Ideology and endogenous constitutions
From the text: The raison d'être of this paper is mathematical justification of legislative decision making with position-taking preference. Reviewing a lot of the literature in this area the author presents his own model. A three-person legislature \(N = \{l,c,r\}\) has to select a one-dimensional policy \(x\) in the continuous interval \(X\subset\mathbb R\). The indexes \(l\), \(c\), and \(r\) stand for the legislator who represents the left-, center-, and right-leaning constituency, respectively. \(x\) is decided after playing an agenda-setting game under closed rule. Let \(q\in X\) denote the status quo alternative. Concerning preferences, it is assumed that legislators have a double objective. In particular, the utility of each policy maker \(i\in N\) is given by \[ u_i(p_i,x)=-\frac{1}{2}|x|-\theta_i|p_i-i|. \tag{1} \] The first term in (1) depends on \(x\), the policy that is implemented in the economy. The second term is less standard and reflects electoral considerations on the part of legislators. More specifically, it depends on the position \(p_i\), taken by legislator \(i\) in the voting game, where \(p_i\) also takes values in \(X\). In order to maximize the second term, \(p_i\) should be set equal to \(i\). Note that the index \(i\) denotes the legislator but also the policy that minimizes the legislator's position cost. To streamline the analysis, it is assumed that \(c=0\) and that \(l\) and \(r\) are symmetrically on opposite sides of zero. That is, \[ l<0<r \quad \text{ and} \quad r=-l. \tag{2} \] Moreover, in order to make the model as transparent as possible, it is also assumed that the first term in (1) is the same for all legislators, that is, all legislators agree that the correct policy decision for the economy at large is \(x = 0\). Then, disagreement among legislators arises because of electoral considerations. Throughout this paper, the author often refers to \(l\) and \(r\) as the ideological legislators. Knowing the values of \(r\) and \(l\) can be defined the following measure of ideological polarization: \[ \iota\equiv r-l>0. \tag{3} \] A Bayesian Nash equilibrium in the voting game is a pair of strategies for the two voting legislators such that for each voting player and every possible value of \(\theta_i\), the voting decision is a (weakly undominated) best response to the other's voting decisions. Given the equilibrium in the voting stage, the agenda setter selects the proposal that maximizes her expected payoff. An equilibrium in the agenda-setting game under constitution \(\mathcal C\) is then given by, \(\sigma^*_\mathcal C=[x^*_\mathcal C,s^*_\mathcal C] \) where \(x^*_\mathcal C\) denotes the equilibrium proposal for each possible agenda setter and every possible value of \(\theta_i\), while \(s^*_\mathcal C\) denotes the equilibrium voting strategies for all possible pairs of members in the legislature and every possible type. Bayesian Nash equilibria in the voting game will have the ``cutoff property'', that is, a legislator accepts a proposal if his type (the weight of electoral considerations) is below a certain cutoff point and rejects otherwise. To understand this, note that a vote matters for economic outcomes only when the legislator is pivotal, but it matters for electoral considerations in any event. As a result, the effective importance of policy considerations (relatively to electoral ones) is weakened. Then, equilibrium voting rules under unanimity rule and under simple majority rule are studied. A complete characterization of the equilibrium proposal strategy for every parameter value is more involved and beyond the scope of this paper. Nevertheless, the author is able to determine regions of parameters (identified in Propositions 1--2 below) where equilibrium proposals can be solved for. This allows the author to compare constitutions and provide a set of meaningful conditions under which one voting rule dominates the other. Finally, concerning the proposal strategies of the ideological legislators, the author obtains that when \(\iota\) is high and \(|q|\) is low, members \(l\) and \(r\) may choose to propose a policy that panders to their voters and that is sure to be rejected so as to keep the status quo. {Proposition 1.} Unanimity rule and autocracy yield higher equilibrium welfare than simple majority rule when the value of \(\iota\) is sufficiently low relatively to \(|q|\). Moreover, fix any \(q\neq 0\) and any \(\iota\in (0,\underline\iota)\). Then, there also exists a \(\overline\gamma\in(0,1)\) such that for every \(\gamma\in(\overline\gamma,1)\), we have that \(W_\mathcal U(\iota,q,\gamma)=W_\mathcal A(\iota,q,\gamma)>W_\mathcal M(\iota,q,\gamma,\sigma^\ast_\mathcal M)\). The first part of Proposition 1 also establishes that for every equilibrium \( \sigma^*_\mathcal M\), simple majority rule is weakly dominated in welfare terms by the other two constitutional regimes. As established by the second part of Proposition 1, simple majority rule is then strictly dominated in welfare terms. {Proposition 2.} Simple majority rule yields higher equilibrium welfare than unanimity rule and autocracy when the value of \(\iota\) is sufficiently high relatively to \(|q|\). More specifically, let any equilibrium \(\sigma^\ast_\mathcal M\) under simple majority rule be given. Fix any \(q\neq 0\) and fix any \(\gamma\in(0,1)\). Then, there exists a \(\overline\iota>2|q|\) such that for every \(\iota>\overline\iota\), we have that \(W_\mathcal M(\iota,q,\gamma,\sigma^\ast_\mathcal M)>W_\mathcal U(\iota,q,\gamma)>W_\mathcal A(\iota,q,\gamma)\). This Proposition 2 establishes that when ideological polarization is high relatively to \(|q|\) autocracy is especially inefficient. This is mainly because its welfare is not bounded from below by \(-|q|\) and is decreasing in \(\iota\). In that same region of parameters Proposition 2 also establishes that simple majority rule strictly dominates unanimity rule in welfare terms. To understand this, note that under unanimity rule, an ideological legislator is reluctant to accept (or propose) a reform simply because when \(\iota\) is high and \(|q|\) is low it is quite unlikely to observe a ``yea'' vote from the other ideological legislator. In Section 8 the author briefly considers an extension of his model, endogenizing the probabilities of being recognized agenda setter. {Proposition 3.} Under unanimity rule, both ideological legislators run for office. Under autocracy, neither ideological legislator runs for office and member \(c\) is elected with probability one. A stark implication of Proposition 3 is that autocracy is first best. This occurs because in a model where recognition probabilities are endogenous, member \(c\) is elected with probability one and, consequently, policy zero is implemented regardless of the extent of ideological polarization.
scientific article; zbMATH DE number 6162240
scientific article