Borda Count Method, Slides of Political Systems

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In this lecture we will cover the following

voting methods and fairness criterion.

Borda Count Method

Plurality-with-Elimination Method

Monotonicity Criterion

Borda Count Method

In the Borda Count Method each place on the ballot is

assigned points. The alternative receiving the most points

wins.

Borda point assignment for n alternatives

Last place 1 point Next-to-last place 2 points

Third place n-2 points Second place n-1 points First place n points

Problems with Borda Count

Math Lovers Club Election

The 11 members of the Math Lovers Club choose a president from among four candidates by preference ballot.

MLC Election Borda Count

Nbr of voters 6 2 3

1 st^ choice: 4 A: B: C:

2 nd^ choice: 3 B: C: D:

3 rd^ choice: 2 C: D: B:

4 th^ choice: 1 D: A: A:

What does A think of this?

Totals:

A:

B:

C:

D:

Winner:

Observations

Disadvantages of the Borda Count Method o Borda count method violates the majority criterion. o Consequently, Borda count method violates the Condorcet criterion. (Why? Explain.) Advantages of the Borda Count Method o Borda Count Method uses all the available voter preferences, not just first choices. o Borda Count Method often produces the best compromise winner.

So far, we have two voting methods applied to the MAC election and two different winners!

Voting Method Winner Plurality Alisha Borda Count Boris

MAC Election Plurality-with-Elimination

Number of voters 14 10 8 4 1

1 st^ choice A C D B C

2 nd^ choice B B C D D

3 rd^ choice C D B C B

4 th^ choice D A A A A

1. Candidates A^ B^ C^ D

1 st^ place votes

2. Candidates

1 st^ place votes

3. Candidates

1 st^ place votes

Winner:

Example: Young Liberals Election

The UAB Young Liberals elect a president of their club from among five candidates A, B, C, D, and E using the plurality-with-elimination method. There are 24 preference ballots.

YL Election Preference Schedule

Number of voters 8 6 2 3 5 1 st^ choice A B C D E 2 nd^ choice B D A E A 3 rd^ choice C E E A D 4 th^ choice D C B C B 5 th^ choice E A D B C

What is the maximum number of rounds that might be needed to decide the winner of this election by the plurality-with-elimination method?

Problems with Plurality-with-Elimination

The UAB Young Conservatives elect a president of their club from among three candidates A, B, and C using the plurality-with- elimination method. There are 29 preference ballots.

YC Election Preference Schedule

Number of voters 7 8 10 4 1 st^ choice A B C A 2 nd^ choice B C A C 3 rd^ choice C A B B

1. Candidates A^ B^ C

1 st^ place votes

2. Candidates

1 st^ place votes

Winner:

Because of election irregularities, the original election is declared void. Meanwhile, candidate C convinces the 4 voters represented by the last column of the preference schedule that she is better than candidate A. They switch their preference order to C, A, B. The re- election results are as follows.

YC Re-Election Preference Schedule

Number of voters 7 8 14 1 st^ choice A B C 2 nd^ choice B C A 3 rd^ choice C A B

1. Candidates A^ B^ C

1 st^ place votes

2. Candidates

1 st^ place votes

Winner:

Summary of Voting Methods

and Fairness Criteria

Fairness Criterion

Voting Method

Satisfied Violated

Plurality Majority Monotonicity Condorcet

Borda Count Monotonicity Majority Condorcet Plurality-with- Elimination Majority Monotonicity Condorcet

In the MAC election, we have used three voting methods and have three different winners!

Voting Method Winner Plurality Alisha Borda Count Boris Plurality-with- Elimination Dave