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The document discusses the concept of preferences and utility in political decision-making. It explores how individuals' preferences can be described by utility functions, allowing them to maximize utility and guide their behavior. The text delves into the Downsian model of representative democracy, the probabilistic model of voting, and the swing voter model. It also examines factors influencing voter turnout and the concept of electoral competition, where candidates strategically position their platforms to appeal to the median voter.

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2023/2024

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Scarica Preferences and Utility in Political Decision-Making - Prof. Gagliarducci e più Appunti in PDF di Politica Economica solo su Docsity! POLITICAL ECONOMY AND PUBLIC PROCUREMENT 19/02/24 Any individual wants to maximise utility and minimise costs, given a constraint which is usually the budget or time. Economical tools allow to do so, such as Lagrangian, to formalise this behaviour. This is the perspective of a rational individual. It is assumed that politicians do the same. PW: PE202223 for the syllabus Political economics can be defined in different ways. it is devoted to understanding the economic process of the political activity. Political economy is a much broader term, economic policies are the actions taken by the government. Political economics, a vibrant field exploring the intricate relationship between economics, politics, and society, boasts a rich history deeply rooted in various disciplines. While often associated with influential figures like Adam Smith and David Ricardo, its origins delve deeper, encompassing diverse perspectives on individual and collective well-being. Economists try to understand the right policy to reach specific goals. Know that the government relies on democratic support. Whatever the goal is, there should be the approval of the population. Sometimes it is known that something should be done, i.e. figth climate change, but under a political perspective it is more complicated. Early Threads: Welfare Economics: This branch focused on measuring and maximizing societal welfare within an economic framework. It tackled questions like how government interventions could improve overall well-being. In this field, we are concerned with the ways in which it is possible to measure welfare, and how to maximise it. Social Choice Theory: Kenneth Arrow and Amartya Sen spearheaded this field, examining how individual preferences can be aggregated into collective decisions. It grappled with challenges like voting paradoxes and the impossibility of finding a single "best" outcome that satisfies everyone. Social choice: how do we make a choice as a collective set of individuals? Not easy, aggregation of preferences. Political Economics: Emerging from these earlier areas, political economics broadened the scope, analysing how political institutions, power dynamics, and social structures shape economic outcomes. It challenged the often-assumed neutrality of markets and explored the political processes driving economic policies. Key Approaches Political economists have some key approaches: 1. Methodological Individualism: This principle says that to understand large-scale economic phenomena, we need to dive deep into the individual level. It's like building a mosaic picture - each individual action forms a part of the wider economic landscape. This approach encourages building micro-foundations, explaining aggregate outcomes based on individual decisions and motivations. 2. Rational Choice Theory: Humans aren't robots, but this approach assumes individuals generally act in ways they perceive as serving their goals and preferences. It is a framework to analyze decision-making based on expected benefits and costs. It helps understand, for example, why consumers choose certain products or firms make specific investments. Behavioural economics deviate from rationality, but we assume rationality as default. It is easier to understand the economic policies assuming rationality, since it represents behaviour in most cases. 3. Institutionalism: Rules, norms, and social structures (institutions) shape what individuals can and cannot do, influencing their motivations and ultimately, the overall economic outcome! This approach emphasizes the critical role of institutions in shaping economic behaviour. A Powerful Equation: P (Preferences) x B (Beliefs) x E (Environment) x I (Institutions) → A (Actions) A (Actions) x E (Environment) x I (Institutions) → O (Outcomes) This equation simplifies the complex interplay between individual and institutional factors. Preferences, beliefs, and the surrounding environment (including institutions) influence individual actions, which in turn, along with the environment and institutions, shape broader economic outcomes. Positive vs. Normative Analysis: Positive: This approach asks, "what is?" It seeks to explain and understand how political and economic systems actually function. Think of it as uncovering the mechanics of a complex machine. Normative: This approach asks, "what should be?" It seeks to evaluate and potentially improve economic and political systems based on values and ethical considerations. Think of it as trying to optimize the performance of that complex machine. The making of public policy The diagram shows a simplified view of the public policy process, which involves the following: Citizens: These are the people who are affected by public policy. They can make their voices heard through voting, lobbying, and protesting. Interest groups: These are groups of people who share a common interest, such as businesses, labour unions, or environmental groups. They lobby policymakers to try to influence policy in their favour. Parliament: This is the legislative body that makes laws. It is elected by the citizens. Bureaucracy: This is the executive branch of government that implements laws and regulations. It is appointed by the parliament. It is a necessary challenge so that it is possible to implement what the government decides. Government: This is the overall governing body of the country. It includes the parliament, the bureaucracy, and the judiciary. The arrows in the diagram show how these different actors interact with each other. By assuming citizens can become part of the Parliament and the Government, it changes perspective. The graph generally describes how policies are created and influenced. This is a deviation from models from the 90s, where the political sphere was considered coming from another dimension. limitations. This utility is derived from consuming two goods, with their respective prices and the individual's available income determining the feasible consumption bundles. The utility function, representing the individual's preferences, serves as the objective function in the maximization problem. Conversely, the budget constraint, determined by the prices of the goods and the individual's available income, imposes limitations on the feasible consumption bundles. In general, maximizing or minimizing such functions subject to constraints is a common optimization problem in economics. Graphically, utility maximization is depicted by the tangency point between the budget constraint and an indifference curve representing the individual's preferences. The budget constraint is represented by a line indicating the combinations of goods that can be purchased given the individual's income and the prices of the goods. Lagrange multiplier In the context of utility maximization, the Lagrangian plays a critical role in solving constrained optimization problems. Specifically, it helps us find the optimal bundle of goods or services that maximizes a consumer's utility while considering their budget constraint. Problem Setup: 1. Imagine a consumer with a fixed budget (𝐵) who wants to maximize their utility (𝑈) by consuming different goods, represented by quantities 𝑥 , 𝑥 ….𝑥 . 2. There's a constraint, however, as the total cost of those goods cannot exceed the budget: 𝑝1𝑥1 + 𝑝2𝑥2 + . . . + 𝑝𝑛𝑥𝑛 ≤ 𝐵 (where p represents the price of each good). Solving this problem directly can be difficult, especially with multiple goods and complex constraints. The Lagrangian method introduces a new variable called the Lagrange multiplier (λ). It forms a Lagrangian function: 𝐿(𝑥1, 𝑥2, . . . , 𝑥𝑛, 𝜆) = 𝑈(𝑥1, 𝑥2, . . . , 𝑥𝑛) + 𝜆(𝐵 − 𝑝1𝑥1 − 𝑝2𝑥2 − . . . − 𝑝𝑛𝑥𝑛). This function combines the objective function (utility) and the constraint into a single equation. Solution Steps: Find the partial derivatives of the Lagrangian function with respect to all variables (𝑥1, 𝑥2, . . . , 𝑥𝑛, 𝜆) and set them equal to zero. This creates a system of equations. Solve the system of equations for the optimal values of 𝑥1, 𝑥2, . . . , 𝑥𝑛, 𝑎𝑛𝑑 𝜆. These values represent the optimal bundle of goods, and the Lagrange multiplier helps ensure the budget constraint is satisfied. This method effectively incorporates various constraints into the optimization problem, making it applicable to scenarios beyond simple budget limitations. The Lagrange multiplier would tell you how much their utility would increase if their budget was slightly relaxed. Minimum squares (OLS) The Ordinary Least Squares (OLS) method is a statistical technique used to estimate the parameters of a linear regression model. In simpler terms, it's a method used to figure out the best-fitting line through a set of data points. Imagine a scatter plot of data points, where one variable (the independent variable) is plotted on the x-axis and another variable (the dependent variable) is plotted on the y-axis. These two variables might be related in a linear way, meaning that changes in one variable cause proportional changes in the other. The OLS method helps find the line that best represents this relationship. The "least squares" part of the name refers to the fact that the method works by minimizing the sum of the squared differences between the actual y-values of the data points and the y-values predicted by the line. In other words, it finds the line that gets as close as possible to all the data points. This line can be used to make predictions about the dependent variable based on values of the independent variable. We want to understand the relationship between years of schooling (independent variable) and wages (dependent variable). We know that the income might be influenced by other factors, but with the Covariance assumption, we state that such factors are not influent, also because the goal is to depict a relationship between years of schooling and wages. The OLS method is specifically designed for linear regression models, which posit a linear relationship between the dependent variable (Y) and one or more independent variables (X). Mathematically, this relationship is expressed as: 𝑌 = 𝛽 + 𝛽 𝑋 + 𝛽 𝑋 + ⋯ + 𝛽 𝑋 + 𝜀 Where: - 𝑌 is the dependent variable (in our example, wages) - 𝑋 , 𝑋 are the independent variables. - 𝛽 , 𝛽 are the coefficients (parameters) that represent the effects of the independent variables on the dependent variable. Each coefficient represents the change in the dependent variable associated with a one-unit change in the corresponding independent variable, holding other variables constant. - 𝜀 is the error term, representing the discrepancy between the observed values of the dependent