Shepsle, K. (1979), Institutional Arrangements and Equilibrium in Multidimensional Voting Models

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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]