Boolean functions: noise stability, non-interactive correlation distillation, and mutual information

Let $T_{\epsilon}$ be the noise operator acting on Boolean functions $f:\{0, 1\}^n\to \{0, 1\}$, where $\epsilon\in[0, 1/2]$ is the noise parameter. Given $\alpha>1$ and fixed mean $\mathbb{E} f$, which Boolean function $f$ has the largest $\alpha$-th moment $\mathbb{E}(T_\epsilon f)^\alpha$? This question has close connections with noise stability of Boolean functions, the problem of non-interactive correlation distillation, and Courtade-Kumar's conjecture on the most informative Boolean function. In this paper, we characterize maximizers in some extremal settings, such as low noise ($\epsilon=\epsilon(n)$ is close to 0), high noise ($\epsilon=\epsilon(n)$ is close to 1/2), as well as when $\alpha=\alpha(n)$ is large. Analogous results are also established in more general contexts, such as Boolean functions defined on discrete torus $(\mathbb{Z}/p\mathbb{Z})^n$ and the problem of noise stability in a tree model.Comment: Corrections of some inaccuracie

Reelection or term limits? The short and the long view of economic policy

An incumbent's drive for reelection can lead to political budget cycles. The distortion cycles cause in economic policy may be offset by the information they indirectly provide about the incumbent's competency. The informative content of cycles depends on the sophistication of voters, i.e. on whether they are rational or near rational. In a framework of individual candidates, constitutional clauses that prohibit the reelection of the president eliminate political budget cycles. One-term limits that allow non-immediate reelection also shift the focus from short-run cycles to the long-run soundness of economic policies, and have superior welfare properties. Hence, the choice is not reelection or not, but rather immediate or non-immediate reelection.rotation principle, term limits, non-immediate reelection, political budget cycles, rational and near rational voters.

How not to respond to populism

Although the nature and definition of populism are a source of considerable disagreement, there seems to be a minimal consensus by now that populism poses a number of threats to liberal democracy, and that public authorities should therefore act in defence of the latter. In searching for appropriate responses, however, most scholars draw from strategies for combatting anti-democratic or extremist parties, without considering the important differences between populist parties and these other political actors. We argue that the two central types of democratic defence—the ‘intolerant’ militant democratic defence and the ‘tolerant’ defence—do not offer satisfying responses to populist parties precisely because they were conceived and developed as responses to different phenomena. For public authorities to successfully address populism, responses need to contain its most egregious characteristics, yet salvage its productive side

Causes and Consequences of Elections in Nondemocracies

In this dissertation, I offer an answer to one of the most important questions about authoritarian politics today: why do dictatorships hold elections? In order to answer this broad question, I study the causes and consequences of elections as well as the role of elections in nondemocratic settings. First, I develop a theory about the causes of elections in dictatorships, which is based on the different threats that dictatorships face and the different goals that they have in order to lessen or avoid these threats. I argue that dictatorships opt for elections for the effective executive if they need to avoid violent removal. In contrast, dictatorships begin elections for a national legislature if they seek to maintain the unity and cohesion of elites in the ruling circle and/or to coopt elites from outside of the regime. Second, I present a theory about the consequences of elections in dictatorships. I contend that two seemingly competing effects of elections are mutually complementary. Individual elections can create a momentum for regime change, leading to the collapse of dictatorships and democratic transitions. At the same time, once dictatorships survive elections, election results convey useful information for the purpose of cooptation and send a signal that deters future challenges to the regime. Tests of my theory on a sample of dictatorships after World War II show robust support for my theory about the causes and consequences of elections. Finally, I revisit the information collection role of elections in nondemocratic settings. I theorize that elections can be either informative or less informative depending on the strategic decisions that major opposition parties make. I develop a formal theory to describe this causal mechanism. An important implication of my theory is that informative elections are associated with post-electoral redistribution of goods and patronage while less informative elections in which major opposition parties boycott elections are not. I test this implication by using original data collected from Serbia in 1990s and present results that are consistent with my theory

