First, Assume No Elections

Dixit, Grossman, and Gul (2000), hereafter DGG, study a setting in which two groups repeatedly divide a fixed surplus over an infinite horizon. The basic ingredients are:

• Two groups, $A$ and $B$, each with concave utility over their share of a pie normalized to 1.
• In each period, one group "holds power" and unilaterally chooses the allocation.
• Power evolves according to an exogenous Markov process: if $A$ is in power today, it remains in power tomorrow with probability $\rho$, and $B$ takes power with probability $1-\rho$.
• Both groups discount the future at rate $\delta$.

The crucial assumption is that the actor in power has complete discretion over the allocation in that period. There are no elections, no institutional vetoes, etc. Under these conditions, DGG characterize the efficient self-enforcing allocations: divisions of the surplus from which neither group would deviate, given the threat of future punishment.

The Core Result

Let $x_A$ denote group $A$’s share when $A$ is in power, and $x_B$ denote $A$’s share when $B$ is in power (so $B$’s shares are $1 - x_A$ and $1 - x_B$, respectively).

In the one-shot version of the game, the group in power would simply grab the entire surplus. With repetition, this is no longer optimal: if a group grabs everything today, it invites harsh treatment when the other group later takes power, and risk aversion makes such extreme fluctuations unattractive.

In equilibrium, each group moderates. When $A$ is in power, it chooses some $x_A < 1$; when $B$ is in power, it grants $A$ some positive share $x_B > 0$.

A typical self-enforcement constraint when $A$ is in power can be written as:

$$u(x_A) + \delta \big[ \rho V_A^A + (1-\rho) V_A^B \big] \geq u(1) + \delta \big[ \rho \tilde V_A^A + (1-\rho) \tilde V_A^B \big]$$

where:

• $u$ is $A$’s period utility from its share,
• $V_A^A$ and $V_A^B$ are $A$’s continuation values when $A$ or $B$ is in power under the equilibrium allocation rule,
• $\tilde V_A^A$ and $\tilde V_A^B$ are the continuation values following a deviation and subsequent punishment.

The left-hand side is the value of complying with the equilibrium allocation rule (moderation today plus continuation play). The right-hand side is the value of deviating (grabbing everything today, then facing a punitive allocation in the future).

From this structure, DGG derive several comparative statics:

1. As $\delta$ increases (players are more patient), the set of self-enforcing allocations expands and the difference $|x_A - x_B|$ shrinks: more patience supports more symmetric sharing.
2. As $\rho$ decreases (power alternates more frequently), the difference $|x_A - x_B|$ also shrinks: more frequent alternation strengthens punishment and encourages moderation.
3. Greater risk aversion likewise pushes toward smoother, more equal allocations.

The intuition behind (2) is often emphasized: when alternation is frequent, any harsh action you take while in power will be "paid back" soon, making extreme allocations less attractive.

How the Paper Gets Cited

In political economy, DGG is often cited as showing that exogenous rotation of power can lead to policy moderation. The typical use is heuristic:

"Institution $X$ rotates power between groups. Following Dixit, Grossman, and Gul (2000), this rotation creates dynamic incentives for moderation: today’s incumbent restrains itself because it anticipates being an out‑group tomorrow."

Dunning and Nilekani (2013) invoke this logic in their study of caste quotas in Indian village councils. They note that:

"Regular exogenous alternations in power may moderate how much policy changes whenever the identity of the group in power shifts. For example, Dixit, Grossman, and Gul (2000) construct an infinite-horizon model in which two groups rotate in power according to some fixed exogenous probability... The key insight of their dynamic model is that each group alters policy less dramatically when in power than it would in a one-shot interaction."

They present this as one way to think about why reserving council presidencies for Scheduled Castes (SCs) might not visibly shift distribution toward SCs: if quotas induce, or reflect, a pattern of regular rotation across groups, DGG-style dynamics could moderate behavior.

Similar citations appear in work on:

• Term limits and political compromise,
• Power-sharing in post-conflict settings,
• Coalition governments with rotating prime ministers,
• Ethnic or sectarian quota systems.

In all of these applications, the DGG logic is used as a stylized account of how rotation plus repeated interaction might dampen policy swings.

Electoral Selection

As we note above, in DGG, the actor in power has unconstrained discretion over the allocation each period. There are no voters, no parties, no nomination processes, no institutional vetoes. In most democratic settings, these are precisely the elements that structure behavior. Mapping "group in power" directly to "group preference implemented" therefore embeds a strong assumption: that once a member of a given group holds office, they act on that group's preferences, constrained only by dynamic punishment from other groups.

Consider what actually happens when a panchayat presidency is reserved for SCs.

Stage 1: Candidate emergence and nomination

Multiple SC individuals may be potential candidates. They differ in their preferences over caste-targeted policies, their class interests, and their attachments to party networks. Parties and local elites may back some types over others. Even before voters enter, there is intra-group and intra-party selection that filters which SC types are likely to appear on the ballot.

Stage 2: Electoral competition with a fixed electorate

Reservation changes who may stand for office, not who may vote. The electorate is unchanged. An SC candidate must therefore appeal broadly: where SCs constitute 20–30 percent of the population, victory requires substantial non-SC support, typically mobilized through party networks.

In a simple Downsian benchmark with a unidimensional policy space and full electoral competition, candidates’ platforms converge toward the median voter’s ideal point $m$:

$$p^* \to m$$

This logic does not depend on candidates’ identities. An SC candidate in a reserved race and an upper-caste candidate in an unreserved race both face essentially the same median voter and thus similar electoral incentives.

Stage 3: Post-election governance and multiple principals

Once in office, a president is typically not a pure discretionary actor either. They may:

• Want to be re‑nominated or elected to higher office,
• Depend on party support and resources,
• Care about reputation with local brokers and co-partisans.

These create accountability relationships that tie behavior to the preferences of parties, voters, and organizational elites, not only to the preferences of "their" caste. In such a setting, much of the moderation observed in practice may arise from who gets selected and how they are disciplined rather than from inter-group dynamic bargaining of the DGG sort.

A Median-Voter Benchmark

It is useful to contrast the DGG logic with a simple electoral-competition benchmark.

Let:

• $\theta_i$ denote politician $i$’s ideal point on some policy dimension (e.g., the degree of caste-targeted spending), with the distribution of $\theta_i$ depending on group identity;
• $m$ denote the median voter’s ideal point;
• $p_i$ denote the policy implemented by politician $i$.

DGG-style interpretation

In a literal DGG-style mapping, one might think of policy under group $g$ as:

$$p_i \approx \theta_g - \text{(moderation term due to repeated-game discipline)}$$

so that the policy when an SC president is in power is close to the "SC ideal," tempered by fear of future punishment when a non-SC president takes over. Changes in the rotation process (e.g., more frequent alternation) then affect the size of the moderation term and hence the distance between policies under different groups.

Electoral-competition benchmark

In a simple Downsian world with a fixed electorate and strong electoral competition, the mapping is instead:

$$p_i \approx m + \varepsilon_i$$

where $\varepsilon_i$ is a small disturbance capturing, for example, valence, incomplete convergence, or multidimensionality. In that benchmark, the location of the median voter rather than the leader’s group identity is the primary determinant of policy; leader identity matters only through second-order channels such as candidate selection or issue salience.

These two perspectives yield different comparative statics:

Under the electoral-competition benchmark, if the electorate is unchanged, reservation of a seat does not, by itself, move the median:

$$p^*_{\text{unreserved}} \approx m \approx p^*_{\text{reserved}}$$

Quotas can then have small or null effects on policy even without any dynamic bargaining logic.