«The Politician and the Judge: Accountability in Government Jean Tirole∗ Eric Maskin First version, April 2001 Revised, March 2004 Abstract We build ...»
Now consider a nonideological type (N, b) oﬃcial. If she chooses b, her payoﬀ, from the above claim, is at least δq. If instead she chooses a, her payoﬀ is at most 1+δ (1 − q). But, by hypothesis, the former exceeds the latter. Hence, in equilibrium, type (N, b) cannot choose b, and the same for (C, b) (since (C, b)’s preference for b is even stronger). Similarly, types (N, a) and (C, a) choose a in equilibrium, establishing that any equilibrium must be FLP.
Suppose that a has been chosen in the ﬁrst period. In equilibrium, nonideological types (C, a) and (N, a) and ideological types (C, a) and (N, b) choose a. Hence, if there has been no feedback, the probability that the oﬃcial is congruent conditional on the choice of a is strictly greater than π, and so she will be reelected. Similarly, she will not be reelected if she has chosen b and there is no feedback 1+δ Proposition A3 When qδ 1, one limit of PBEs as ρ → 0 is an FLP equilibrium 2 in which, if there is no feedback, the electorate randomizes over reelection. The only other possible limit (if δ (1 − 2q) ≥ 1) is a full pandering equilibrium.
Fix ρ 0. From the proof of Proposition A2, in any equilibrium, if the Proof.
electorate obtains feedback about an oﬃcial’s ﬁrst-period choice, then the oﬃcial will be reelected if and only if the decision was optimal. Suppose that there exists an equilibrium in which nonideological type (N, a) chooses b with positive probability. Then, (N, b) and (C, b) both choose b with probability 1 (since for δq 1 their preference for b is even 33 stronger than that of (N, a)). Hence, without feedback (and in view of the ideological types (N, a) and (C, b) who choose b), the probability that an oﬃcial is noncongruent conditional on b having been chosen is strictly greater than 1 − π, and so an oﬃcial who chooses b will not be reelected. This means that (N, a)’s payoﬀ from choosing b is 1. By contrast, if she chooses a, she will be reelected (whether or not there is feedback), and so her payoﬀ will be δ, which, by hypothesis, is greater, a contradiction. We conclude that (N, a) must choose a with probability 1 in equilibrium, which implies that the same is true of (C, a).
Suppose that there exists an equilibrium in which nonideological type (N, b) chooses b with probability 1. In that case, the probability without feedback that an oﬃcial is noncongruent conditional on her having chosen b is strictly greater than 1 − π (thanks to the fact that, in the absence of feedback, the probability that an ideological oﬃcial is noncongruent conditional on her having chosen b is strictly greater than 1 − π), and so (N, b)’s payoﬀ from b is δq. By contrast, if she chooses a, she will be reelected if there is no feedback, and so her payoﬀ will be 1 + δ (1 − q), which, by hypothesis, is greater, a contradiction. We conclude that, in any equilibrium, (N, b) must choose a with positive probability.
Consider an equilibrium in which nonideological type (N, b) randomizes between a and b. Then δq + δ (1 − q) β = 1 + δ (1 − q) α, (1) where the left- and right-hand sides of (1) correspond to the payoﬀs from b and a respectively, and β and α are the probabilities of reelection in the absence of feedback when, respectively, b and a have been chosen. From (1) and hypothesis, we obtain
That is, when there is no feedback, the electorate must randomize between reelecting and not reelecting, either when the oﬃcial has chosen a, or when she has chosen b (or in both cases). This implies that the probability of an oﬃcial’s being congruent conditional on a 34 having been chosen is π. Now, the nonideological types other than (N, b) who choose a in equilibrium are (C, a) and (N, a) and the ideological types are (C, a) and (N, b). Hence, the probability that (N, b) chooses a must be only big enough to oﬀset the eﬀect of the ideological oﬃcials. Thus, as ρ → 0, equilibrium converges to one in which (N, b) (and hence (C, b)) plays b with probability 1 – i.e., an FLP equilibrium – and the electorate randomizes over reelection when there is no signal, as the Proposition claims.
The only remaining equilibrium possibility is that nonideological type (N, b) chooses a with probability 1. Now, if (C, b) does so too, then we are done, because this will be a pure pandering equilibrium. Hence, assume that (C, b) chooses b with positive probability.
