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Bargaining in Legislatures over Particularistic and Collective Goods
Unformatted Document Text:  20 legislature size, because there are no particularistic goods given to non-proposers and because the next proposer is already selected at the time of the pivotal decision (rather than based on a probabilistic function of being chosen from among the other n-1 members). Proposition 3 states that the proposer receives no extra benefits in the collective part of the equilibrium, receives greater benefits as α increases and δ decreases in the particularistic part, and receives greater benefits as q increases and δ decreases in the mixed part. Additionally, the proposal power benefits increase in α in the mixed case only for certain parameter values. All of these conditions continue to hold in the open rule case, for the same reasons. In the particularistic case, the utility of the proposer’s greater particularistic benefits rises as legislators value such goods more highly. But the proposer receives fewer such benefits when other legislators are more patient – both in the particularistic and the mixed cases. Also in the mixed case, as the return on collective goods increases, the proposer is able to put less in the collective, yielding a greater particularistic utility gain for himself. Finally, as in the closed rule case, the complex relationship with respect to α is due to the proposer’s particularistic-goods-based utility increasing in α, partially or more-than-fully offset by his need to put more in the collective good as α increases. Finally, as in the closed rule case, the effect of the parameters in moving among cases is different than their effect within each case, which could lead to some interesting empirical phenomena. For example, as the value of particularistic goods relative to collective goods ( α) rises, we move from the collective part of the equilibrium to the mixed part to the particularistic part. Within the mixed part, however, spending on the collective increases along with α. Thus the following pattern occurs: complete spending on the collective good for low values of α, until we reach the mixed part. Then collective spending dips dramatically, rising again as α increases

Authors: Volden, Craig. and Wiseman, Alan.
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20
legislature size, because there are no particularistic goods given to non-proposers and because
the next proposer is already selected at the time of the pivotal decision (rather than based on a
probabilistic function of being chosen from among the other n-1 members).
Proposition 3 states that the proposer receives no extra benefits in the collective part of
the equilibrium, receives greater benefits as
α increases and δ decreases in the particularistic
part, and receives greater benefits as q increases and
δ decreases in the mixed part. Additionally,
the proposal power benefits increase in
α in the mixed case only for certain parameter values.
All of these conditions continue to hold in the open rule case, for the same reasons. In the
particularistic case, the utility of the proposer’s greater particularistic benefits rises as legislators
value such goods more highly. But the proposer receives fewer such benefits when other
legislators are more patient – both in the particularistic and the mixed cases. Also in the mixed
case, as the return on collective goods increases, the proposer is able to put less in the collective,
yielding a greater particularistic utility gain for himself. Finally, as in the closed rule case, the
complex relationship with respect to
α is due to the proposer’s particularistic-goods-based utility
increasing in
α, partially or more-than-fully offset by his need to put more in the collective good
as
α increases.
Finally, as in the closed rule case, the effect of the parameters in moving among cases is
different than their effect within each case, which could lead to some interesting empirical
phenomena. For example, as the value of particularistic goods relative to collective goods (
α)
rises, we move from the collective part of the equilibrium to the mixed part to the particularistic
part. Within the mixed part, however, spending on the collective increases along with
α. Thus
the following pattern occurs: complete spending on the collective good for low values of
α, until
we reach the mixed part. Then collective spending dips dramatically, rising again as
α increases


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