Voting and Lobbying - 3 Models

Transcription

1 Voting and obbying - 3 Models Series of 3 aers eloring the effects of olitical actions on market outcomes. Current theories of regulation unsatisfying (to me!: Toulouse School: Agency Model regulators seeking economic efficiency must deal with information asymmetry. Great mathematics oor olitics. Do real regulators actually care about economic efficiency? I don t think so! Chicago School: Vote-seeking oliticians rent-seeking firms; demand and suly of regulation Great olitics but no general model. An aealingly jaundiced view of regulators and firms behavior but no unifying analytic engine that brings it together. These aers are my attemt to fi the roblem Information and Disinformation Slide 1

2 Voting on Prices Voters θ [01] have heterogeneous references for 2 monooly services 2 candidates run for election for regulator on latform of rices Regulation erfect : latforms always imlemented at no cost; everything is common knowledge Prices maimize utility of median voter (Downs 1957 Comare aggregate surlus of median voter rices to unregulated monooly rices: Result: median voter rices can be less efficient than monooly rices. US telecoms data fits model amazingly well! Information and Disinformation Slide 2

3 Voting on Prices - 1 Constant elasticity linear costs median voter consumes only one service (M. Regulation vs. Monooly Relative Efficiency 1 Regulation More Efficient 0.75 $ c M M 0.5 Regulation ess Efficient e M Information and Disinformation Slide 3

4 obbying and Voting... In the first aer the voter/consumer is king; non-voting firms have no effect on electoral outcome Gary ecker (1983: elections driven by number of votes markets by number of dollars. Permitting economic (non-voting agents to have voice via lobbying can make electoral outcomes more efficient. Richard Posner (1975 oints out that rent-seeking uses resources which can outweigh any efficiency gains. Second aer: build lobbying into voting model assess which effect redominates. Information and Disinformation Slide 4

5 obbying and Voting... Two firms also consume monooly services; oosing interests in outcome Each can send resources to affect outcome Get out the vote ; firms send to increase robability voters vote Micro-targeting : send messages to some voters but not all Result: only send on voters favorable to your cause (secialization Simulation results Posner effect (resource cost of rent-seeking outweighs ecker effect (greater efficiency of outcome by a lot Firms send lots of resources to little effect; they largely offset one another Prisoners Dilemma Game (like advertising Information and Disinformation Slide 5

6 Information and Disinformation Today s aer (done at IAE: generalize lobbying Get out the vote one tye of lobbying; how about Change voters minds? What does it mean to change eole s minds? Change their references? A No-no! Change what they know about candidates? es Candidate announces olicy latform; voters erceive actual olicy imlemented to be a random variable with known distribution. This distribution can be modified at a cost. ow would lobbyists behave? Information and Disinformation Slide 6

7 Probabilistic Voting Introducing uncertainty into voting models changes the game Coughlin (1992: candidate uncertainty about voters references Alvarez (1997: voter uncertainty about candidates but no equilibrium model. Primarily emirical: what do voters really knowabout candidates? Early work by Shesle (1972; unavailable asic results on voting when candidates are random variables need to be established. What s the equilibrium? When candidates choose latforms but not distributions When candidates choose both latforms and distributions (costlessly When distributions are costly to adjust (lobbying otential Information and Disinformation Slide 7

8 Probabilistic Voting - The asics Voters θ have heterogeneous references over olicies [01]: V θ ( single-eaked Candidates A and announce olicy latforms A [01] Voters erceive latform uncertainty; distribution F with suort [ - + ] with mean. latforms and distributions common knowledge; default distributions identical for both candidates (u to the mean. Voters vote for candidate that maimizes + eected utility: V f V ( f ( d Shae of V θ (? Most olitical science literature assumes concave over olicies. OK if olicies are income-redistributive. ut what of more general olicies? I assume local concavity only! θ ( θ Information and Disinformation Slide 8

9 The asics (cont d Proosition 1: if (C {V θ is concave on [ θ -2 θ +2 ]} then V θ ( f is singleeaked in for any distribution. Single-eak V θ does not imly single-eak Proosition 2: if (C then the unique ure strategy equilibrium with endogenous mean and eogenous F is A θ ˆ ( f median voter s ( θˆ olicy eak of eected utility under F. follows from Downs + Pro. 1 ut what about endogenous choice of distribution? What if candidates can choose both the latform and the distribution without cost? V θ ( f Information and Disinformation Slide 9

10 Information and Disinformation Slide 10 ut First A ittle Infrastructure... Definitions: degenerate distribution at : ernoulli distribution: at 0 <½< 1 the set of all distributions on [ - + ] with mean emma:if V θ is on [ ] then this defines the most certain and the least certain distributions; the first is obvious the second not < D 1 0 ( < < ½ 0 ( 1 0 F conve concave + + F D d f V ( ( ma arg θ F

