I need help with numbers 1,2,3,6 and 7.

Exercises 1. Use Preference Schedule II (Table 2) to determine which candidate wins according to the plurality method. Be sure to show all work. 2. Does the election depicted in Preference Schedule II have a Condorcet winner? If so, which candidate is the Condorcet winner? Be sure to show all work. 3. Use Preference Schedule II to determine which candidate wins according to the instant runoff method. Justify your reasoning.Number of votes 18 12 10 1st choice A B and choice D E B C B 3rd choice E D E E D 4th choice C C D B C 5th choice B A A A A A Table 2: Preference Schedule II. 4. In this question, we introduce a voting method used by several countries to determine winners in political elections. It is known as the Two Round Runoff Method. The method works as follows. In round one, only first choice votes are counted. If a candidate has a majority of first choice votes, then they win. If no candidate has a majority of first choice votes, then the method progresses to round two. In round two, you simulate an election between only the two candidates with the most 1st choice votes. Each ranked ballot counts as one vote for whichever of the two candidates was ranked higher on that ballot. The candidate with the most votes in round two wins. Use Preference Schedule II to determine which candidate won according to the two round runoff method. Be sure to show all work. 5. In this problem, you will design a preference schedule that is vulnerable to strategic voting. The math club is taking a vote on what one toping they should have on the pizza at their weekly meeting. The options are pepperoni, sausage, mushrooms, or olives. Twenty one members of the math club cast their ranked ballots and they decide to use the two round runoff method to determine a winner. Ana is one of the members casting a vote and a vegetarian. She loves mushrooms, is neutral toward olives and would be unhappy with either meat option. Construct two preference schedules: one where Ana votes honestly and pepperoni is the winner and one in which Ana votes strategically (but all other votes remain the same) and olives is the winner. Carefully justify your preference schedules by showing all work need to calculate the winners.7. "Voters have great difficulty ranking more than four or five candidates," said Steven Brams, a professor of politics at New York University. "So what do you do in a presidential primary where there are 17 Republican candidates? I consider myself an educated voter and I could not have ranked 17 candidates. It's forcing voters to do something that they have insufficient information to do." Professor Brams thinks a simple voting method called, approval rating, works even better than instant runoff voting. Brams argues that the approval rating method is one the best voting methods out there. In this exercise, you will learn how this method works. To understand approval voting, imagine your family of thirteen is ordering takeout. You have five different choices. In plurality voting, you can only vote for one; in ranked voting, you rank your preferences; in approval voting, you simply check off all the options that you find acceptable. Table 3 shows the results of your votes. What kind of food should your family go with under the approval rating method? Chinese Italian Mediterranean Mexican Sandwich Person 1 V Person 2 Person 3 Person 4 Person 5 Person 6 Person 7 Person 8 Person 9 Person 10 Person 11 Person 12 Person 13