# De Figueiredo (2002) - Electoral Competition Political Uncertainty And Policy Insulation

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## Reference(s)

de Figueiredo, R. J. P., Jr. (2002), Electoral Competition, Political Uncertainty, and Policy Insulation, American Political Science Review 96, 321-333. pdf

## Abstract

Scholars argue that electoral uncertainty is a crucial factor that influences policy implementation: current holders of public authority, nervous that they might lose their position, seek to insulate the agencies they create so that policies will survive their creators. These theories, however, ignore crucial variation in the electoral prospects of groups competing for public authority. In this paper, I examine the effect of electoral volatility on the degree to which groups in power will dismantle their opponent’s agencies and programs and insulate their own policies from such destructive behavior. Through the analysis of two repeated games, I derive four propositions which fully characterize the conditions under which cooperative behavior can provide stability in the face of electoral uncertainty and instability. First, I show that if gains from cooperation are sufficiently large, compromise and cooperation can occur in the face of uncertainty. Second, I show that electoral uncertainty increases the possibility of cooperation, a result counter to the informal literature. Third, when electoral uncertainty is low, only one group - that with a low probability of electoral success - will insulate their programs. Finally, as electoral uncertainty increases, a wider set of the parameter values support the extreme cases of either both insulating or not insulating. I conclude by discussing some implications, examples and potential further extensions of the models.

## The Reciprocity Game (RG)

The game in an infinitely repeated two-player game.

In each period:

• Nature selects player $A\,$ to move with probality $\gamma \in (0,1)\,$ and $B\,$ to move with $1-\gamma\,$. $\gamma\,$ is the probability of being elected.
• Political uncertainty is modelled by $\gamma\,$ close to $\frac{1}{2}\,$. With $\gamma=1\,$ or $\gamma=0\,$, $A\,$ or $B\,$ are certain to be elected, respectively.
• Political uncertainty is decreasing in $|\gamma - \frac{1}{2}|\,$
• If elected a player implements their program with certainty.
• A player may also choose $A_it=\{O, NO\}\,$, that is $Overturn\,$ or $Not\,Overturn\,$ with respect to the other players program if one is in place.

Stage payoffs are calculated as:

$u_{At} = \begin{cases} (1,0) & \mbox{ if only A program is in place} \\ (0,1) & \mbox{ if only B program is in place} \\ (\beta ,\beta ) & \mbox{ if both A and B programs are in place} \\ \end{cases} \,$

And likewise for $B\,$, where $\beta \in (0,1)\,$. Note that for $\beta \gt 0.5\,$ choosing NO is welfare improving as $\beta+\beta \gt 1\,$.

The total payoffs to the game are the discounted sums of the players stage payoffs:

$U_it = \sum_{t=0}^{\infty} \delta^t u_it \quad i \in \{A,B\}\,$

A player's strategy at $t\,$ describes what he will do given all possible histories $H_t\,$, where $H_t\,$ is made up of the choices of nature $N_t\,$ and the action sets of both players $A_{At}\,$ and $A_{Bt}\,$, where $N_t = (n_1, \ldots, n_t)\,$ and $A_{At} = (A_{A1},\ldots, A_{A(t-1)})\,$, and likewise for $A_{Bt}\,$. The game is one of complete information.

The cooperative equilibrium is one where both players play $NO\,$ in every stage. This can be sustained by a Grim Trigger where a player plays $O\,$ for all time if either player has played an $NO\,$ at any time previous, provided that $\delta,\gamma \mbox{ and } \beta\,$ are sufficiently high. To prove this, recall that the sum of a geometric series is given by:

$s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}\; \mbox{ or }\; \sum_{k=m}^\infty ar^k=\frac{ar^m}{1-r}$

provided that $r\,$ is less than 1 (which is needed for convergence).

Then one can solve for $\beta_A^*\,$, the threshold $\beta\,$ if $A\,$ defects as:

$\underbrace{\sum_{t=0}^{\infty} \delta^t \beta}_{\mbox{Cooperate}} \ge \underbrace{1 + \sum_{t=1}^{\infty} \delta^t \gamma}_{\mbox{Defect and prob(elected)}=\gamma \,}\,$

$\therefore \beta \ge 1-\delta + \delta \gamma\,$

And likewise for $\beta_B^*\,$:

$\beta \ge 1 - \delta \gamma\,$

Then cooperation can be sustained iff:

$B \ge max( \beta_A^*, \beta_B^*)\,$.

