Reliability and Responsibility: A Theory of Endogenous Commitment

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Reliability and Responsibility A Theory of
Endogenous Commitment

• Matteo Triossi
• Universidad Carlos III
• December 2005

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• Do Electoral Campaigns convey relevant
  information to voters?

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• Most of the models of electoral
  competition assume that politicians are committed
  to their electoral announcements.
• They do not explain why electors should be
  influenced by such promises.

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• The paper presents a model characterized by
• Costless electoral campaign
• Asymmetric information
• Finitely repeated elections

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• which is able to account for
• Informative electoral campaign
• Endogenous Commitment
• Control of elected politicians through a
  credible threat imposed to reelection

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Related Literature

• Alesina (1988) Finitely repeated elections,
• complete information no informative campaigns
• (backward induction)
• Harrington (1992a) One election, asymmetric
• information no informative campaign (candidates
• maximize probability of election)

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• In Harrington (1993) beliefs are not consistent.
• Electors do not control politicians (each elected
• candidate implements her favorite policy). Policy
• preferences do not interact with reelection
• pressure.
• Here large (continuous) type space, consistent
• beliefs. The interaction between reelection
  pressure and
• policy preferences shapes implemented policies.

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• Electoral accountability and career concerns
  in
• politics Barro (1973), Ferejohn (1986),
  Austen-
• Smith and Banks (1989), Harrington (1993b),
• Persson Roland and Tabellini (1997),
• Dewatripoint, Jewett and Tirole (1999).

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• Informative (costly) Campaigning Banks (1990),
• Baron (1994), Callander and Wilkie (2005), Prat
• (2002) , Coase (2003)
• Negative Campaigning Skaperdas and Grofman
• (1995), Harrington and Hess (1996), Polborn and
• Yi (2005)

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The Model

• Two Candidates L and R
• ygt0 value of the office
• kgt0 degree of policy implication
• a candidates type aL? -D,0, aR ? 0,D, Dgt0
• aLand aR are drawn from symmetric cdf FL and FR
• s policy implemented by the incumbent

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• Candidates preferences
• U(s,a)y-k(a-s)²
• if elected
• U 0 otherwise

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• Voters' preferences
• V(s,a)-(a-s)²
• a voters type a ? -D,D
• s policy implemented by the elected politician
• The median voter is drawn from the distribution
  G,
• symmetric with respect to 0.

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The electoral Game

• Each candidate makes an electoral announcement
• from her type space, mR and mL ,respectively.
• 1st election each voter casts her vote for one
• candidate.
• The elected politician implements a policy from
  her
• type space.

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• 2nd election each voter casts her vote for one
• candidate.
• The elected politician implements a policy from
  her
• type space.

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Campaign
1st election voting
Policy Implementation
2nd election voting
Policy Implementation
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• At the second election the opponent is
• randomly drawn from her original
• distribution.
• At each election the median voter is
• selected randomly from G.

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• Type a Candidates expected utility is
• U(p1,p2,s,a)p1y-k(a-s)²p2dy
• pi, probability of winning the i-th election
• dgt0 factor discount

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• An electoral equilibrium is given by electoral
  announcements, policies, voting strategies and
  beliefs such that
• Electoral announcements maximize candidates
  expected utility given beliefs and other agents
  strategies
• (ii) 1st election voting strategies maximize
  electors expected utility in the term following
  the election given beliefs and other agents
  strategies.

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• 1st term policies maximize incumbents expected
  utility at the term following the 1st election
  given beliefs and other agents strategies.
• (iv) 2nd election voting strategies maximize
  electors expected utility given beliefs in the
  term following the election given beliefs and
  other agents strategies and other agents
  strategies

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• (v) 2nd election policies maximize incumbents
• utility
• Beliefs are computed using Bayes rule whenever
• possible.
• We will consider symmetric equilibria
• mR(a)mL(-a) and sR(a)sL(- a)

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• We look for a significant and intuitive family of
• equilibria in which electoral campaign is
• meaningful.
• We devote the attention to equilibria in which
  more
• centrist candidates are elected with higher
• probabilities and implement more centrist
  policies.

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Monotonic electoral equilibrium

• Definition An electoral equilibrium is monotonic
  if
• sR is weakly increasing in a and p1R and p2R are
  weakly decreasing in a
• sL is weakly decreasing in a and p1L and p2L are
  weakly increasing in a

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• Proposition In all nonmonotonic equilibria the
  electoral campaign is meaningful.