Media Power and Nigeria's Consolidating Democracy

In emerging democracies with weak public institutions, low literacy level, deep-seated ethnic rivalry, and history of centralized, authoritarian rule; to what extent does media agenda-setting influence the political process? The press/politics nexus in consolidating democracies is critical to understanding intricate yet overlapping connexion between politics and development in the Third World. This study examined if media-power shape elections and regime outcomes in Nigeria? Using semi-structured interviews (and incorporating News-Game research tool), findings indicate that Nigeria's two-decade-old democracy remains volatile, fragile, and vulnerable. This vulnerability is complicated by long-standing religious, ethno-regional political suspicions; and overburdened with shifting media ecology, particularly social media disinformation and propaganda. These complexities allow a politics of privilege, class, and power that not only ensures its preservation but also insulates the political elite from public outcry and media pressure. In conclusion, evidence indicates that media power exerts limited influence on elections and regime outcomes. The study recommends renewed effort to investigate power. Keywords: Nigerian politics, agenda-setting, mass media, democracy, underdevelopmen

Essays in Economic Theory

This thesis consists of five chapters on topics in mechanism design and voting. In Chapter 1, we study a committee deciding collectively whether to accept a given proposal or to maintain the status quo. Committee members are privately informed about their valuations and monetary transfers are possible. According to which rule should the committee make its decision? We consider strategy-proof and anonymous social choice functions and solve for the decision rule that maximizes utilitarian welfare, which takes monetary transfers to an external agency explicitly into account. For regular distributions of preferences, we find that it is optimal to exclude monetary transfers and to decide by qualified majority voting. This sheds new light on the common objection that criticizes voting for its inefficiency. In Chapter 2, we study welfare-optimal decision rules for committees that repeatedly take a binary decision. Committee members are privately informed about their payoffs and monetary transfers are not feasible. In static environments, the only strategy-proof mechanisms are voting rules which are inefficient as they do not condition on preference intensities. The dynamic structure of repeated decision-making allows for richer decision rules that overcome this inefficiency. Nonetheless, we show that often simple voting is optimal for two-person committees. This holds for many prior type distributions and irrespective of the agents' patience. In Chapter 3, we study binary, sequential voting procedures in settings with privately informed agents and single-peaked (or single-crossing) preferences. We identify two conditions on binary voting trees, convexity of divisions and monotonicity of qualified majorities, ensuring that sincere voting at each stage forms an ex-post perfect equilibrium in the associated extensive form game with incomplete information. We illustrate our findings with several case studies: procedures that do not satisfy our two conditions offer ample space for strategic manipulations. Conversely, when the agenda satisfied our conditions, sincere behavior was indeed the most likely outcome. In Chapter 4, we study how a principal should optimally choose between implementing a new policy and keeping status quo when the information relevant for the decision is privately held by agents. Agents are strategic in revealing their information, but the principal can verify an agent's information at a given cost. We exclude monetary transfers. When is it worthwhile for the principal to incur the cost and learn an agent's information? We characterize the mechanism that maximizes the expected utility of the principal. This mechanism can be implemented as a weighted majority voting rule, where agents are given additional weight if they provide evidence about their information. The evidence is verified whenever it is decisive for the principal's decision. Additionally, we find a general equivalence between Bayesian and ex-post incentive compatible mechanisms in this setting. In Chapter 5, we are interested in strategy-proof mechanisms that maximize the agents' residual surplus, that is, the utility derived from the physical allocation minus transfers accruing to an external entity, in an independent private value auction environment. We find that, under the assumption of an increasing hazard rate of type distributions, an optimal deterministic mechanism never extracts any net payments from the agents, that is, it will be budget-balanced. Specifically, optimal mechanisms have a simple "posted price'' or "option'' form. In the bilateral trade environment, we obtain optimality of posted price mechanisms without any assumption on type distributions