Note that cooperation can not be sustained if $\beta \lt \frac{1}{2}\,$.

$\beta\,$ could be high because:

• Groups value policy continuity ($\beta\,$ is endogenously high)
• Groups are risk averse
• Policies could be more effective with lower policy volatility
• Much political bargaining takes place across many dimensions - if players care about two dimensions and their indifference curves are elliptical then compromise positions will yield benefits.

The paper then considers the comparative statics of the relationship between uncertainty and cooperation. The results include:

• As $\gamma\,$ approaches $\frac{1}{2}\,$ cooperation can be sustained over a wider range of parameters.
• Therefore as political uncertainty increases it is easier to sustain cooperation.
• The diagram on p16 shows that the 'cooperative payoff' that can be supported is a V shaped (parabolic) function with respect to $\gamma\,$, with a vertex at $\frac{1}{2}\,$
• As long as players are sufficiently risk averse, this will hold even if conflict is one-dimensional.
• The basic results also hold if there are n institutions which must be controlled to pass the legislation.
• In general the stronger player will have weaker incentives to cooperate.

## The Insulation Game (IG)

Insulation, in this context, means making institutional changes to help prevent legislation from being overturned. For example passing a requirement that the legislation could only be overturned with a supermajority, is a form of insulation.

Again there are two players, $A\,$ and $B\,$, who play an infinitely repeated game. Players can implement their program with certainty, and the moving player has the opportunity to $Overturn\,$ or $Not Overturn\,$ the other players existing legislation. However, now players can additionally choose to $Insulate\,$ or $Not Insulate\,$, denoted $I\,$ and $NI\,$. This action is only available in the first period that a player is recognized.

If a player plays $NI\,$, the game is identical to the RG game above. If a player chooses $I\,$, then his payoffs are modified by $\alpha \in (0,1)\,$, but his program remains in place forever, so that the player recieves $\alpha\beta\,$ if the other players program is in place, and $\alpha\,$ if not. Note that $1 \gt \alpha \gt \alpha\beta \gt 0\,$. $\alpha\,$ can be thought of as modelling 'the cost of insulating'.

Insulation can be thought of as:

• A way to avoid punishment strategies
• A way to trade benefits while in power for benefits while out of power.

The paper provides three propositions (3a,3b,3c) on pages 22-23:

• If $\alpha\,$ is sufficiently large, both players play$\{(I,O)\}\,$
• If $\alpha\,$ is not sufficiently large to play $\{(I,O)\}\,$, an equilibrium is either: $\{(I,O);(NI,0)\}\,$ or $\{(NI,O);(I,0)\}\,$ if $\alpha\,$ is sufficiently large
• If $\alpha\,$ is sufficiently small, the neither player will insulate

Proposition 4 states: As political uncertainty increases the parameter space over which the 1st and 3rd equilibria hold increases, while the parameter space over which the 2nd equilibrium holds decreases.

From above, it is clear that the equilibrium strategy depends on the cost of insulating ($\alpha\,$). A diagram showing how the strategy space varies with both the costs of insulating and the political uncertainty (i.e. who is favoured to be relected). The following results are important for intuition:

• As the costs become very high ($\alpha\,$ becomes very small), only those with a very small chance of getting reelected will insulate (to get some on-going benefits, as this will outweigh the costs).

The paper claims that public agencies will therefore be less effective (c.f efficient) than private ones:

• Electoral uncertainty leads to inefficient insulation - as political uncertainty increases, so does insulation.
• However, as per proposition 4, increasing political uncertainty also increases the range over which no insulation occurs - actually it is groups that are electorially weak that will insulate.
• If the costs of insulation are high, groups will choose not to insulate their programs - only groups with extremely weak future election prospects will do so.
• Most agencies created by policy will not be insulated (on average the strong players win and don't insulate), and therefore inefficiency can not be attributed to political uncertainty in most cases.

## Other Notes

In the context of regulation being requested by the radio industry (to avoid congestion, etc), the paper references:

• Stigler's (1972) capture model
• Wilson's (1989) "client politics"

The FCC and related institutions were created during a period of policy certainty and ended up independent and self-governing. Trade policy, on the other hand, was close to the Reciprocity Game - when one party gained power the tariffs where increased, when the other gained power the tariffs were decreased. The Democrats found an IG type answer to this in 1930, when they created the RTAA, ceding power over tariffs to the president; presidents (even Republican ones) were inherently more liberal on trade than legislators.