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In this lab you will experiment with different voting schemes. You have a number of web pages that explain different voting schemes that were also discussed in class.
Problem 1. Preference schedule for 5 beverages.
On the web pages for this lab, you are asked to determine the winner according to each of the different voting schemes, starting from a given preference schedule, that is, a table that gives you the numbers of voters who ranked the candidates in several possible orders.
Here is a different preference schedule for the same five beverages. The numbers in bold type across the top are the numbers of voters that ranked the 5 alternatives as listed in the columns below. There are 6 groups of preference rankings.
15
11
10
8
5
3
Killians
1
5
5
5
1
1
Molson
4
1
2
4
5
4
Samuel Adams
3
2
3
3
3
2
Guinness
5
4
1
2
2
5
Meister Brau
2
3
4
1
4
3
Work out the winner according to each of the five different voting schemes (described in the webpages for this lab). Attach pages showing how you got each of the answers below.
Answer:
Winner for:
Problem 2. Preference schedule for a different set of 5 beverages.
On the web page "More Practice" you can work another example, with the following preference schedule, which has 5 groups of preference rankings (where again, the numbers in bold type across the top give the numbers of voters that ranked the 5 alternatives as listed in the columns below):
5
2
3
3
4
Absolut
1
5
5
5
5
Jim Beam
2
1
2
3
2
Jose Cuervo
3
2
1
2
3
Jack Daniels
4
3
3
1
4
Southern Comfort
5
4
4
4
1
What are the results you get in this case?
Answer:
Winner for:
Problem 3. Preference schedule with 7 groups of preference rankings.
Now can you work out what the result would be from this preference schedule which has seven groups of voters:
13
12
10
9
7
4
2
Killians
4
4
1
2
3
4
2
Molson
1
5
5
1
5
5
5
Samuel Adams
5
1
2
5
2
2
4
Guinness
3
2
3
4
4
1
1
Meister Brau
2
3
4
3
1
3
3
Please give here the results you found:
Answer:
Winner for:
After you have worked all this through, please go to the web page "Make your own preference schedule".
Problem 4. Working within the applet's limitations.
The applet on this webpage only works when there are exactly six groups of voters (i.e. all the columns are filled in). If you have more than 6 groups, then this applet cannot be used.
a) If you have fewer than 6 groups of voters, however, this applet can be used (in a way other than by placing a zero for the number of people at the top of a column). Explain how.
Answer:
b) If you have less than 6 people voting, would it still be
possible to use this applet? Explain how you would do it (in a way
other than by placing a zero for the number of people at the top of a
column).
Answer:
Problem 5. Make your own preference schedule.
To start with, the table is already filled in. But on this web page, you can clear the table, and write in your own entries. Please adjust also the names of the alternatives: fill in the alternatives you chose when you polled friends to make up a preference schedule; don't forget to adjust the number of people who agreed on each ranking as well. If you have fewer than 5 alternatives, you will have some blank lines in your table. The software can deal with this - you may have to click a button twice if it tells you to do so. (Note that if you have only 3 alternatives, then you can have at most 6 possible rankings; you can also use this table for preference schedules with up to 5 alternatives, provided there are no more than 6 distinct ranking groups.)
Please repeat here the preference schedule you found:
The buttons on the web page tell you automatically what the winner is under the different schemes. Please give the results here:
Answer:
Winner for:
Do they all agree? Try experimenting with the preference schedule table. Can small changes in the numbers of people who voted one way rather than the other make a difference? (To try out changes, you don't have to clear the whole table and fill it in again; you can just type in only the changes you want, and click the different voting scheme buttons again.)
List here the changes you tried out, and their results under the different voting schemes. Discuss your results.
Answer:
Changes:
Winner for:
Changes:
Winner for:
Changes:
Winner for:
Problem 6. Name change for APC 199.
Two years ago a name change for APC 199 was considered, and votes were collected on three other possibilities.
a) The preference schedule after 28 people were asked was
7
6
5
4
3
3
Math at Work
3
1
1
3
2
2
Practical Mathematics
2
2
3
1
1
3
The Unreasonable Effectiveness of Mathematics
1
3
2
2
3
1
Try this in the applet table, and give the winners:
Answer:
Winner for:
b) Suppose now that one person in the right-most group makes a change, and decides to rank The Unreasonable Effectiveness of Mathematics third and Practical Mathematics first (instead of the other way around). Try it out to see what the winners are now:
Answer:
Winner for:
(As you know, we decided to keep the name "Math Alive" for the course.)
c) After all this experimenting, do you feel there is a scheme that is "better" than the others? Please explain!
Answer:
Problem 7. Example of sincere vs. insincere voting.
Sincere voting is voting according to one's own preferences and beliefs, while insincere voting is voting in an effort to get a particular overall outcome rather than specifically according to preferences and beliefs.
Describe a recent voting or decision-making situation (personal or general) in which voting sincerely would have led to a different outcome than voting insincerely.
Answer:
Problem C1. Effects of insincere voting.
For each of the voting schemes (plurality, plurality with runoff, sequential runoff, Borda count and Condorcet method) is it possible to change the outcome by insincere voting? If it is, give an example, if it isn't, explain why. (Attach extra sheets, if necessary.)
Answer:
| Start the Lab | Last modified: Wed Jul 30 17:03:30 EDT 2003 |