## Quantitative Measurements

1. 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

1. Which is the median position?
2. 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?
3. 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?
4. 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?
5. 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?
6. 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?

2. 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

1. Which is the median position?
2. 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?
3. If a third party wants to enter the competition and win the election against the other two parties, where ought to locate itself?

3. 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 1.4
Note: Numbers are percentages of votes.

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 Socialist/Left 8.1 11.9 Green 8.1 10.7 Others 4 6
Note: Numbers are percentages of votes.