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Grossman Helpman (2001) - Special Interest Politics Chapters 4 And 5 (view source)
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|Has page=Grossman Helpman (2001) - Special Interest Politics Chapters 4 And 5
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|Has article title=Special Interest Politics Chapters 4 And 5
|Has author=Grossman Helpman
|Has year=2001
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*This page is referenced in [[BPP Field Exam Papers]]
These chapters reference:
*Crawford, Vincent P. and Joel Sobel (1982), "Strategic Information Transmission", Econometrica, Vol. 50, No. 6 (Nov.), pp. 1431-1451 [http://www.edegan.com/pdfs/Crawford%20Sobel%20(1982)%20-%20Strategic%20Information%20Transmission.pdf pdf]
*Krishna, Vijay and John Morgan (2001), "A Model of Expertise", The Quarterly Journal of Economics, Vol. 116, No. 2 (May), pp. 747-775 [http://www.edegan.com/pdfs/Krishna%20Morgan%20(2001)%20-%20A%20Model%20of%20Expertise.pdf pdf]
==Abstract==
:<math>\theta_2 \ge 2\theta_1 +4\delta - \theta_{min}\,</math>
If the truth is in <math>\theta_2\,</math>, then the SIG would prefer to report this rather than <math>\theta_1\,</math> iif: :<math>(\theta_2 + \delta) - \frac{(\theta_1 + \theta_2)}{2} \le (\theta_1 + \delta) - \frac{(\theta_{min} + \theta_1)}{2}\,</math> This solves to: :<math>\theta_2 \le 2\theta_1 +4\delta - \theta_{min}\,</math> Putting these two together we have that: :<math>\theta_2 = 2\theta_1 +4\delta - \theta_{min}\,</math> More generally, as these equations have to hold for each and every interval: :<math>\theta_j = 2\theta_{j-1} +4\delta - \theta_{j-2}\,</math> There are two boundaries where <math>\theta_n = \theta_{max}\,</math> and <math>\theta_0 = \theta_{min}\,</math>, which can be used together to solve the general solutions for <math>\theta_j\,</math>: :<math>\theta_j = \frac{j}{n}\theta_{max} +\frac{n-j}{n}\theta_{min} -j(n-j)\delta\,</math> Considering that <math>\theta_1 > \theta_{min}\,</math> it must be the case that: :<math>2n(n-1)\delta < \theta_{max} - \theta_{min}\,</math> There are some things to note:#Partitions get bigger to the right#There always exists an equilibrium with <math>n=1\,</math> - it is the babbling equilibrium#As <math>\delta\,</math> gets smaller, more partitions can be sustained. #If <math>n\,</math> partitions can be sustained then so can <math>k<n\,</math>. ===Welfare considerations=== More partitions are more informative and yield greater welfare. The equilibrium with the greatest number of partitions is the one preferred by both the SIG and the policymaker. ===Two Lobbies - Like bias=== Suppose that <math>0 < \delta_1 \le \delta_2\,</math> so that SIG 1 is more moderate. There are three cases to consider: secret meetings, private meetings and public meetings. With secret meetings the SIGs do not know if the other SIG has met with the policy maker, and with private meetings they know the meeting has taken place but do not know the contents. ====Secret Meetings==== The SIGs behave as if they alone are providing information and the policy maker combines informations. The combined information is more informative, but there is no actual equilibrium (because of the implicit assumption of no strategic response). ====Private Meetings==== Using each SIG to discipline the other, the policy maker can gain full relevation. However, this is a fragile equilibrium. ====Public Meetings==== When information is reported sequentially there can not be full relevation. There can be a partition equilibrium from combining the two reports. The number of partitions can not be greater than the number that would arise from a single lobby with the smaller (more moderate) bias, and so both would agree to allow only this SIG to report. ===Two Lobbies - Opposite Bias=== With two lobbies where <math>\delta_1 < 0\,</math> and <math>\delta_2 > 0 \,</math> the policy maker can use the competition to become more informed, though not fully informed. Crucially, define <math>\theta_2^* \equiv \theta_{max} - \delta_2\,</math> It is not possible to reveal the state of the world when <math>\theta > \theta_2^*\,</math>. See the paper for further information. ===Multi-dimensional Information=== When the groups differ in their relative bias on a single dimension there is full revelation. By choosing new dimensions through the multidimensional space it is possible (given the necessary dimensionality of the choices and alignment conditions) to establish full relevation through-out the space.