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MD1 Refinement

• This refinement (Bernheim and Severinov (2003)
• and Kartik (2005)) selects out of equilibrium
  beliefs
• with respect to totally unexpected policies.
• It adapts the D1 (Cho and Kreps) (1987))
• refinement to the monotonic setup.

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• plR(s) and phR(s) are defined such that a
• R politician implementing the totally
• unexpected policy s should expect to be
• elected with probability within plR(s),phR(s).
• plL(s) and phL(s) are defined such that a
• R politician implementing the totally
• unexpected policy s should expect to be
• elected with probability within plL(s),phL(s).

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• Then it selects the individual that most have
• to gain from implementing policy s.
• Let p be the probability D is elected against
• an opponent randomly drawn from FL (or FR) and
• let p be the probability 0 is elected against an
• opponent randomly drawn from FL (or FR).
• In the D1 refinement
• plR(s),phR(s) plL(s),phL(s) p,p

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• Definition An electoral equilibrium survives the
  monotonic D1 (MD1) criterion if
• Is monotonic
• (R) If policy s is implemented with 0 probability
  in the first mandate and type aR does not benefit
  from implementing policy s and being elected with
  probability p in plR(s),phR(s) then to a is
  assigned 0 probability
• (L) If policy s is implemented with 0
  probability in the first mandate and type al does
  not benefit from implementing policy s and being
  elected with probability p in plL(s),phL(s)
  then to a is assigned 0 probability

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Equilibrium characterization and existence

• Proposition There exists no fully separating
• equilibrium in campaign, nor in policy.
• A proportion of the candidates is ambiguous

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• Proposition There exists no equilibrium in which
  m(?)? and s(?)? for all ??(?1, ?2), for some
  ?1lt?2
• Citizens control politicians imposing a credible
  threat to reelection which forces the incumbent
  to fulfill her electoral promise (endogenous
  commitment)

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• All MD1 equilibria are characterized by a cut-off
  
• type
• Proposition For each MD1 equilibrium
• there exists a(k) ? (0,D such that
• sR(a)0 on 0,a(k)
• (2) If a(k)ltD then sR(a) is separating on
• (a(k) ,D and sR(D)D.
• Analogous condition holds for candidate L
• There are four kinds of equilibria

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k k0 babbling equilibria
sR
mR
Campaign
Policy
a
a
D
D
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k0 lt k campaign is irrelevant, extremists
separate in policy
sR
mR
Campaign
Policy
D
D
a
a
D
D
a1(k)
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k1 ltk centrists and extremists make different
campaigns, extremists separate in policy
sR
mR
Campaign
Policy
D
D
a
a
D
D
a2(k)
a2(k)
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k2 lt k centrists pool, extremists
differentiate both in campaign and in policy
sR
mR
Campaign
Policy
D
D
a
a
D
D
a3(k)
a3(k)
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• Theorem An MD1 equilibrium exists for all kgt0.
• There exist k0 ltk1 lt k2 and cutoff
• types a1(k),a2(k),a3(k) such that all MD1
• equilibria are of the following form
• k k0 m(a)m(0) and s(a)0 for all a?0,D.
  If k gt k0 such an equilibrium is not MD1
• k0 k, there exists an equilibrium such that
  m(a)m(0) for all for all a ? 0,D, s(a)0 a ?
  0,a2(k), s(a) is separating on (a(k),D.

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• k1k there exists a equilibrium in which
  m(a)m(0) for all a ? 0,a2(k) and m(a)m' for a
  ? a2(k),D. s(a)0 for a ? 0,a2(k) and s(a) is
  separating on (a2(k),D
• k2k there exists an equilibrium in which
  m(a)m(0) for all a ? 0,a3(k) and m(a)a for
  a ? a3(k),D. s(a)0 for a ? 0,a3(k) and s(a)
  is separating on (a3(k),D

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• Corollary a1(k),a2(k),a3(k) are strictly
  decreasing
• functions of k and limk?8ai(k)0 for i1,2,3.
• Equilibria (2) and (3) converge to each other
• as k?8.
• Equilibrium (4) is fully separating both
• campaign and in policy as k?8.

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Comments

• Similar results can obtained by introducing
• electoral deception as an idiosyncratic shock on
• electors.

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• Electoral campaign can convey relevant
• information to electors, but there is always is
• unavoidable portion of ambiguous politicians
• Lying has an endogenous costs to lose electoral
• support
• Imitation can be unbearable for extremists
• .