Informational loss in bundled bargaining
| Published date | 01 July 2013 |
| Author | Hülya Eraslan,Ying Chen |
| DOI | 10.1177/0951629813482232 |
| Date | 01 July 2013 |
| Subject Matter | Articles |
Article
Informational loss in bundled
bargaining
Journal of Theoretical Politics
25(3) 338–362
©The Author(s) 2013
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DOI:10.1177/0951629813482232
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Ying Chen
Arizona State University, Tempe, AZ, USA
Hülya Eraslan
Johns Hopkins University, Baltimore, MD, USA
Abstract
We analyze a legislative bargaining game over an ideological and a distributive issue. Legislators
are privately informed about their ideological positions. Communication takes place before a
proposal is offered and majority-rule voting determines the outcome. We compare the outcome
of the ‘bundled bargaining’ game in which the legislators negotiate over both issues together to
that of the ‘separate bargaining’ game in which the legislators negotiate over the issues one at
a time. Although bundled bargaining allows the proposer to use transfers as an instrument for
compromise on the ideological issue, we identify two disadvantages of bundled bargaining under
asymmetric information: (i) ‘risk of losing the surplus’ (failure to reach agreement on ideology
results in the dissipation of the surplus under bundled bargaining, but not under separate bargain-
ing); (ii) ‘informational loss’ (the legislators may convey less information in the bundled bargaining
game). Even when there is no risk of losing the surplus, the informational loss from bundling can
be sufficiently large that it makes the proposer worse off.
Keywords
Cheap talk; communication; information; legislative bargaining
1. Introduction
Legislative policy making typically involves bargaining over multiple issues. In some
cases, the issues are not easily separable, so they are decided together. In others there
does not seem to be an obvious link between the issues. Forexample, in the recent health-
care legislation in the US, whether to provide public funding for abortion or not was an
issue that seems orthogonal to other provisions in the bill such as whether to ban denial
Corresponding author:
Hülya Eraslan, Johns Hopkins University, Baltimore, MD 21218, USA.
Email: eraslan@jhu.edu
Chen and Eraslan 339
of insurance coverage due to pre-existing conditions. Yet at some point, the passage of
the entire healthcare bill hinged on the abortion language.1One benefit of bundling
unrelated issues in bargaining is that it provides more opportunities for legislators to
reach compromise. Indeed, in an environment of complete information, Jackson and
Moselle (2002) show that negotiating over multiple issues simultaneously is better than
negotiating over them separately. However, in practice, legislators often have private
information about their preferences. Is bundled bargaining still better than separate
bargaining under asymmetric information?
To tackle this question, we introduce a bargaining model over a distributive and an
ideological issue where the legislators are privately informed about their positions on a
unidimensional ideological spectrum, and communication takes place before a proposal
is offered. Specifically, in our model: (1) three legislators bargain over an ideological
and a distributive decision; (2) one of the legislators, called the chair, is in charge of
formulating the proposal; (3) each legislator other than the chair is privately informed
about his own preferences; (4) legislators send costless messages (cheap talk) to the chair
before a proposal is offered; (5) majority-rule voting determines whether the proposal is
implemented. In what we call the ‘bundled bargaining’ game, the chair makes a proposal
on the ideological dimension and the distributive dimension simultaneously, and the two
dimensions are accepted or rejected together. By contrast, in the ‘separate bargaining’
game, the chair makes one proposal on only the ideological dimension and another on
only the distributive dimension, and each proposal is voted on separately. Unlike in the
bundled bargaining game, it is possible in this game that a proposal on one dimension
passes while the proposal on the other dimension fails to pass.
Since each legislator’s ideological position is his private information, the chair is
unsure about what is the optimal policy to propose and how much private benefit she has
to offer to a legislator to gain his support for a policy decision. But if the legislators’
communication is informative, then the chair can use their messages to make inferences
about the legislators’ ideological positions (which we call their types). We show that
under some conditions, equilibrium messages from the legislators may convey limited
information and dispel some uncertainty about their preferences. In particular, in the bun-
dled bargaining game, a legislator can signal whether he will ‘cooperate,’ ‘compromise,’
or ‘fight,’ depending on how close his position ist othe chair’s. If either legislator signals
his willingness to cooperate, the chair responds by proposing her ideal policy without
giving out any private benefit. If both legislators make tough demands by sending the
‘fight’ message, the chair gives up on the ideological issue and extracts the whole surplus
in the distributive dimension. Otherwise, she proposes a compromise policy somewhere
in between the status quo and her ideal and gives out some private benefit. Only the pro-
posal induced by a ‘compromise’ message may fail to pass in equilibrium whereas the
proposals induced by the ‘cooperate’ or ‘fight’ messages always pass.
In a separate bargaining game, the chair is unable to use private benefits to reach
compromise on ideological decisions, so she captures the entire surplus on the dis-
tributive dimension. But her proposal on the ideological dimension may still depend
on the legislators’s messages. We show that legislators can signal whether they will
‘cooperate’ or ‘compromise.’ Similar to the bundled bargaining game, if either legislator
signals willingness to cooperate, the chair responds by proposing her ideal policy.If both
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