Snyder (1991) - On Buying Legislatures - Revision history

Ed at 23:15, 29 September 2020

2020-09-29T23:15:15Z

Maintenance script at 17:23, 29 September 2020

2020-09-29T17:23:51Z

Maintenance script at 17:20, 29 September 2020

2020-09-29T17:20:42Z

Maintenance script at 17:13, 29 September 2020

2020-09-29T17:13:55Z

Maintenance script at 17:07, 29 September 2020

2020-09-29T17:07:01Z

Ed at 16:48, 29 September 2020

2020-09-29T16:48:14Z

imported>Bo: /* Proposition 2 */

2011-11-04T07:09:28Z

Proposition 2

imported>Bo: /* Proposition 2 */

2011-11-04T07:08:58Z

Proposition 2

imported>Bo at 07:07, 4 November 2011

2011-11-04T07:07:52Z

imported>Bo at 23:37, 7 October 2011

2011-10-07T23:37:33Z

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 {{Article
 |Has page=Snyder (1991) - On Buying Legislatures
-|Has title=On Buying Legislatures
+|Has bibtex key=
 |Has author=Snyder
 |Has year=1991

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 |Has page=Snyder (1991) - On Buying Legislatures
 |Has title=On Buying Legislatures
-|Has author=
+|Has author=Snyder
 |Has year=1991
 |In journal=

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 |Has title=On Buying Legislatures
 |Has author=
-|Has year=
+|Has year=1991
 |In journal=
 |In volume=

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 {{Article
 |Has page=Snyder (1991) - On Buying Legislatures
-|Has title=
+|Has title=On Buying Legislatures
 |Has author=
 |Has year=

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 {{Article
-|Has page=
+|Has page=Snyder (1991) - On Buying Legislatures
 |Has title=
 |Has author=

← Older revision		Revision as of 16:48, 29 September 2020
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		+	\|In number=
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		+	}}
	[http://www.edegan.com/wiki/images/d/da/On_Buying_Legislatures_by_James_Snyder.pdf Full-text PDF]		[http://www.edegan.com/wiki/images/d/da/On_Buying_Legislatures_by_James_Snyder.pdf Full-text PDF]

← Older revision		Revision as of 07:09, 4 November 2011
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−	The more interesting case is when <math>-L<s<L</math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L</math>; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.	+	The more interesting case is when <math>-L<s<L</math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L</math>; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/\partial s<0, \partial x_{D}^{\ast}/\partial L>0</math> and <math>{\partial} x_{D}^{\ast}/\partial \alpha<0</math>.

	====Rui's Notes ====		====Rui's Notes ====

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-The more interesting case is when <math>-L<s<L</math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.
+The more interesting case is when <math>-L<s<L</math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L</math>; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.
 ====Rui's Notes ====
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 Groseclose:
 * Models suggest cut points in models with no vote buying and incomplete OR complete info.
 * For models with vote buying, cut point appears in complete information but not incomplete information.
 ==Without Price Discrimination (2) ==

← Older revision		Revision as of 07:07, 4 November 2011
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−	The more interesting case is when <math>-L<s<L<math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.	+	The more interesting case is when <math>-L<s<L</math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.

	====Rui's Notes ====		====Rui's Notes ====

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 The model examines a policy space <math>x\in R</math> and a lobbyist's efforts to bribe legislators to adopt a policy near his ideal point. The lobbyist's utility function is <math>u(x,B)=-(x-L)^{2}</math>, where x is the policy chosen, L is the lobbyist's ideal point and B is the total number of bribes paid to legislators. The lobbyist is assumed to have an infinite budget.
-The legislature is infinitely sized and consists of individual legislators whose ideal points <math>z</math> are distributed uniformly over [-0.5,0.5] (so z~<math>U[-0.5,0.5]</math>). Legislators preferences preferences are also negative quadratic. A legislator will choose policy x over policy y iff <math>b_{x}-\alpha(x-z)^{2}>b_{y}-\alpha(y-z)^{2}</math>, where <math>b_{x},b_{y}</math> refer to the amount of bribes offered for voting for position x or y, and z is the legislator's ideal point. The parameter <math>\alpha</math> represents the "intensity" of the legislator's preferences -- ie, how much he cares. One might alternatively think of <math>\alpha</math> as how much his constituents care.
+===Rui's Notes about what the setup means===
 ==With Price Discrimination (1) ==
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 Suppose s is the status quo and let <math>x>s</math> be an alternative proposal. If <math>0<(x+s)/2\leq 1/2</math>, then the least cost payment function <math>b_{D}(\dot,x,s)</math> which insures that x ties or defeats s is given by the following: If <math>z\in[0,(s+x)/2], b_{D}(z,x,s)=\alpha(x^2-s^2-2(x-s)z)</math>, and <math>b_{D}(z,x,s)=0</math> otherwise. Proof is in the appendix and is not complicated. Note that the above discusses proposals <math>x</math> only when <math>0<(x+s)/2\leq 1/2</math>, because otherwise the proposal passes without any bribes.
 Note: Highest bribes paid to legislators whose ideal points are close to the median, but close to his side of the median. The lobbyist does not bribe his close supporters, but rather his marginal supporters. Close supporters will vote for a motion even without bribes.
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 The more interesting case is when <math>-L<s<L<math>. Here, there exists an <math>s_{D}\in(0,L)</math> such that (i) if <math>-L<s<s_{D}</math>, then the lobbyist's optimal proposal <math>x_{D}^{\ast}</math> is unique, and satisfied <math>\max(s,-s,s_{D})<x_{D}^{\ast}<L; and (ii) if <math>s\geq s_{D}</math>, then the lobbyist does nothing and s remains the policy outcome. In case (i), <math>\lim_{s\rightarrow s_{D}}x_{D}^{\ast}=s_{D}</math> and has comparative statics of <math>\partial x_{D}^{\ast}/partial s<0, \partial x_{D}^{\ast}/partial L>0</math> and <math>{\partial} x_{D}^{\ast}/partial \alpha<0</math>.
 ==Without Price Discrimination (2) ==
 The paper continues to solve for equilibrium strategies in which the lobbyist does NOT know the individual legislator's ideal points and must offer all legislators the same bribe.