# Suppose we have single-peaked voters located on a one-dimensional left-right dimension.Suppose that

Suppose we have single-peaked voters located on a one-dimensional left-right dimension.Suppose that voters vote for the candidate closest to them in distance and that they flip a coin iftwo candidates are equally distant (so that we can count one-half vote for each candidate fromthat voter). Further suppose that we know which party each voter belongs to, and that the elevenvoters are located as follows:VoterAlbertBethCurtEusticeFrankGailHopeIvanJoeKatherineLarryIdeological Location113466789910PartyDDDDDRRRRRRThe letter â€œDâ€ stands for â€œDemocratâ€ and the letter â€œRâ€ for Republican. These are the partyaffiliations of the voters.a) [2 pts] Given this distribution of voters, where should the two parties, Democrats andRepublicans, locate in a general election (where everyone can vote) if they can locateanywhere they want to and they know this distribution of voters and all they care about iswinning elections.b) [4 pts] Suppose there are primaries in each party in which only the members of that partycan vote:i. If there are two candidates in the Democratic primary, where should they locate ifthey can move anywhere they want to and if they only care about winning theprimary?j. If there are two candidates in the Republican primary, where should they locate ifthey can move anywhere they want to and if they only care about winning theprimary? Write in space below:c) [4 pts] Suppose once the partyâ€™s candidates have taken a position in the primary as in (b)above, they must stay there. Who will win the general election (when everybody canvote and one candidate emerged victorious in each partyâ€™s primary)? Indicate what thevote will be in the general election for each candidate.d) [3 pts] NOW suppose that as in (b) above there are primaries in each party but theDemocratic party primary is uncontested (no opposition for the candidate) while theRepublican party primary is contested with two candidates.i. [1 pt] If there is only one candidate in the Democratic primary (which assures thevictory of that candidate), where should the candidate locate if he or she can moveanywhere and would also like, if possible, to be in a good position for the generalelection?j. [2 pts] If there are two candidates in the Republican primary, where should theylocate if they can move anywhere they want to and if they must first win theprimary, but would also like, if possible, to be in a good position for the generalelection?e) [2 pts] Suppose once the partyâ€™s candidates have taken a position in the primary as in (d)above they must stay there. Who will win the general election (when everybody canvote)? Indicate what the vote will be (for each party) in the general election.f) [5 pts] Comment on this: â€œPrimaries can put a partyâ€™s candidates in a bad position to winthe general election.â€ Is this always true? What has to be true of the party for it to betrue?

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