Suppose there are 3 voters in a legislature, and two projects are up for consideration. Project A creates benefits of 3 for district 1 but benefit of -1 in district 2 and -3 in district 3. Project B creates benefits of 3 in district 2, -1 in district 1 and -3 in district 3.
a. Would either of these projects be implemented under simple majority rule voting (where each project is approved or not approved on its own)?

b. How would your answer to (a) change if the projects can be bundled?
c. Is it efficient to fund these projects?
d.  Suppose the Coase Theorem applies to legislatures -- i.e. suppose legislators can create alternatives with cash side-payments. What might voter 3 do to prevent the outcome in (b)?
e. True or False: If transactions costs are low and side-payments are allowed, only efficient projects will pass under vote trading.

What will be an ideal response?

a. No -- each would only get one vote.

b. The projects could be bundled -- and the bundle would get the votes of individuals 1 and 2 (who both would then get a net benefit of 2.)

c. No, it is not efficient to fund these projects. They generate net social benefit of -1 each.

d. Voter 3 could structure an alternative bill that would tax district 3 enough to raise revenue of 4 and then divide this equally between districts 1 and 2. Voters 1 and 2 would be indifferent between this and the bundled bill (from (c)) -- in both cases they get a benefit of 2. But voter 3 would be better off -- losing only -4 instead of -6.

e. Whenever projects are inefficient, there is enough surplus to be gained from not building them to pay off the proponents of the bill.