Difference between revisions of "Shepsle, K. (1979), Institutional Arrangements and Equilibrium in Multidimensional Voting Models"
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| − | In first stage we vote on <math>x_{i}</math>. and obtain policy equal to median voters bliss point <math>x_{m}</math>. In second stage we vote on <math>y_i</math> and obtain policy equal to median voters bliss point <math>y_m</math>, so we obtain unique outcome <math>z=(x_m, y_m)</math> | + | In first stage we vote on <math>x_{i}</math>. and obtain policy equal to median voters bliss point <math>x_{m}</math>. In second stage we vote on <math>y_i</math> and obtain policy equal to median voters bliss point <math>y_m</math>, so we obtain unique outcome <math>z=(x_m, y_m)</math>. Notice, that with this sequential voting, we do not get the median policy, but the median policy by dimension. |
Revision as of 15:26, 14 May 2012
Back to BPP Field Exam Papers 2012
Paper's Motivation
McKelvey's Chaos Thm: In a multidimensional spacial settings, unless points are distributed in a rare way (like radially symmetric), there is no Condorcet winner, and whoever controls the order of voting can make any point the final outcome.
In response, the author considers voting on one 'attribute' or dimension at a time.
Model
Consider a two-dimensional case. Any policy [math]z_{i}[/math] is characterized by coordinates [math](x_i, y_i)[/math].
Result
In first stage we vote on [math]x_{i}[/math]. and obtain policy equal to median voters bliss point [math]x_{m}[/math]. In second stage we vote on [math]y_i[/math] and obtain policy equal to median voters bliss point [math]y_m[/math], so we obtain unique outcome [math]z=(x_m, y_m)[/math]. Notice, that with this sequential voting, we do not get the median policy, but the median policy by dimension.
