Suppose local councils spend money only on roads and clean water. The share of the expenditures for clean water is [0,1]. Voter preferences are

Suppose local councils spend money only on roads and clean water. The share of the expenditures for clean water is α ∈[0,1]. Voter preferences are Ui = −|α−pi|, where pi is the bliss point of voter i. Suppose for men pi ∼ U[0; 0.75] (uniform distribution), whereas for women pi ∼U[0.25; 1]. There are equal shares of men and women in the population.
(a) Are these preferences single-peaked?
(b) What is the policy outcome if only men can vote?
(c) What is the policy outcome if everyone can vote?
(d) Which outcome does better represent what women want?