variable and the values predicted by the model. The OLS method aims to find the values of the coefficients 𝛽 , 𝛽 that minimize the sum of squared differences between the observed values of the dependent variable and the values predicted by the regression model. These differences are called residuals or errors. Beta tells the relationship between years of schooling and wages. There can be other factors explaining such relationship. For instance, welfare of the family. Some factors are observable and can be easily included in the objective function, such that it is possible to control the, but in other cases, there might be the unobserved component affective the objective function, such that the covariance is no longer equal to zero. The OLS method minimizes the sum of squared residuals, often denoted as the residual sum of squares (RSS) or the sum of squared errors (SSE). Mathematically, this criterion can be expressed as: 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 (𝑌 − 𝑌 ) Where 𝑛 is the number of observations, 𝑌 is the observed value of the dependent variable for observation 𝑖, 𝑌 is the predicted value of the dependent variable for observation 𝑖 based on the regression model. By squaring the residuals (the differences between the observed values and the predicted values), both positive and negative errors contribute to the overall measure of fit. This ensures that the model is penalized equally for deviations above and below the predicted values. Squaring the residuals magnifies larger errors more than smaller ones. This is because squaring a larger number results in a much larger value than squaring a smaller number. Consequently, the model prioritizes minimizing larger errors, which are typically of greater concern in regression analysis. The OLS method relies on several assumptions, including linearity, independence of errors, homoscedasticity (In simpler terms, it means that the spread of the residuals should be consistent across the range of predicted values), and absence of multicollinearity (two or more independent variables in the regression model are highly correlated with each other). While covariance and correlation both measure the relationship between two variables, correlation provides a standardized measure that is easier to interpret and compare across different datasets, while covariance gives a measure of the strength and direction of the relationship but is influenced by the scale of the variables. Covariance can be positive, negative or zero - Positive covariance: When two variables tend to increase or decrease together. Imagine ice cream sales and temperature: as temperature rises, ice cream sales typically increase, leading to a positive covariance. - Negative covariance: When one variable increase while the other decreases. - Zero covariance: When the changes in one variable are unrelated to the changes in the other. Imagine shoe size and vocabulary: their changes typically wouldn't be related, leading to a covariance of zero. Having a causal interpretation in statistics means that you can go beyond correlation and make inferences about cause and effect. Here's a breakdown: Correlation vs. Causation: - Correlation: Simply means two variables are related, implying they move together in some way. But correlation doesn't tell you which variable causes the other, or if some third factor is influencing both. - Causation: Establishes a direction and a mechanism behind the relationship. A change in one variable directly causes a change in the other. Approaches to Causal Inference: Randomized controlled trials (RCTs): Considered the "gold standard" for causal inference. By randomly assigning participants to different groups (e.g., treatment or control), RCTs help control for confounding variables and isolate the effect of the intervention. Causal Inference for Policymakers - From Correlation to Causation: Understanding the Impact of Policies As policymakers, we are constantly seeking effective and impactful solutions to societal issues. However, simply observing a correlation between two variables (e.g., policy implemented and improved outcome) isn't enough. Establishing the causal relationship, whether the policy actually caused the improvement, is crucial for informed decision-making. Achieving causality requires addressing the limitation of confounding variables. These are factors other than the policy that might influence the observed outcome, creating a misleading association. They are extraneous factors that can distort the apparent relationship between two variables. The gold standard for establishing causality is randomized controlled trials (RCTs). In an RCT, individuals are randomly assigned to either a treatment group (receiving the policy) or a control group (not receiving the policy). This randomization helps to ensure that the two groups are, on average, similar in all other respects, except for their exposure to the policy. Any observed differences in outcomes between the groups can then be more confidently attributed to the policy itself. While powerful, RCTs are not always feasible in policy settings. Real-world interventions often cannot be randomly assigned to individuals or communities. The Aspirin Example: Simply observing that people who take aspirin live longer does not imply that aspirin causes them to live longer. Other factors, like health consciousness or socioeconomic status, could also influence both aspirin use and lifespan. The Impossibility: Arrow's Impossibility Theorem states that no collective choice function can satisfy all five of these seemingly reasonable axioms simultaneously. This implies that there is no perfect way to aggregate individual preferences consistently while ensuring all