If this probability is high enough to outweigh the eﬀect of the ideological type (N, a), who chooses b, then, without feedback, an oﬃcial who chooses b will be reelected, implying that (N, b)’s payoﬀ from b is δ, whereas that from a is only 1, a contradiction of the fact that (N, b) chooses a. We conclude that the probability that (C, b) chooses b must be suﬃciently small and converge to 0 as ρ → 0. Thus, in the limit, we obtain a full pandering equilibrium, as claimed.
Proposition A4 When δ 1 and 0 qδ 1, one limit of PBEs as ρ → 0 is a PP equilibrium (which is also a Markov equilibrium). The only other possible limit (if δ (1 − 2q) ≥ 1) is a full pandering equilibrium.
Fix ρ 0. Again, it can be shown that, in any equilibrium, an oﬃcial Proof.
is reelected when there is feedback if and only her ﬁrst-period decision was optimal.
Suppose that there exists an equilibrium in which nonideological type (N, a) chooses b with probability 1. Then the probability that an oﬃcial is noncongruent conditional on her having chosen b is greater than 1 − π, and so, without feedback, an oﬃcial choosing b will not be reelected. Thus, (N, a)’s payoﬀ from b is 1, whereas her payoﬀ from a is δ, a contradiction, since the latter is bigger. We conclude that nonideological type (N, a) must choose a with positive probability in equilibrium. If she also chooses b with positive probability, then, since 0 qδ 1 implies that ∆ (C, a) ∆ (N, b) ∆ (N, a) ∆ (C, b), type ∆ (C, b) will choose b and types (C, a) and (N, b) will choose a : the equilibrium is 35 P P. Notice that because all four types have diﬀerent preferences, this is also a Markov equilibrium.
Assume, therefore, that (N, a) chooses a with probability 1. Now if nonideological type (C, b) chooses b with high enough probability to outweigh the eﬀect of the congruent ideological types (C, b) and (N, a), who choose b, then, without feedback, an oﬃcial who chooses b will be reelected, implying that (N, a)’s payoﬀ from b is 1 + (1 − q) δ, whereas that from a is δq. But, by hypothesis, the former is bigger than the latter, a contradiction.
We conclude that nonideological type (C, b) can choose b with probability at most on the order of ρ. But as ρ → 0, (C, b)’s strategy converges to one in which a is chosen with probability 1, implying that the limiting equilibrium is full pandering.
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Footnotes *Maskin: Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, U.S.A.
and Princeton University; Tirole: Institut d’Economie Industrielle, Manufacture des Tabacs, Bureau MF529-Bat. F, 21 allees de Brienne, 31000 Toulouse, France and GREMAQ (UMR 5603 CNRS), Toulouse, CERAS (URA 2036 CNRS), Paris, and MIT. We are grateful to the participants of the CEPR-ESF conference on “The Institutions of Restraint” (Toulouse, June 24-28, 2000), the Annual Meeting of the European Public Choice Society (Paris, April 18-22, 2001), the Southeastern International Trade and Economic Theory Conference (Miami, November 16-18, 2001), the Canadian Economic Theory Conference (Toronto, May 24-26, 2002), the Modeling the Constitution Conference (Pasadena, May 16-17, 2003), and many seminars for their observations on oral presentations, and to Tim Besley, Mathias Dewatripont, John Matsusaka, Stephen Morris, Ian Shapiro and two anonymous referees for helpful comments on previous drafts.
1. Ballot referendums constitute the largest class of decisions made through direct democracy, but even in the U.S. and Switzerland, where they are especially popular, they touch on only a small fraction of public policy issues.
2. See, however, the sympathetic fourteen-page survey on direct democracy in The Economist (December 21, 1996). Many have argued that once the digital divide is eliminated, e-voting will enhance the appeal of referendums.
3. The view that governments are better informed than citizens is emphasized in James Madison (1787) and Abbé Siéyès (1789) (see also the introduction to Bernard Manin, 1997).
4. Joseph Schumpeter (1942) puts it in characteristically acerbic fashion: “The average citizen expends less disciplined eﬀort on mastering a political problem than he expends on a game of bridge.” 41
5. Summarizing the case against direct democracy, David Butler and Austin Ranney (1994) write: