Minorities in dictatorship and democracy.

How does the level of democracy in a country affect the government’s treatment of ethnic minorities? I find that, on average, when the largest ethnic group in a society exceeds half of the population, ethnic minorities are treated better in autocracies and full democracies than in semi-democratic countries. The intuition is that under autocracy a leader needs little popular support, and therefore a coalition of several minorities can rule. By contrast, in a semi-democracy, the leader needs the support of more people, so a coalition of small ethnic groups is insufficient; the largest group is enough and no other groups are necessary. Finally, highly democratic countries require broad support, and most ethnic groups get benefits. My model is based on the Baron-Ferejohn bargaining game and my empirical tests use the Ethnic Power Relations dataset.


Introduction
This paper finds that in states where the largest ethnic group exceeds half of the population, autocrats often favor minorities. An autocrat is likely to include small groups if she represents one of them. If an autocrat represents a large ethnic group, minorities will be excluded. In a semi-democracy, they are very likely to be excluded, regardless of the group the leader belongs to. In a full democracy, minorities will be more likely to be included than in a semi-democracy. To make the analysis meaningful, in this paper minority rights are not included in the definition of democracy, and democracy is understood in the electoral sense.
I explain the regularity above using the logic of winning coalitions (Riker and Ordeshook 1973, Bueno de Mesquita et al 2005). The winning coalition is a group of people whose support a leader needs to stay in power. In my model, a state is more democratic if it has a larger winning coalition. For the purposes of this paper, the winning coalition size is assumed to be exogenous. In an autocracy, the winning coalition is small, so a leader may build her support base from several minority groups. Due to their small size, minorities have worse outside options to form a coalition than other groups do. This makes them favorable coalition partners for a dictator since they demand relatively little in return for loyalty. Thus, we should observe a lot of autocracies where a dictator provides benefits to minorities and has their members in the inner circle.
A prominent example is Syria. Syria under the Assads was an autocracy that treated ethnic minorities relatively well. The core supporters of Another side of the coin is that when the dictator's own group is large enough, she will rely on them and require no coalition partners. So, in autocracies, the outcome for minorities depends on whether the dictator comes from a small or large group. In other words, the outcome for minorities in dictatorships is volatile. It is well-known that many dictators are brutal to small groups. The model simply shows that often autocrats favor minorities and provides micro-foundations for this fact.
There are regimes where the winning coalition is of medium size. In those regimes, leaders have to win elections, but intimidation, vote-buying, and fraud play a large role. Parliaments and courts cannot strictly constrain the executive. In this situation, several minorities cannot rule alone. However, the leader of the largest group can appeal to her coethnics only and control the state. The model predicts that, contrary to the autocratic case, in such a regime minorities will be excluded regardless of who the leader is.
Turkey may serve as an example. The country had a polity score be- In a full democracy, the winning coalition is very large. Aside from winning the votes, the leader cannot pass laws that are turned down by courts and needs the consent of the parliament. Changing rules of the Constitution often requires the parliamentary supermajority. Moreover, mass demonstrations of the citizens may endanger the government's survival.
Because the leader needs broad support, even small groups need to be included in sharing the benefits. Western European states, which are the most democratic, are the most tolerant to minorities.

Literature
Several theoretical papers study the link between democracy and minority rights. Mukand and Rodrik (2015) build a model where both the regime type and minority rights protection are endogenous and depend on the preferences of the rich elite, the poor majority, and minorities. This paper's approach is different from mine, since I study the impact of institutions on minority welfare, and thus assume that the regime type is exogenous. Fernandez and Levy (2008) model redistribution between groups in the society in democracy and look at the impact of diversity on the amount of redistribution. Trebbi et al (2015) model transfers between ethnic groups in Africa made by leaders under the revolution constraint. These two papers only analyze redistribution given a single regime type, unlike my study which compares different regime types. However, these papers are similar to mine in that they model groups in the society as actors seeking to maximize their share of resources.
On the empirical side, Sorens (2010) finds that more executive constraints and more competitive political participation decrease the likelihood of discrimination, however, a more competitive executive selection increases it. Contrary to that and to my results, Fox and Sandler (2003) find that repression against minorities is least likely in semi-democracies.
One criticism of the latter finding is that the authors use the Minorities at Risk dataset which includes groups only if they are at risk, thus creating a bias. In line with my study, using the Ethnic Power Relations dataset Beiser and Metternich (2016) find that smaller ethnic groups tend to choose other minorities as coalition partners.
Bueno de Mesquita et al (2005) propose the concept of the winning coalition as key to the way leaders redistribute resources. In their model, the winning coalition is a group of people whose support the leader needs to stay in power. The size of the minimum winning coalition is exogenous and determined by the political regime type, with more democratic regimes corresponding to larger coalitions. The leader's goal is to keep her winning coalition loyal by providing private and public goods, while at the same time trying to spend as little resources as possible. My model uses the same taxonomy of political regimes, which is convenient for analyzing distributive politics.

Model
Environment Consider a society that consists of one large group of voters and m ≥ 2 small groups of the same size. The large group has share k > 1 2 , so each small group has share s ≡ 1−k m < k. I assume that the largest group has more than 50% since in such a society it is easy to distinguish the largest group from the minorities. Each group is a unitary actor. The groups have to divide a dollar among themselves. The division is implemented if a winning coalition of size w > s votes for it. Define r ≡ w s − 1, the number of minorities that a minority proposer needs in order to complete a winning coalition. The minimum winning coalition size w is exogenous. The voting procedure is as follows.

The political process
At each time period, one group is randomly selected to propose the division of the dollar to other players. The selections are independent and the group's probability to be chosen equals its share of the population. This assumption is justified by the fact that larger groups are more likely to oc- the proposer, is greater than or equal to w, the game ends and the proposal is implemented. Otherwise, the game is repeated and the resource is discounted by δ , where 0 < δ < 1. The model is a version of a classic Baron and Ferejohn bargaining game (1989). The total size of players required to pass a decision, w, is interpreted as the level of democracy. If w is high, more people are needed to pass a decision, so the regime is more democratic. If w is small, the converse is true, so the regime is more autocratic.
Assume w > 1−k m , so that a single minority group cannot rule alone. The latter simplifying assumption does not change the results in a significant way.

Timing
The sequence of play is as follows.
1. A proposer is randomly selected, with the probability for each group to be selected equal to its share of the population.
2. The selected player proposes a division of a dollar.
3. The remaining players vote Yes or No.
4. If the total size of those who voted Yes, including the proposer, is greater than or equal to w, the proposal is implemented. Otherwise, the prize is discounted and the game goes to stage 1.

Payoffs
Define v ma j to be the ex-ante expected payoff of the majority and v min -the expected ex-ante payoff of the minority. These are not normalized by the group size. As I show later, this has no implications for the comparative statics. These payoffs are the measure of minority welfare.  The following graph is obtained by simulations and illustrates the comparative statics. The proof is for the general case. The same applies to all proofs and graphs in this paper. Intuition Consider the case when w < 1 − k, so either a coalition of minorities or the largest group alone can form a winning coalition. The largest group has a high expected ex-ante payoff from turning down an offer. So, it is a better choice for a minority proposer to make an offer to a coalition of minorities because they will demand less. As the minimum winning coalition size w increases, this calculation stays true, until w is greater than 1 − k, so a coalition of minorities cannot be winning anymore. Thus, as w < 1 − k, the payoffs are the same regardless of w. Suppose w exceeds 1 − k. In this case, a minority proposer chooses the largest group as a coalition partner, paying a lot, while the largest group rules alone if it becomes the proposer. The reason the largest group accepts an offer from a minority is that the resource is discounted after each round, so the bargaining range is not empty.

How to solve for the equilibrium
Finally, if w > k, the largest group cannot rule alone. So, if the largest group is the proposer, it makes offers to minority groups. If a minority becomes the proposer, it makes an offer to both the largest group and several other minorities. As w increases, more minorities are needed to complete the winning coalition, so their expected ex-ante payoff grows.

Hypothesis
There is a U-shaped relationship between the level of democracy and the level of ethnic minority welfare in societies where the largest ethnic group exceeds half of the population.

Data
The unit of analysis is a country-year. I use data from the Ethnic Power

Control variables
The control variables are GDP per capita, growth, the share of the largest ethnic group in the population, ethnic fractionalization, years as a colony, oil production per capita, the dummy for the ongoing civil war, and regime change in the past 3 years. All of these variables come from EPR.

Regression type
The levels of executive constraints and minority representation vary little within the same country. So, it is hardy possible to use a fixed-effects regression. Instead, I use the random-effects and pooled OLS regression.
In the pooled OLS regression, I include regional fixed effects and display robust standard errors.

Results
The index for executive constraints in the Database of Political Institutions is robustly associated with the share of included minorities. The linear term has a negative sign and the quadratic term has a positive sign, which creates a U-shaped relationship. The result is robust to including random effects.
The results are presented in Tables 1 -6 in Appendix B. Figures 2A -2C below plot the data and fit it using a quadratic function.     The majority gets v ma j = δ k since it proposes to itself. Now, this is an equilibrium iff: There are no other equilibria given these values of parameters by Eraslan's Theorem.
Let 1 − k < w < k. Then each minority proposes to the majority, and the majority proposes to itself, therefore Finally, let w > k. Then the payoffs are given by: The derivative dv min dw is positive given the relevant parameter values.
The Baron-Ferejohn model with equal recognition proba-

bilities.
Consider the same model as the main model, but in which recognition probabilities are equal for all players. Lemma: The subgame stationary payoffs are given by Condition Payoff Proof: The model breaks down into several cases depending on which winning coalitions can be formed. I compute the payoffs for the interesting case when w < 1 − k < k and omit the algebra for the other cases due to their simplicity.
Let w < 1 − k < k. Then a winning coalition can consist of the majority, of w s minorities, or of 1 minority plus the majority. Obviously, since k > 1 − k > w, the majority does not invite anyone into the coalition if it becomes a proposer. The minority player who becomes the proposer has two options: to make an offer to the majority or to r ≡ w s − 1 other minorities. Consider a mixed equilibrium in which the minority makes an offer to the majority with probability p and to w s − 1 other minorities with probability 1 − p. The minority proposer must be indifferent between proposing to the minorities or the majority. The payoffs and probability of making an offer to the majority are given by a system of equations: For this to be an equilibrium, it must be true that 0 It is easy to verify that there is no equilibrium in which minorities propose only to minorities. If this were true, the majority would get a SSP payoff of v ma j = δ m + 1 since it would propose to itself. Each minority would get Each minority proposer then would prefer to propose to the majority instead of r minorities, so this can not be an equilibrium.
Suppose that each minority proposer makes an offer to the majority.
Then the payoffs are given by the system: Since, by Eraslan's Theorem (2013), the SSP payoffs given a set of parameters are unique, this is an equilibrium when If 1 − k < w < k, then every winning coalition includes the majority, so each minority proposer makes a proposal to the majority. If w > k, then every winning coalition includes the majority and (w−k)/s minorities.
Setting up systems of equations as in the first example and solving them gives the payoffs for the remaining cases.
Taking derivatives shows that the minority welfare v min decreases in w and increases otherwise. Since and there are no discontinuous upward jumps.
Clearly, the majority could pick p ma j = 1 − ε where ε is very small and get accepted. Hence, p i = 0 for any i are the unique equilibrium prices of votes. So, the expected continuation payoff of the minority is v min = δ m+1 . Let now 1 − k < w ≤ k. The majority, again, chooses itself as a winning coalition. Define v ma j and v min, j as the expected continuation payoffs of the majority and generic minority, respectively. They are time-invariant by the stationarity assumption. Since the only winning coalitions that are played in equilibrium consist of just the majority, or the majority plus one minority, the minorities only earn their payoffs in case they serve as formateurs. Now, consider a minority player j that is the formateur. Let the majority price be p ma j . If j rejects, the only time she will be able to earn a positive payoff in the future will be the same strategic situation. That is, the next round in which i is a formateur. Hence, i accepts any p ma j , so p ma j = 1. So, v min = 0.
Let k < w < 1. Then all winning coalitions contain some minorities and the majority. If the majority is a formateur, all minorities announce a price of 0. Otherwise any minority player not included in the winning coalition can gain by reducing her price. If a minority is a formateur, then all other minorities set 0 prices by the same logic. As in the case when 1−k ≤ w < k, the majority sets a monopoly price of 1. Again, v min = 0.
Finally, let w = 1. This is unanimity rule, so all players are essential.
There is a family of silly equilibria in which at least one player posts a very high price, and all formateurs pass the move. Assume however that ∑ i p i ≤ 1. Because all players are now equivalent and we assume stationarity, all prices must be the same, so p i = p j for any i, j. Since a formateur must agree on the proposals, it must be that:

The Shapley value
The Shapley value is a way to assign payoff to players in a cooperative setting. That is, the game specifies the payoff that each coalition of players can achieve, but not the structure of the game. Since the value is given axiomatically and does not assume any protocol of interaction, this approach has an advantage over the Baron-Ferejohn model. The Shapley value always exists and is unique. I will invoke the computational method and various properties in the proof and refer the reader to Winter (2002) for a thorough exposition. I will keep the notation from the main model and the assumption that the majority is larger in size than all minorities together. The Shapley value is easier to compute using the number of votes versus shares. I assume that each minority group has 1 vote. I also add several new variables. Define n ≡ m 1−k as the total number of votes available, q = n − m as the amount of votes the majority group has, and W = wn as the number of votes in the minimum winning coalition. Now I will prove that in our setting the prediction of the Shapley value is the same as of the Baron-Ferejohn model (though in general they are not the same).
Hence the payoff of each minority player is which decreases in w.
Let m < W < q . Then, obviously, v ma j = 1 and v min = 0.
Let W ≥ q. Then the majority is pivotal if her position is from W − q + 1 to m + 1. There are m + 1 − (W − q + 1) + 1 = m −W + q + 1 such positions and m! orderings of minorities which correspond to each, which gives Since there are (m + 1)! possible orderings, the proba-bility for the majority to be pivotal is: Hence the minority payoff is So, similar to the Baron-Ferejohn case, the utility of a minority first decreases, then stays constant, then increases in the level of democracy.