onsider the policy determination game as described in Lecture 1-10. In the lecture, we assumed that each partys objective is to maximize the number of votes. Instead, we consider the following setting:

1. Each party has its own ideal policy. The Democrats ideal policy is \frac{2}{5} 52, while the Republicans ideal policy is \frac{4}{5} 54.

2. The party that obtains the highest number of votes wins the election. If the number of votes obtained by each party is the same, each party wins the election with a probability of \frac{1}{2} 21.

3. The party that wins the election implements the promised policy.

4. Each party's objective is to minimize the distance between the party's ideal policy and the policy implemented by the winner.

Note that voters ideal policies are uniformly distributed over \left[ 0, 1 ight] [0,1] and that the policy is chosen between \left[ 0, 1 ight] [0,1].

Under this condition, select all the correct sentences from the options below. The set \left[ \mathbf{a}, \mathbf{b} ight] [a,b] represents the position of promised policies: the position of the Democrats promised policy is \mathbf{a} a, and that of the Republicans is \mathbf{b} b.

e.g., \left[ \frac{2}{5}, \frac{4}{5} ight] [52,54] indicates that the location of the Democrats promised policy is \frac{2}{5} 52, and that of the Republicans is \frac{4}{5} 54.