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Shepsle and Bonchek Ch. 5: Spatial Modeling. Utility. U5. U4. U3. U2. U1. 2. 4. 6. 8. 10. A Corporate Board made up of 5 bankers wants to decide what interest rate to charge this year for mortgage loans. Utility. U5. U4. U3. U2. U1. x 1. x 2. x 3. x 4. x 5. 2. 4. 6. 8.
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Shepsle and Bonchek Ch. 5: Spatial Modeling Utility U5 U4 U3 U2 U1 2 4 6 8 10 A Corporate Board made up of 5 bankers wants to decide what interest rate to charge this year for mortgage loans.
Utility U5 U4 U3 U2 U1 x1 x2 x3 x4 x5 2 4 6 8 10 Assume these preferences over interest rates, what is xm and thus the majority choice?
Utility U5 U4 U3 U2 U1 x1 x2 x3 x4 x5 2 4 6 8 10 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.
P2(5) P3(5) Utility U5 U4 P1(5) P4(5) U3 U2 P5(5) U1 Any proposal for an interest rate in this range will defeat 5% by a vote of 3 to 2. x1 x2 x3 x4 x5 2 4 6 8 10 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.
Utility U5 U4 U3 U2 U1 A B C D x1 x2 x3 x4 x5 2 4 6 8 10 Banker 3 is the median voter In general, anything higher or lower than x3 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 (xm) is the only unassailable position.
x0 xm x* Spend $10 on guns Spend $4 on guns and $6 on butter Spend $10 on butter 1 0 Gun Nuts Butter Eaters 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 xm. 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.
x0 xm xc1 xc2 Spend $0 on butter Spend $6 on butter Spend $10 on butter Spend $20 on butter 1 0 Gun Nuts Butter Eaters Now let’s consider just the amount to spend on butter. Under closed committee rule, the committee’s proposal (xc1) will win because the status quo (x0) is less preferred by a majority of legislators than is the committee proposal. However, if the committee overreaches (for example, if they propose xc2), then what will happen? The distance from the new proposal exceeds the distance to the status quo, and the status quo will prevail.
Liberalized civil rights laws Benign neglect Back to Jim Crow xm x0 xc Spend $0 on butter Spend $6 on butter Spend $20 on butter 1 0 Gun Nuts Butter Eaters 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.
