A dynamic theory of fidelity networks with an application to the spread of HIV/AIDS

We study the dynamic stability of fidelity networks, which are networks that form in a mating economy of agents of two types (say men and women), where each agent desires direct links with opposite type agents, while engaging in multiple partnerships is considered an act of infidelity. Infidelity is punished more severely for women than for men. We consider two stochastic processes in which agents form and sever links over time based on the reward from doing so, but may also take non-beneficial actions with small probability. In the first process, an agent who invests more time in a relationship makes it stronger and harder to break by his/her partner; in the second, such an agent is perceived as weak. Under the first process, only egalitarian pairwise stable networks (in which all agents have the same number of partners) are visited in the long run, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) are. Next, we apply these results to find that under the first process, HIV/AIDS is equally prevalent among men and women, while under the second, women bear a greater burden. The key message is that anti-female discrimination does not necessarily lead to higher HIV/AIDS prevalence among women in the short run, but it does in the long run.fidelity networks; anti-female discrimination; stochastic stability; HIV/AIDS; union formation models

Political Influence in Multi-Choice Institutions: Cyclicity, Anonymity and Transitivity

We study political influence in institutions where members choose from among several options their levels of support to a collective goal, these individual choices determining the degree to which the goal is reached. Influence is assessed by newly defined binary relations, each of which compares any two individuals on the basis of their relative performance at a corresponding level of participation. For institutions with three levels of support (e.g., voting games in which each voter may vote "yes", "abstain", or vote "no"), we obtain three influence relations, and show that the strict component of each of them may be cyclical. The cyclicity of these relations contrasts with the transitivity of the unique influence relation of binary voting games. Weak conditions of anonymity are sufficient for each of them to be transitive. We also obtain a necessary and sufficient condition for each of them to be complete. Further, we characterize institutions for which the rankings induced by these relations, and the Banzhaf-Coleman and Shapley-Shubik power indices coincide. We argue that the extension of these relations to firms would be useful in efficiently allocating workers to different units of production. Applications to various forms of political and economic organizations are provided.Level-based influence relations, Multi-choice institutions, cyclicity, anonymity, transitivity

Political Design Meets Policy Complexity

The rules that are employed to pass policies in legislative bodies vary widely. It is generally argued that policies that differ in complexity or importance level should be decided under different kinds of voting rules. While this question has been examined for static legislative mechanisms, an analysis of the precise relationship between the level of policy complexity and the type of voting rule is still missing for dynamic mechanisms. We address this problem from the perspective of a preference-blind political designer. Given the level of complexity of the decision that is to be made, the political designer\u27s goal is to select the supermajority rule that avoids (1) policy instability; (2) guarantees efficiency; and (3) minimizes institutional status quo bias. We provide an answer to this objective problem, deriving a closed-form relationship between voting rule and policy complexity. Our analysis rationalizes the use of different rules to adopt different types of policy only when preferences are weak. When preferences are strong, the optimal rule is unique, and it does not vary by level of policy complexity. These findings significantly differ from those obtained for static mechanisms. Our study also implies that more complex policies are more likely to be persistent, even after a change in political preferences

A Political Reciprocity Mechanism

We consider the problem of designing legislative mechanisms that guarantee equilibrium existence, Pareto-efficiency, and inclusiveness. To address this question, we propose a finite-horizon voting procedure that embeds clauses of reciprocity. These clauses grant voters the right to oppose actions that are not in their interest, retract actions that face opposition, and punish harmful actions. We study voters\u27 strategic behavior under this voting procedure using two classical approaches. Following the blocking approach, we introduce two related solution concepts---the reciprocity set and the sophisticated reciprocity set---to predict equilibrium policies. We then show that these solution concepts (1) are always non-empty; (2) only select Pareto-efficient policies; (3) strategically protect minority interests; and (4) are compatible with classical notions of fairness and Rawlsian justice in distributive problems. Following the non-cooperative approach, we provide an implementation of each of these solution concepts in subgame perfect equilibrium, which makes them applicable in a wide range of legislative settings. We also extend them to effectivity functions, a large class of games that includes strategic form games. A comparative analysis shows that the reciprocity mechanism has other desirable features and properties that distinguish it from other well-known voting mechanisms and solution concepts

Twin Estimates of the Effects of Prenatal Environment, Child Biology, and Parental Bias on Sex Differences in Early Age Mortality

