Question

Consider again the election in question HW3, under the Borda Count method.a. Is there a Condorcet candidate in this election, and how can you tell?b.Does the result of this election under the Borda Countmethod violate the Condorcet Criterion? Explain briefly why or whynot.

Answer 1

Answer:

a. yes there is a condorcet candidate in the election and is Ann. She defeated every other candidates in head to head competition.

b. The result does not violate the condorcet criterion.

Explanation:

based on the result of the election, Ann defeated every other candidates in the election head to head.

Ann vs. Bob:

11 + 6 = 17 voters rank Ann higher than Bob, while 7 + 8 + 1 = 16 voters rank Bob higher than Ann. Therefore Ann defeats Bob head to head, i.e. a majority of voters prefer Ann over Bob.

Ann vs. Claire:

11 + 6 = 17 voters rank Ann higher than Claire, while 7 + 8 + 1 = 16 voters rank Claire higher than Ann. Therefore Ann again defeats Claire head to head, i.e. a majority of voters prefer Ann over Claire. Claire is now out of the running to be a Condorcet candidate.

Ann vs. Dave:

7 + 8 + 6 = 21 voters rank Ann higher than Dave, while 11 + 1 = 12 voters rank Dave higher than Ann. Thus Ann defeats Dave head to head, i.e. a majority of voters prefer Ann over Dave. Behold!

Ann defeats all opponents in head to head competition, and is therefore a Condorcet candidate. According to the Condorcet criterion, Ann should win. [In general, in order to find out if a Condorcet candidate exists, we consider head to head competitions between candidates until a Condorcet candidate appears (because one candidate defeats all others head to head), or we find that there is none (because every candidate loses at least one head to head matchup). So Ann should win.

Answer 2

Answer:

a)Not enough information

b)A Borda count election will likely violate the Condorcet Criterion. There usually is a Condorcet winner in a borda count election, however, this candidate will not be declared winner due to the point tally at the end of a borda count election.

Explanation:

The question fails to provide details of the election referenced in "question HW3". Notwithstanding, an attempt has been made to answer said question based on general principles

Borda count is a voting system in which voters rank the candidates in an order of preference. Points are given for the position of a candidate in a voter's rank order. The candidate with the most points wins.

The Borda count does not comply with the Condorcet criterion in the following case. Consider an election consisting of five voters and three alternatives, in which three voters prefer A to B and B to C, while two of the voters prefer B to C and C to A. The fact that A is preferred by three of the five voters to all other alternatives makes it a Condorcet Winner. However the Borda count awards 2 points for 1st choice, 1 point for second and 0 points for third. Thus, from three voters who prefer A, A receives 6 points (3 x 2), and 0 points from the other two voters, for a total of 6 points. B receives 3 points (3 x 1) from the three voters who prefer A to B to C, and 4 points (2 x 2) from the other two voters who prefer B to C to A. With 7 points, B is the Borda winner.