desirable properties are met. This theorem doesn't render collective decision-making impossible, but it highlights the inherent challenges and the absence of a universally "fair" and "efficient" solution. If there are at least three voters, and the set of available outcomes of X contains three or more elements, any collective choice function that satisfies conditions 1-4 (Pareto efficiency, collective rationality, unrestricted preferences and IIA) violates condition 5 (there must be a dictator) Arrow proved that if those are the desired principles, no collective voting rule with such principles exist. All 5 properties might be working if individual preferences allow for it, but it is not always verified, also because preferences and societies change. A rule ALWAYS going to deliver a decision does not work. For such a bulletproof rule, one of the 5 principles has to be given up. For instance, giving up "no dictatorship". Restriction of preferences are also is possible, so removing unrestricted domain, but there can also be the influence of institutions. SO far an assumption: vote sincerely, there can be cases in which we vote strategically. Paths out of the impossibility The challenge presented by Arrow's Impossibility Theorem might seem like a dead end for achieving fair and efficient collective decision-making. However, there are actually two main routes to explore for potentially overcoming this obstacle: 1. Relaxing Unrestricted Domain: This approach loosens the assumption that any individual preference ordering is permissible. In other words, it allows for some restrictions on individual preferences.This might involve designing voting rules that take into account specific characteristics of preferences or establishing criteria for valid preferences. It's important to carefully consider the ethical implications and potential biases associated with this approach. 2. Analyzing Institutional Arrangements: This approach focuses on exploring how institutions can influence the outcome of voting even when individual preferences remain the same. It aims to understand how different voting rules, procedures, and decision-making frameworks can lead to different collective outcomes from the same set of individual preferences. By studying the impact of various institutional arrangements, we might find ways to mitigate the effects highlighted by Arrow's Impossibility Theorem, even though the theorem itself remains valid under its original assumptions. These two approaches are not mutually exclusive and can be explored in combination. Removing unrestricted domain While Arrow's Impossibility Theorem highlights potential challenges in achieving perfect collective decision- making, scholars have proposed avenues to explore for navigating these limitations, such as relaxing the unrestricted domain of individual preferences. Context: - We consider a society with N citizens making decisions on public policies. - The set of available policies (A) contains at least three options - Each citizen has a rational preference ordering represented by a utility function Ui(x), where i represents the individual and x represents a specific policy option. - Decisions are made by pairwise majority rule: When comparing two policies (x and x'), an individual prefers x if their utility for x is greater than their utility for 𝑥′ (𝑈 (𝑥) > 𝑈 (𝑥′)). If the majority of citizens prefer x over x' in this pairwise comparison, we say x is socially preferred to x' (written as x ≻ x'). 1. Condorcet Winner: Definition: An alternative 𝑥 in the set A is a Condorcet winner if and only if it defeats all other alternatives in pairwise comparisons. In simpler terms: 𝑥 wins against every other option in a head-to-head vote. This means no other option receives a majority of votes from individuals when compared to 𝑥 . Winset, is the set of actions that win against others. For each action, there could be a corresponsing winning set, a set of alternatives that can beat a given action. When the winset of an action is empty, it means that there are no other preferred alternatives. For instance, the median in a set of single peaked preferences has an empty winset. 2. Ideal Policy: The ideal policy for an individual 𝑖, denoted by 𝑥∗, is the alternative in the set A that offers them the highest level of utility according to their preference function. It's the option that maximizes their individual satisfaction. 3. Single-Peaked Preferences: An individual's preferences are single-peaked if their utility function has one global maximum and no other local maxima. Imagine their preference function as a graph, with utility (satisfaction) on the vertical axis and policy options on the horizontal axis. In single-peaked preferences, this graph rises towards a single peak (the ideal policy) and then steadily declines on either side of the peak, with no other significant peaks or dips. When representing them, it is actually not right to represent them with a continuous graph. 