3. Public Choice in a Direct Democracy

Transcription

1 3. Public in a Direct 4. Public in a 3. Public in a Direct I. Unanimity rule II. Optimal majority rule a) Choosing the optimal majority b) Simple majority as the optimal majority III. Majority rule a) Exploitation of the minority b) Cyclical preferences c) Multidimensional issues IV. Log-rolling V. genda manipulation VI. lternatives to the majority rule VII. Exit, voice and disloyalty VIII. Summary: normative properties of majority rule asic Literature is Mueller, 2003, pp Freytag

2 3. Public in a Direct 4. Public in a For decision making in a direct democracy, the choice of a voting rule seems decisive. Where can the voting procedure be of relevance in today s world? clubs, parliament (onn-erlin decision), EU (treating member states as individuals), Two rules (Rousseau) for setting the voting rule: import topics demand unanimity, and fast decisions demand minimal majorities. Freytag

3 3. Public in a Direct 4. Public in a I. Unanimity rule To reach Pareto-optimal results for public decisions, unanimity is needed for. Otherwise, single individual preferences would be neglected, and the decision would leave losers. See following slides and Mueller (2003), pp n important implication is that the rule determines whether or not and if so where, a Pareto optimum can be met. Shortcomings of the unanimity rule: much information needed, much time needed, and strategic behaviour possible. Freytag

4 3. Public in a Direct 4. Public in a X X U U The unanimity rule U U Y Y ( Y ( Y tg ( 1 (1 t) G tg, G ) t) G, G ) U U U X U X U U ( t) dg dg ( G) dt G X U U ( 1 t) dg dg ( G) dt G X 3.3 Freytag

5 Freytag ) / ( / ) (1 / ) ( ) / ( / / ) ( X U G X U t G U dg dt X U G X U t G U dg dt / / / / X U G U X U G U 3.5 ) (1 / / / / t X U G U t X U G U Introduction 3. Public in a Direct 4. Public in a

6 3. Public in a Direct 4. Public in a X Y 1 Figure 3.1: Optimal quantities for a voter at different tax prices 0 2 G 1 t 1 G 0 t.5 G 2 t.33 G Freytag

7 3. Public in a Direct 4. Public in a t t.5 t.33 Figure 3.2: Mapping of voter preferences into tax-public good space G 1 G 0 G 2 G Freytag

8 Percentage of tax paid by 1. Introduction 3. Public in a Direct 4. Public in a t 0 t 100 Figure 3.3: Contract curve in public good-tax space C` 5 t E E t F t L L F C 5 t 100 t 0 G F G Freytag

9 3. Public in a Direct 4. Public in a II. Optimal majority Unanimity is not realistic, not so much because of individual strategic behaviour but because of its enormous cost. uchanan and Tullock (1962) show that the optimal majority depends on cost related to the decision. a) Choosing the optimal majority Two types of cost occur: (external) cost C of the losers of the decision and cost D of achieving the required majority. Whereas C is decreasing with the number of people who agree on the decision, D is increasing with the number of citizens who have to agree. Freytag

10 3. Public in a Direct 4. Public in a Expected costs Figure 3.4: Choosing the optimal majority C+D D C 0 Freytag K Number of indivduals whose agreement is required for collective action N

11 3. Public in a Direct 4. Public in a Obviously, the optimal majority is not the same for all decisions to be made. External cost C may vary depending on the nature of the decision and on the size N of the community. The cost curve D associated with the number of individuals necessary to form a consensus may shift rightwards with increasing N. b) Simple majority as the optimal majority So, generally speaking, what is the optimal majority? It can t be below N/2. See Figure 3.5, which shows a special case in that there is a kink at N/2. pproximately, N/2, i.e. simple majority can be assumed to be the optimal majority in big communities. Freytag

12 3. Public in a Direct 4. Public in a Expected costs Figure 3.5: Conditions favouring a simple majority as the optimal majority C+D D C+D D C 0 N/2 Number of indivduals whose agreement is required for collective action Freytag N

13 3. Public in a Direct 4. Public in a III. Majority rule a) Exploitation of the Minority Consider a society which is better off with a collective good (such as redistribution) than without; consider also two groups, the rich and the poor. tax introduced would finance the collective good, depending on the kind of tax, either both groups would gain or one of the groups would lose. Unanimity rule would lead to one of many Pareto optima, because either the society would remain at the status quo ante, or both groups win. Majority voting would not lead to a Pareto optimum, as the majority is likely to exploit the minority. See Figure 3.6. Freytag

14 3. Public in a Direct U R Majority rule outcomes, rich in majority Figure 3.6: Outcomes under the unanimity and the simple majority rule 4. Public in a X Y Unanimity rule outcomes C S E Z Majority rule outcomes, poor in majority W U P Freytag

15 3. Public in a Direct 4. Public in a One lesson from the discussion of a collective good is to restrict the decisions to those individuals directly involved both in the decision and its consequences. In other words, it is highly sensible to reduce the number of public goods and to increase the number of club goods. For the European Union, this lesson is also of importance. s long as the unanimity rule holds for many issues but also if not the process should come up with modest harmonisation efforts to minimise the number and cost of losers. Subsidiarity principle, implying that measures should be taken on the lowest possible level. Freytag

16 3. Public in a Direct 4. Public in a b) Cyclical preferences Consider three persons who shall divide 100 among themselves. Possible outcome: (1): 55/45/0, (2): 50/0/50, (3): 0/60/40, V1: (1) > (2) > (3) < (1), V2: (1) > (2) < (3) > (1), V3: (1) < (2) > (3) > (1). Community under majority rule: (1) > (2) > (3) > (1). The community cannot find a first best solution but produces a cycle. See Figure 3.7. Freytag

17 3. Public in a Direct 4. Public in a U Figure 3.7: Voter preferences that induce a cycle V 2 V 3 V 1 X Y Z Q Freytag

18 3. Public in a Direct 4. Public in a c) Median voter theorem If society has to decide about a single issue and if all voters have single peaked preferences, then the median position cannot lose under majority. Plott s theorem (Figure 3.13). d) The median and multidimensional issues How does it work when multidimensional issues are discussed? Then, the outcome depends on the number of committee members who decide: committee of 1: no problem (Figure 3.8). committee of 2: contract curve (Figure 3.9), committee of 3: no solution (Figure 3.10) or like a committee of 2 (Figures 3.11 and 3.12). Freytag

19 3. Public in a Direct 4. Public in a x 2 Figure 3.8: Outcome for a committee of one U x 1 Freytag

20 3. Public in a Direct 4. Public in a x 2 Figure 3.9: Outcomes for a committee of two D U E U x 1 Freytag

21 3. Public in a Direct 4. Public in a x 2 Figure 3.10: Cycling outcomes for a committee of three Z U D U C x 1 Freytag

22 3. Public in a Direct 4. Public in a x 2 Figure 3.11: Equilibrium outcome for a committee of three E x 1 Freytag

23 3. Public in a Direct 4. Public in a x 2 Figure 3.12: Outcome for a committee of five E F G x 1 Freytag

24 Figure 3.13: Plott s theorem x 2 3. Public in a Direct 4. Public in a G E F x 1 Freytag

25 3. Public in a Direct 4. Public in a IV. Log-rolling The trading of votes is illegal in democracies. Nevertheless, it happens regularly. Reasons are: differences in preference intensities across issues; inclination to trade. Voters Issue 1 Issue C -2 5 The figures show net utility if the respective laws pass the committee of three, otherwise utility is zero. Freytag

26 3. Public in a Direct 4. Public in a Each law would fail if individually decided upon. If and C trade votes, both laws will pass log-rolling. This is not Pareto-optimal. However, (under cardinal utility), can be compensated, and the community is better off (net utility is +2). Imagine s net utility for both issues is -4. Then, the community faces a net utility of -2. Policy implications are different, depending on the net results: too many and to generously provided public goods (negative); reforms are possible (general compensation); bluffing and cheating may take place. Freytag

27 3. Public in a Direct 4. Public in a final judgement of log-rolling depends on the very case. Log rolling is not possible with transitive social preference orderings. In reality, log-rolling can be observed in US Congress as well as in the European Union. Testing for log-rolling cannot be done directly (as it is illegal), but indirectly by analysing the voting behaviour in single cases. Freytag

28 3. Public in a Direct 4. Public in a V. genda manipulation If individual preference ordering might produce cyclical voting under the majority rule, a committee member in control of the agenda of pairwise voting can manipulate the committee. The outcome will be the one the agenda setter prefers most (Figure 3.14). Policy implications: power of agenda setter may be substantial; decisions reached by committees are not necessarily reflecting the preferences of the median; agenda setters may influence distributional issues to their advantage. Freytag

29 U 3. Public in a Direct x 2 U 4. Public in a Z U S Z Z C U U C Figure 3.14: genda manipulation possibilities Freytag x 1

30 3. Public in a Direct 4. Public in a VI. lternatives to the majority rule One can think of a number of alternatives to the majority rule: majority rule, runoff election; plurality rule; Condorcet criterion; Hare system; Coombs system; pproval voting; orda count; These systems are relatively simple and easy to apply. Indeed, many of them are regularly applied in daily life (often without knowing). Freytag

31 3. Public in a Direct 4. Public in a There are more complicated and tricky alternatives to the majority rule: demand revealing process; point voting; voting by veto. Freytag

32 3. Public in a Direct 4. Public in a VII. Exit, voice and disloyalty So far, we have concentrated on the provision of pure public goods voice is the only option for the individual. However, pure public goods are rare (see chapter 2). Therefore, we turn to club goods. Clubs have an optimal size, as the marginal benefits of additional members decreases, whereas their marginal cost increase (James uchanan). In addition, clubs are competing for members exit as a second option becomes available (Charles Tiebout). We may overcome problems of the majority rule by concentrating on clubs. Freytag

