Given the replica set shown, which member is most likely to be elected if an election takes place? (Select one.)A. Priority 99B. Priority 50C. Priority 1

Consider the following preference orderings of 1000 agents for candidates O = {a, b, c}147 agents: a b c401 agents: b a c32 agents: c b a420 agents: a c b(a) Who wins under Plurailty? Explain.(b) Who wins in the Borda voting? Explain.(c) Who is the Condorcet winner? Explain.(d) If you are the agenda setter and strongly prefer b. What ordering would you chose forpairwise elimination such that b wins.

Consider the given preference schedule with the number of voters ranking the candidates in a local community plebiscite.Rank13155121stWXYY2ndXWZX3rdZZXW4thYYWZ21. Determine the winner by Majority Rule.Group of answer choicesNo winnerCandidate YCandidate XCandidate W

The student government is holding elections for president. There are 4 candidates (labeled A, B, C, and D for convenience). The preference for the election is as follows:Candidates Ranking Ranking Ranking Ranking Ranking RankingA 4 3 2 1 1 3B 3 1 3 3 4 2C 1 2 4 2 3 4D 2 4 1 4 2 1# of votes 120 50 40 90 60 100Questions:How many voters voted in this election?How many voters are needed for a majority? For a plurality?

In modern American politics, most party nominees for elected public offices are chosen through:Select one:a. leadership votes.b. primary elections.c. conventions.d. party caucuses

Consider majority voting over pairwise alternatives subject to agenda manipulation. Use thefollowing voting rules and preference profiles. There are three propositions to choose amongcandidates, A, B, and C. There are three voters, 1, 2, 3. The notation indicates strictpreference.Rules: There is a designer who sets the agenda, the order of voting. She announces twopropositions to choose between; the winner of that vote faces a runoff against the remainingalternative.Profile I:Voter 1: A B CVoter 2: B C AVoter 3: C A BProfile II:Voter 1: A B CVoter 2: B C, B A, (C vs. A preference is unspecified)Voter 3: C B AClaim: Under Profile I the designer can arrange that any one of the three propositions bethe winner by the chair’s choice of the order of voting.Under Profile II, the choice is independent of the order of the agenda.(a) Demonstrate the claim.(b) Show that Profile II fulfills the concept of single peaked preferences and that Profile Idoes not.