4. Median Voter: In a group of N voters with ideal policies denoted by {𝑥 ∗ 1, 𝑥 ∗ 2, . . . , 𝑥 ∗ 𝑁}, the median voter is the voter whose ideal policy, 𝑥 , divides the set of alternatives in half. When the ideal policies of all voters are arranged in ascending or descending order, the median voter's ideal policy is the one that has 50% of the alternatives (policies) on either side of it. These definitions provide essential building blocks for understanding social choice theory, particularly when analyzing different voting systems and collective decision-making processes. Median Voter Theorem (Black, 1948): According to the Median Voter Theorem, if all citizens' preferences are single-peaked along a single dimension, the median ideal preference emerges as a Condorcet winner. Furthermore, the social preference order is transitive, with the median standing highest in the order.This theorem suggests that in situations where preferences are single-peaked, there exists a clear preference ordering that facilitates decision-making based on majority rule. In practice, the application of the Median Voter Theorem relies on the existence of at least one way to line up alternatives on a graph such that all voters' preferences exhibit a single peak. When this condition is met, the theorem can be effectively applied to analyze decision scenarios. The median represents the central value in a distribution, where 50% of the population lies to the left and 50% to the right. It is located at the middle of the distribution and provides a measure of central tendency. In symmetric distributions, the mean and median coincide, reflecting a balanced distribution. However, in asymmetric distributions, the mean and median may differ, indicating skewness in the distribution. In the context of the Condorcet Paradox, where no clear majority preference emerges due to conflicting individual preferences, the Median Voter Theorem offers insights into potential resolutions. By assuming preferences are single-peaked, the theorem suggests that there will be a single Condorcet winner, and this winner will coincide with the median voter's preference. This implies that the median voter holds significant influence in decision-making processes. 26/02/24 MULTIDIMENSIONAL POLICIES 1. Majority voting in multidimensional policy space Imagine a society having to decide simultaneously on two dimensions, e.g., fiscal policy and foreign policy, or immigration policy and gay marriage Remember: the median voter theorem relies on voters having single peaked preferences on a unidimensional issue (e.g., left-right). Multidimensional case is more complicated, depending on the number of dimensions and voters. Assumption: individual indifference curves (between two dimensions/issues) are circular, i.e., always prefer points that are closer to those further away (distance-based spatial preferences). 1. The Contract Curve: Imagine a two-dimensional space where each point represents a policy combination on two issues (e.g., taxation and environmental regulation). Utilities are represented in a circle form as this allows to clearly state that beside a certain level of consumption, utility starts decreasing, hence it assumes the existence of satiation. The assumption is that the closer we get to the bliss point, the higher the level of utility. The contract curve is the set of points where it is possible to find a solution, and no majority beating it can be spotted. No point outside the contract curve is preferred. Interestingly, no point on the contract curve is universally preferred (a Condorcet winner with majority rule). This means there's always some disagreement. We know a solution along the curve will be found, but it is difficult to perfectly determine where. Finding a consensus policy in a multidimensional setting is challenging. Even when compromises are made (contract curve), there's rarely a universally preferred option. Plott's theorem states that a vector policy 𝑥∗ is a Condorcet winner (wins against any other option in pairwise comparisons) only if it's median with respect to all dimensions. This means 𝑥∗ is "in the middle" of The expected utility for agent 𝑖 is given by equation (1), where 𝑃(𝑥 |𝑎 , 𝑎 ) represents the probability that outcome 𝑥 is implemented given the voting strategies of all agents. The optimal choice will maximise the function, given the probability of voting of other players. In voting scenarios, the expected utility relies on the actions of other agents and the probability of policies being enacted based on both individual and collective choices. Agents attach a value to each policy, considering not only their personal preferences but also the likelihood of their preferred policy being adopted, influenced by the decisions of others. As a result, agents often face a decision between voting sincerely for their most preferred policy or strategically voting for a moderate option that may have a higher probability of being adopted. This strategic behavior is commonly observed in political economics, where individuals aim to maximize their expected utility by anticipating the actions of others and adjusting their own voting strategies accordingly. While voting sincerely aligns with making a statement or expressing preferences, strategic voting is driven by the desire to maximize utility within the constraints of the voting system. In the rational choice framework of political economics, agents are assumed to act rationally by seeking to maximize their expected utility, which may involve strategic voting to achieve higher utility outcomes. Nash equilibrium A Nash equilibrium in voting strategies occurs when each voter's strategy is a best response to the strategies chosen by the other voters. In other words, no voter can improve their utility by unilaterally changing their strategy. Formally, for each agent 𝑖, the best response 𝑎∗ is the vote that maximizes the expected utility, given the strategies chosen by other players. A Nash equilibrium in voting strategies is a situation where each agent's vote maximizes their expected utility given the votes of the other agents. This implies that no agent has an incentive to deviate from their chosen strategy, as doing so would not lead to higher utility. A voting profile constitutes a Nash equilibrium if there is no player who can exploit a profitable deviation. ONE ROUND ELECTIONS Suppose one round elections, are preferences are such that x ≻ y ≻ z, but if I know x can never win, and y might instead have a chance over z, I might vote for y. Suppose non-simultaneous voting with run-off elections: a voting system in which elections are conducted in multiple rounds rather than all at once. In this system, if no candidate receives an absolute majority (more than 50%) of the votes in the initial round, a second round of voting is held between the top two candidates from the first round. Why vote? Does it truly make a difference? Considering the costs associated with voting and the slim probability of influencing the outcome, it may seem irrational to participate. Yet, despite this rational calculation, many still choose to cast their votes. This paradox challenges the notion of rational behaviour in voting decisions. 