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References in periodicals archive ?
If N [greater than] 2, then ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) is a majority rule equilibrium only if [Mathematical Expression Omitted] and [Mathematical Expression Omitted].
If n = 2, then there exists a unique majority rule equilibrium.
A1) What are the properties of majority rule equilibrium in a district?
The answer to A1 is that a majority rule equilibrium exists within each district and coincides with the ideal confederation of the median value of [Theta] in that district.
As is typical in such cases, a majority rule equilibrium may fail to exist due to majority voting cycles.
Thus, a strict majority prefers ([Mathematical Expression Omitted], 0) to ([Beta][prime], [Mu][prime]), which cannot be a majority rule equilibrium.
Since we have supposed that ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) is a majority rule equilibrium, it must be the case that [Mathematical Expression Omitted] for 50% of the voters and [Mathematical Expression Omitted] for 50% of the voters If not, then one could either increase or decrease [Beta] slightly, keeping [Mu] fixed at [Mathematical Expression Omitted], and a majority would vote for the new proposal.
Therefore, ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) cannot be a majority rule equilibrium if [Mathematical Expression Omitted].
Finally, suppose that ([Mathematical Expression Omitted], 0) is a majority rule equilibrium, where [Mathematical Expression Omitted].
Obviously, no other point can be a majority rule equilibrium in this case.
Therefore, ([Mathematical Expression Omitted], 0) is a majority rule equilibrium.