposal in the next Round of that Period.

7. The amount of money to be divided shrinks by 20% following each rejection of a proposal

in a given Period.

Are there any questions?

25