HW XXXXXXXXXXFederalism, Parliamentary Elections XXXXXXXXXXConsider a parliamentary election in a country with six political parties, who compete for 100 seats by adopting platform policies in a...

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HW XXXXXXXXXXFederalism, Parliamentary Elections

XXXXXXXXXXConsider a parliamentary election in a country with six political parties,
who compete for 100 seats by adopting platform policies in a one-dimensional
policy space. Citizens’ preferences are single-peaked, and each citizen votes
sincerely for the party whose platform is closest to her ideal policy. The outcome of
this is that parties ??, ??, ??, ??, ??, and ?? receive 26, 7, 14, 19, 12, and 22 seats,
espectively. From this position, parties must form a coalition government.
a. Is there a majority party?
. Identify all minimum winning coalitions.
c. Identify the minimum winning coalition(s) with the fewest parties.
d. Identify the minimum winning coalition(s) with the fewest seats.
e. Identify all minimum connected winning coalitions.
f. Identify the minimum connected winning coalition(s) with the fewest parties.
g. Identify the party of the median voter.
h. What coalition do you predict will form, and why?
XXXXXXXXXXConsider the following variation on the Downsian model: there are a
continuum [0,1] of policy alternatives and a continuum of voters with single-peaked
preferences distributed uniformly across [0,1] , plus two parties, ?? and ?? , with
preferences for left- and right-wing policies, respectively. Specifically, the two parties
have utility ???? = 1 − ?? and ???? = ?? , respectively, where ?? ∈ [0,1] is the policy
outcome. The two parties simultaneously adopt policy positions ???? and ????, and each
citizen then votes for whichever party is closest to his own ideal point. That is, a
fraction ???? = �
????+????
2
− 0� vote ?? and a fraction ???? = �1 −
????+????
2
� vote ?? . The
esulting policy outcome is a weighted average ?? = ???????? + ???????? of the two parties’
platforms.
a. (+2) Before working things out formally, conjecture what platforms the
parties will adopt in equili
ium. What is the basis for your conjecture?
. (+4) Now work things out: in equili
ium, what platforms do the
parties adopt?
c. (+2) How does this compare with the predictions of a standard
Downsian model? What is an intuition for why they are the same, or why
they are different?
    HW XXXXXXXXXXFederalism, Parliamentary Elections
Answered 1 days AfterApr 09, 2022

Solution

Komalavalli answered on Apr 11 2022
10 Votes
Parties
A,B,C,D,E,F
Votes receive:
    A – 26
    B – 7
    C – 14
    D – 19
    E – 12
    F – 22
a.) Based on the given information we can say that the majority party is A.
.) Minimum winning coalition is D and F = 41, C and F = 14+22 =36 ,F and B = 22+7 =29
c.) Minimum winning coalition with few parties is D and F = 41
d.) Minimum winning coalition with few seats is F and B = 29
e.) Minimum connected winning coalition D and F = 41
f.) Minimum connected winning coalition with few parties is D and F = 41
g.) The party of median voter is C
h.)...
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