Sex differences in early age mortality have been explained in prior literature by differences in biological make-up and gender discrimination in the allocation of household resources. Studies estimating the effects of these factors have generally assumed that offspring sex ratio is random, which is implausible in view of recent evidence that the sex of a child is partly determined by prenatal environmental factors. These factors may also affect child health and survival in utero or after birth, which implies that conventional approaches to explaining sex differences in mortality are likely to yield biased estimates. We propose a methodology for decomposing these differences into the effects of prenatal environment, child biology, and parental preferences. Using a large sample of twins, we compare mortality rates in male-female twin pairs in India, a region known for discriminating against daughters, and sub-Saharan Africa, a region where sons and daughters are thought to be valued by their parents about equally. We find that: (1) prenatal environment positively affects the mortality of male children; (2) biological make-up of the latter contributes to their excess mortality, but its effect has been previously overestimated; and (3) parental discrimination against female children in India negatively affects their survival; but failure to control for the effects of prenatal and biological factors leads conventional approaches to underestimating its effect by 237 percent during infancy, and 44 percent during childhood

Supermajority Politics: Equilibrium Range, Policy Diversity, Utilitarian Welfare, and Political Compromise

The standard Bowen model of political competition with single-peaked preferences (Bowen, 1943)predicts party convergence to the median voter’s ideal policy, with the number of equilibrium policies not exceeding two. This result assumes majority rule and unidimensional policy space.We extend this model to static and dynamic political economies where the voting rule is a supermajority rule, and the policy space is totally ordered. Voters’ strategic behavior is captured by the core in static environments and by the largest consistent set in dynamic environments.In these settings, we determine the exact number of equilibria and show that it is an increasing correspondence of the supermajority’s size. This result has implications for the depth of policy diversity across structurally identical supermajoritarian political economies. We also examine equilibrium effects of supermajority rules on utilitarian welfare and political compromise under uncertainty

Power theories for multi-choice organizations and political rules: Rank-order equivalence

AbstractVoting power theories measure the ability of voters to influence the outcome of an election under a given voting rule. In general, each theory gives a different evaluation of power, raising the question of their appropriateness, and calling for the need to identify classes of rules for which different theories agree. We study the ordinal equivalence of the generalizations of the classical power concepts–the influence relation, the Banzhaf power index, and the Shapley–Shubik power index–to multi-choice organizations and political rules. Under such rules, each voter chooses a level of support for a social goal from a finite list of options, and these individual choices are aggregated to determine the collective level of support for this goal. We show that the power theories analyzed do not always yield the same power relationships among voters. Thanks to necessary and/or sufficient conditions, we identify a large class of rules for which ordinal equivalence obtains. Furthermore, we prove that ordinal equivalence obtains for all linear rules allowing a fixed number of individual approval levels if and only if that number does not exceed three. Our findings generalize all the previous results on the ordinal equivalence of the classical power theories, and show that the condition of linearity found to be necessary and sufficient for ordinal equivalence to obtain when voters have at most three options to choose from is no longer sufficient when they can choose from a list of four or more options

Fidelity Networks and Long-Run Trends in HIV/AIDS Gender Gaps

More than half of the HIV/AIDS-infected population today are women. We study a dynamic model of (in)fidelity, which explains the HIV/AIDS gender gap by the configuration of sexual networks. Each individual desires sexual relationships with opposite sex individuals. Two Markov matching processes are defined, each corresponding to a different culture of gender relations. The first process leads to egalitarian pairwise stable networks in the long run, and HIV/AIDS is equally prevalent among men and women. The second process leads to anti-egalitarian pairwise stable networks reflecting male domination, and women bear a greater burden. The results are consistent with empirical observations

Optimally Targeting Interventions in Networks during a Pandemic: Theory and Evidence from the Networks of Nursing Homes in the United States

This study develops an economic model for a social planner who prioritizes health over shortterm wealth accumulation during a pandemic. Agents are connected through a weighted undirected network of contacts, and the planner’s objective is to determine the policy that contains the spread of infection below a tolerable incidence level, and that maximizes the present discounted value of real income, in that order of priority. The optimal unique policy depends both on the configuration of the contact network and the tolerable infection incidence. Comparative statics analyses are conducted: (i) they reveal the tradeoff between the economic cost of the pandemic and the infection incidence allowed; and (ii) they suggest a correlation between different measures of network centrality and individual lockdown probability with the correlation increasing with the tolerable infection incidence level. Using unique data on the networks of nursing and long-term homes in the U.S., we calibrate our model at the state level and estimate the tolerable COVID-19 infection incidence level. We find that laissez-faire (more tolerance to the virus spread) pandemic policy is associated with an increased number of deaths in nursing homes and higher state GDP growth. In terms of the death count, laissez-faire is more harmful to nursing homes than more peripheral in the networks, those located in deprived counties, and those who work for a profit. We also find that U.S. states with a Republican governor have a higher level of tolerable incidence, but policies tend to converge with high death count