11 Endogenous Distributions Proosition 3: If V θ is concave then the unique ure strategy equilibrium is A θˆ and F D (θˆ the certain outcome. Concavity + median voter cometition eliminates all uncertainty and the classic median voter theorem obtains. Definitions: Θ ({θ V θ <0V >0 on [-2 +2 ]} Θ R ({θ V θ >0V >0 on [-2 +2 ]} Θ NR ({θ V θ >0~V >0 on [-2 +2 ]} Θ N ({θ V θ <0~V >0 on [-2 +2 ]} Proosition 4: If Θ R > Θ N or Θ > Θ NR then the unique equilibrium is A ˆ ( and F θ ˆ ˆ + + θ θ θˆ θˆ the most uncertain outcome. Information and Disinformation Slide 11

12 Why More Uncertainty? The Proosition s condition states that A has more conve voters voting for (who refer uncertainty than non-conve voters voting for A (who may not refer uncertainty so it ays to defect to the ernoulli from any other distribution. ut does conveity make sense? es if the voter believes strongly in her ideal oint and erceives everything else quite oorly. Nature lover vs. environmentalists Ideological voters Economists ut we now focus on concave references Information and Disinformation Slide 12

13 Imact of Uncertainty on Platforms Proosition 5: The equilibrium strategy < ( f < as V on [ - + ] θˆ > θ > 0 V θ '" measures the asymmetry of V θ around its eak ( θˆ. If V θ '"<0 there is more mass to the left of the eak; V θ '''>0 more mass to the right; and V θ '''0 symmetry. ow does the equilibrium strategy behave as uncertainty is changed? Cannot well-order distributions by uncertainty. ut a artial order eists: 2nd order stochastic dominance ( Proosition 6: For any family f 2 ( z F ( z1 ( z 2 f 2 z [01] and z 1 >z 2 iff f f with then d dz > < < 0 as V θ > 0 Equilibrium monotonic in uncertainty Information and Disinformation Slide 13

14 Costly Distribution Changes Changing voter ercetions of candidate latform uncertainty likely to be costly etra camaign time media eenditures to convince voters of the candidate s osition encouraging endorsements from others selling out detailed lans to imlement olicies commissioning books articles and television secials to document either the staunchness or the fleibility of the candidate etc. Who ays? We assume 2 grous with a stake in the outcome: a low grou ( and high- grou ( with linear utilities in : b >0>b. Information and Disinformation Slide 14

15 obbying Game What s the interest (in the distribution of the interest grous? θ If V θ '''<0 ˆ < ( then grou has incentive to reduce uncertainty (rovide information to move the equilibrium to a higher ; grou has incentive to increase uncertainty (rovide disinformation to move the equilibrium to a lower. Grous lobby ( send resources to increase/decrease uncertainty for candidates A A A and/or : Assume the feasible distributions can be ordered by 2nd-order dominance: ( z1 ( z 2 z 1 >z 2 iff and (½ F f ( f f default distribution 2 f z [01]; with F (1 Payoff function Z( with Z 1 >0 Z 2 <0 Z ii <0 symmetric same for both candidates. Z is the distribution for this candidate that results from the joint eenditures. Z(00½. θˆ ( z F F 0 ( D Information and Disinformation Slide 15

16 obbying Game Grous lay a lobbying game with strategies... Candidates announce latforms... Voters vote in a one-shot game Questions: What do equilibria look like? If voters like certainty can an increase in uncertainty be an equilibrium? ecker vs. Posner: are equilibrium resource eenditures commensurate with changes in the distributions(s? Information and Disinformation Slide 16

17 Information and Disinformation Slide 17 Equilibrium Conditions - 3 ( A z z F b a A a + (ma( ˆ ma θ ( A z z F b a A a + (ma( ˆ ma θ First-order conditions: A Z dz z z d dz d b A 0 1 ( (ma( A Z dz z z d dz d b A 0 1 ( (ma( The inequalities result from the ma function in the maimands. Under some circumstances the grous lobby only one candidate with zero eenditures for the other.

18 Three Tyes of Equilibria z A z <½. Occurs is is more effective at lobbying (b <-b or Z 1 <-Z 2. oth A s and s distribution must be changed or the unchanged candidate wins. z A z >½. Occurs if is more effective than (b >-b or Z 1 >-Z 2. oth A and have ositive marginal returns to lobbying z A >z ½. Occurs if is much more effective at lobbying. Only A s distribution is changed and A wins the election. z is too far from z A ; marginal benefit of sending on is zero. She chooses the median voter ma as that is a dominant strategy against all inferior distributions Can co-eist with z A z >½. Information and Disinformation Slide 18

19 Conclusions Grous can send on both candidates but will not necessarily do so. One grou sulies disinformation one sulies information. If grou is more effective then there is more uncertainty with lobbying than without. Consider the case in which both grous are equally effective (b -b Z 1 -Z 2. Then they send the same amount on each candidate and the distributions are unchanged from the default. Resource eenditure no effect! Posner trums ecker again. Information and Disinformation Slide 19