33 3. Public in a Direct 4. Public in a Under the following conditions, it is possible to ensure global optimality of excludable public goods provision and apply both the theory of clubs and the theory of exit: full mobility of all citizens; full knowledge of the characteristics of all clubs all desired public goods available in clubs no scale economics in production of the public good no spillovers across clubs no geographical constraints on individual with respect to their earnings It can be shown that voting-with-the-feet can produce global optimality. Freytag

34 3. Public in a Direct 4. Public in a Empirical relevance 3 hypotheses: 1. Individuals move in response to local government expenditure-tax offerings. 2. People with similar preferences for bundles of public goods live together in groups. 3. Individual satisfaction increases when votingwith-the-feet is possible. Empirical evidence is available for the United States. It mainly supports the Tiebout hypotheses. This seems different in Continental Europe. Less club goods and more pure public goods. Freytag

35 3. Public in a Direct 4. Public in a FOCJ normative application* FOCJ stands for Functional, overlapping, competing jurisdictions and implies that individuals select among different clubs to meet their demand for club goods. No one is forced to purchase all public goods at one jurisdiction, but can select. Entry into clubs is not free, but exit has definitely to be free. The authors with a special reference to the European constitution suggest that the EU should be organised according to this proposal. * Frey, runo S. and Reiner Eichenberger (1995), Competition among Jurisdictions: The Idea of FOCJ, Lüder Gerken (ed.), Competition among Institutions, Houndsmill, Macmillan, pp Freytag

36 3. Public in a Direct 4. Public in a Disloyalty - revolution When neither the ballot nor the feet constitute adequate modes of expression, there is still Chairman Mao s barrel of the gun. (Mueller 2003,, p. 204). It may be rational to start a revolution, if exit and voice are no suitable alternatives. The decision to start a revolution and/or to participate is dependent on the expected payoffs and the relative weight of cost (transaction cost, imprisonment, death etc.). For an experimental analysis of the predictions made by an economic approach see bbink and Pezzini.* * bbink, Klaus and Silvia Pezzini (2005), Determinants of Revolt: Evidence from Survey and Laboratory Data, Freytag

37 3. Public in a Direct 4. Public in a VIII. Summary: normative properties of the majority rule fter discussing a number of different voting rules and their properties, we now turn to some normative conclusions. gain Rousseau: ig issues demand unanimity constitutional decision. Urgent issues demand majority rule. Condorcet s Jury theorem: ssume a pairwise comparison of two a priori equally good alternatives by each voter independently. rising (odd) number of voters can increase the probability that the group makes the correct decision. Freytag

38 3. Public in a Direct 4. Public in a ssumptions are the following: a common probability of being good across all individuals, independent voting, honest voting. From this theorem, we can derive a normative justification of the majority rule. The theorem can also justify referenda. Nevertheless, the majority rule is not favourable in every situation. Table 3.1 compares majority and unanimity rule with respect to different circumstances. Freytag

39 3. Public in a Direct 4. Public in a Example: Condorcet s Jury Theorem Decision: guilty or not guilty p i P n probability of the judge i to make the correct decision (assumption in this example: p i for all judges = 0.6) probability of the jury to make the correct decision under majority rule a) One judge: P n = P 1 = 0.6 b) Three judges, and C (intuitive example): Correct decision if 2 or 3 judges are correct (majority) Pn = P3 = 0.6 * 0.6 * * 0.6 * * 0.6 * * 0.4 * 0.6,, C correct, correct, C correct, C correct P 3 = * = > 0.6 Freytag

40 3. Public in a Direct 4. Public in a c) 5 Judges Example: Condorcet s Jury Theorem 5 5! h pn p h!(5 h)! h3 5h P 5 = = > h = 3 h = 4 h = 5 (h = (n+1)/2 = majority) d) 11 Judges: P n = p 11 = Judges: P n = p 51 = more than 100 judges: p n = pretty close to 1 Freytag

41 3. Public in a Direct 4. Public in a Table 3.1: ssumptions favouring respective rules ssumption Majority rule Unanimity rule 1. Nature of game Conflict, zero sum Cooperative, positive sum 2. Nature of issues Redistributions, property rights (some benefit, some lose) Mutually exclusive issues of a single dimension llocative efficiency improvements (public goods, externality elimination) Issues with potentially several dimensions and from which all can benefit 3. Intensity Equal on all issues No assumption made 4. Method of forming committee Involuntary; members are exogenously or randomly brought together Voluntary; individuals of common interests and like preferences join 5. Conditions of exit locked, expensive Free 6. of issues 7. mendment of issues Exogenously or impartially proposed Excluded, or constrained to avoid cycles Proposed by committee members Endogenous to committee process Freytag Source : Mueller, p. 141.