- For a given issue dimension on a scale of 1 to 10, let us consider the following distribution of voters' preferences:
Scale: 1 2 3 4 5 6 7 8 9 10 No. of voters: 3 5 15 20 15 12 10 10 7 3 - Which is the median position?

- Assume that voters with positions from 1 to 5 can be called on the “left,” while those from 6 to 10 are on the “right.” Are there more people on the left or on the right?

- Suppose that this electorate votes for two alternative parties, X on the left and Y on the right, placed respectively at X = 2 and Y = 7. Which party wins a majority?

- Suppose that a third, centrist party, Z, is created and adopts a position at 5. In a three-party competition, which party wins more votes?

- Suppose that now the two parties created earlier get to move toward more centrist positions, X = 3 and Y = 6. Meanwhile, Z remains at 5. In the new three-party competition, which party wins the most votes?

- Suppose that Y’s move away from its traditional rightist position causes a radical branch to leave the party and create a new party placed at the extreme rightist position, W = 10. The other three parties stay at their positions as in question e. In a four-party competition, which party wins more votes?

- Do you have any comments about these moves and results?

- Which is the median position?
- For a given issue dimension on a scale of 1 to 8, let us consider the following distribution of voters’ preferences:
Scale: 1 2 3 4 5 6 7 8 No. of Voters: 7 11 15 16 18 16 11 6 - Which is the median position?

- Suppose that this electorate votes for two alternative parties, X on the moderate left and Y on the right, placed respectively at X = 3 and Y = 7. Which party wins a majority?

- If a third party wants to enter the competition and win the election against the other two parties, where ought to locate itself?

- Which is the median position?
- Calculate the volatility index for two recent United States presidential elections, as for the following results:
Year: 2004 2008 Democrat 48.3 52.9 Republican 50.7 45.7 Others 1.0 1.4 - Calculate the volatility index for two recent parliamentary elections in Germany, as for the following results:
Year: 2005 2009 Christian-democrat & Bavarian 35.2 33.8 Free-democrat 34.2 23.0 Socialist/Left 8.1 11.9 Green 8.1 10.7 Others 4.0 6.0