## Quantitative Measurements

1. Draw a two-dimensional space with positions from 0 to 10 on each dimension. Place the status quo in the space at SQ(4,4). Locate the following voters' ideal points: A(2,2), B(4,6), C(6, 4).
1. Draw the indifference curves of each of the three voters, A, B, and C, with respect to the status quo, SQ. Identify the win-set, that is, the set of all possible winning positions against the status quo by any majority of 2 voters out of the 3.
2. Is position X(5,5,) within the win-set?
3. Calculate, by Pythagoras, the distances from each of the three voters A, B, and C, to SQ and to X. For which party will each voter vote?

2. Let us now assume that in the same two-dimensional space of the previous question the new status-quo is located at SQ(5,5).
1. Is the previous SQ(4,4) within the win-set of SQ?
2. Is position Y(5,4) within the win-set of SQ?
3. Is position Z(4,5) within the win-set of SQ?
4. Is position W(6,6) within the win-set of SQ?
5. Calculate, by Pythagoras, the distances from each of the three voters, A, B, and C, to Y, to Z, to W, and to SQ.

3. Draw a two-dimensional space with positions from 0 to 10 on each dimension. Locate in the space the following parties' positions: X(4,6), Y(7,3), Z(7,8).
1. Draw the bisectors between each pair of party's positions and identify each party's attraction area.
2. For voter A(5,5), which is the closest party?
3. And for voter B(7,5)?
4. And for voter C(7,6)?

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