Technical Appendix for “Voting, Speechmaking, and the Dimensions of Conflict in the US Senate”
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چکیده
We include here several technical appendices. First, we formally derive the expressions for c l and b vote p that appear in section two of the paper. The next contains some details on the choice theoretic model underlying the standard topic model. The remainder contain the details for implementing the SFA model. A The Legislator and Proposal Intercepts from the Voting Model Let’s start with the legislator’s utility from the “aye”: Ul({rpd}d=1) = − 1 2 D ∑ d=1 ad(rpd − xld) + ξ̃ lp (1) and “nay” alternatives: Ul({qpd}d=1) = − 1 2 D ∑ d=1 ad(qpd − xld) + ξ̃ lp (2) Next, let’s calculate the difference between these expressions to get the legislator’s preference intensity for the “aye” outcome. Substituting from expressions (1) and (2) we have: V ∗ lp = Ul({rpd}d=1)− Ul({qpd}d=1) = − 2 D ∑ d=1 ad(rpd − xld) + ξ̃ lp − ( − 2 D ∑ d=1 ad(qpd − xld) + ξ̃ lp ) = D ∑ d=1 ad 2 (q pd − r pd) + D ∑ d=1 ad 2 × 2xpd (rpd − qpd) } {{ } gvote pd +ξ̃ lp − ξ̃ nay lp = ( D ∑ d=1 ad 2 (q pd − r pd) + E{ξ̃ aye lp } − E{ξ̃ nay lp } ) } {{ } cvote l +b vote p + D ∑ d=1 ad 2 × 2xpd (rpd − qpd) } {{ } gvote pd − ( ξ̃ lp − ξ̃ aye lp + E{ξ̃ aye lp } − E{ξ̃ nay lp } ) } {{ } ̃lp (3)
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Voting, Speechmaking, and the Dimensions of Conflict in the US Senate
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