1. Utility 462810 U1 U2 U3 U4 U5 A Corporate Board made up of 5 bankers wants to decide what interest rate to charge this year for mortgage loans. Shepsle and Bonchek Ch. 5: Spatial Modeling

2. Utility 462810 U1 U2 U3 U4 U5 x4x4 x2x2 x3x3 x5x5 x1x1 Assume these preferences over interest rates, what is x m and thus the majority choice?

3. Utility 462810 U1 U2 U3 U4 U5 x4x4 x2x2 x3x3 x5x5 x1x1 I’m a middle road kinda guy, so my guess is 5%, sort of in the middle Can any proposal defeat 5%? Put another way, what is the WINSET (W) for my proposal (5%)? If W(5) > 0 then my proposal will not win.

4. Utility 462810 U1 U2 U3 U4 U5 x4x4 x2x2 x3x3 x5x5 x1x1 My proposal of 5% Each Banker likes something more than 5% (horizontal lines). Can we can identify options preferred by a majority? Yes, W(5) = anything in the shaded region. W(5)>0, thus it can be defeated. P 1 (5) P 2 (5) P 3 (5) P 4 (5) P 5 (5) Any proposal for an interest rate in this range will defeat 5% by a vote of 3 to 2.

5. Utility 462810 U1 U2 U3 U4 U5 x4x4 x2x2 x3x3 x5x5 x1x1 Banker 3 is the median voter In general, anything higher or lower than x 3 will be defeated in pairwise voting. Show this by identifying the majority who defeats at positions A, B, C, D. The position of the median voter (x m ) is the only unassailable position. ABCD

6. 0 xmxm x0x0 x*x* 1 Last legislative session, the gun nuts were in control, and were able to spend our $10 budget all on guns. This year, some butter eaters were elected. Now we are considering a new budget. Under pure majority rule, any proposal (e.g. x * by the butter eaters--spend $10 on butter), is amended on the floor until the outcome converges upon x m. Any proposal to spend more than $4 on guns (by the gun nuts) will be defeated; similarly, any proposal to spend more than $6 on butter will also be defeated. The median voter’s choice = the majority choice. Spend $10 on guns Spend $10 on butter Gun Nuts Butter Eaters Spend $4 on guns and $6 on butter

7. 0 xmxm x0x0 x c1 1 Now let’s consider just the amount to spend on butter. Under closed committee rule, the committee’s proposal (x c1 ) will win because the status quo (x 0 ) is less preferred by a majority of legislators than is the committee proposal. However, if the committee overreaches (for example, if they propose x c2 ), then what will happen? The distance from the new proposal exceeds the distance to the status quo, and the status quo will prevail. Spend $0 on butter Spend $10 on butter Gun Nuts Butter Eaters Spend $6 on butter x c2 Spend $20 on butter

8. 0 xmxm x0x0 1 Now let’s consider one more example. Here, the committee median is to the right of the status quo. Under closed committee rule, the committee will exert its gatekeeping authority to stop any alternative proposals from coming to the floor. Can you think of a real world example where this happened? At least one occurred on a regular basis in the House of Representatives during the late 1950s and early 1960s. The example is civil rights legislation, Southern committee chairs, and a liberal House of Representatives. Legislation was successfully bottled up for almost two decades. Spend $0 on butter Gun Nuts Butter Eaters Spend $6 on butter xcxc Spend $20 on butter Liberalized civil rights laws Back to Jim Crow Benign neglect