Consider a population of citizens with political preferencesxdistributed from left to right on [0,4]. They also have a cost of votingcdistributed on [0,1]. The two parameters are independent and both are distributed uniformly in the population.

Two candidates, A and B, are running for an election, with policy positionspA=1andpB=3.

An individualiwith preferencexreceives utilityU(xi,pj,ci)=1ci|pjxi|+miif he votes for candidatej(wherej= A or B).mis the amount of money individualireceives to vote (if any).

For instance, ifxi=4andci=1, individualireceives utilityU(4,3,1)=111+mi=mi1if he votes for candidate B. Note thatU(xi,pj,ci)can be < 0. Ifidoes not vote, he receives utility 0.

First, suppose there is no vote-buying:mi=0.

Q1) If forced to vote, what is the preference set for those who will vote for candidate A?

Enter the numeric component below as an integer value.

Q2) If forced to vote, what is the preference set for those who will vote for candidate B?

Enter the numeric component below as an integer value.

Q3) Withxon the x-axis andcon the y-axis, graphically consider which citizens vote and which candidate they pick. What fraction ofall citizens(i.e., even including those who don't vote) vote for candidate A?

Enter your answer as a simplified fraction (for example: 2/7).

Q4) In the first example above (1a-1d), what is the minimum payment candidate B must make in order to make this person indifferent between voting or not?

Enter your answer as an integer value.