no offer. We describe the case where F1 has the first opportunity to make an offer followed by
factions F2 and F3, respectively. In other words, the only difference between the three factions is
the order in which they make offers.
[Figure 1 here.]
Offers are of the following form: “If you, faction F1, coalesce with us, faction F2, then
one of our members shall be House conferee and you shall receive utility/power transfer c
2
1
∈ℜ
.”
We denote offers with subscripts representing the faction that makes an offer and superscripts
representing the faction to whom the offer is made. The transfer represents leadership positions,
compromise on policy dimensions not modeled here and office perquisites – items that can
reward one faction for supporting another. Considered as a whole, the power sharing arrangement
in our model is a package that includes the assignment of procedural rights and the distribution of
other resources that House members value.
The faction to whom an offer is made can either accept or reject it. If it is accepted, then a
member of the offering faction becomes the House conferee in the next stage of the game, the
faction who accepted the offer receives something of value in return, and the game moves directly
to the conference stage. If no faction makes an acceptable offer, then the game ends with
legislative outcome is L=q.
Discussion
The idea that conference committee dynamics factor into the House’s organizational
decision making follows Shepsle and Weingast’s (1987) theory. Like them, we portray
conference committees as providing ex post vetoes on House bills. They presume, however, that
“Conferees …come principally from the committees of jurisdiction at the suggestion of those
committees’ chairpersons…the views of the committees chairpersons are dominant” (Shepsle &
6
We also assume the following tie-breaking rule for reactions to an offer: if an offer yields the same utility
as the status quo, accept the offer; if an offer from F1 yields the same utility as an offer from another
faction, then accept F1’s offer. These assumptions simplify our equilibrium statements but do not affect our
main results.
7
Convention