04/03/2024 The turnout rate in elections is typically not 100%, indicating that not all eligible voters choose to participate. However, it's also not close to zero, suggesting that a significant portion of the population still sees value in voting. In the instrumental model, voters consider the potential outcomes of different policies proposed by candidates and base their decision to vote on the expected utility they would derive from those policies being implemented. Voters consider various elements such as probability, benefits, and costs when deciding whether to vote. Suppose there are two candidates, A and B, each proposing different policies. The utility associated with each policy reflects the expected benefits that voters anticipate from the implementation of those policies. Candidate A's policy is associated with a utility of 50, while Candidate B's policy has a utility of 60. The difference in utility between the two policies represents the potential benefit of supporting one candidate over the other. The benefit of voting for a particular candidate is the difference in expected utility between their proposed policy and that of the opposing candidate. In this case, it's 10 (60 - 50 = 10). However, this benefit needs to be discounted by the probability that an individual's vote will actually affect the outcome of the election. This recognizes the reality that in large-scale elections, the probability of an individual vote being decisive is extremely low. The formula rationalising this behaviour is 𝑃 ∗ 𝐵 − 𝐶 > 0, the paradox is such that, if costs are high and the probability of affecting elections is low, the number of people voting should be low. This model can be useful to understand the reason why people do not vote: 𝐵 can be large, 𝑃 however can be so small, such that voting might be considered useless. This would be a rationalising approach. In practice, however, people might decide to vote regardless. Because of this, a different model needs to be formalised. Try to rescue the theory by adding an expressive (non-instrumental) benefit 𝑃 ∗ 𝐵 − 𝐶 + 𝐷 > 0, where the new element stands for civil voting. There is a widespread sense of participation, which is highly subjective and might change for each individual. This can explain voting even in cases in which costs are high and the probability of affecting election decreases. It is difficult to measure civil duty and social capital. Several research have been performed, but since it is a vague concept, tools for measuring are imperfect. For instance, Sapienza and Zingales made research on the propensity of people to donate blood, not only for relatives or friends but for the unknown people, hence collecting data on regular donors. They find that individuals with higher levels of social capital are more likely to donate blood, as they may feel a stronger sense of civic duty or be more connected to community norms that promote altruistic behaviour. Since social capital takes time to change, turnout can also be an indirect although imperfect measure on the size of social capital. Game Theoretic Approach The probability of influencing the outcome of elections is not exogenous, but it is computed from the decisions of other voters. If everybody concludes that it is not worth voting, then a single vote can decide the outcome then it is again rational to vote, provided B > C (Pivotal model). There might start to be coordination among players. Turnout is an inverse U-shaped function of the uncertainty about how many will vote. This model acknowledges that voters often have uncertainty about how many other people will vote. When there is low uncertainty, meaning most voters have a good idea of how many others will participate, turnout is likely to be high. This is because voters can be more confident about the potential impact of their vote. Conversely, when there is high uncertainty, turnout may be low. This is because voters are unsure whether their vote will make a difference, and so they may be less motivated to participate. Behavioural approach This approach is adopted as it is assumed to be more helpful in gaining insights on the choices of actions by individuals. People are in general rational, but some of their behaviours are not. In many cases, individuals may have clear objectives or goals they wish to achieve, such as improving their health or financial status. However, their behaviours may not always align with these objectives. This discrepancy can occur for various reasons, such as cognitive biases, emotional factors, social influences, or habituation. In voting, it can occur that people overestimate 𝑃, meaning that they think their vote is going to be particularly influent. People tend to overestimate their ability to control/affect events. Optimism bias: over-optimism about the positive consequences of actions. This means that the benefit people think of receiving is overestimated. Those phenomena might be helpful in determining the reasons behind the turnout result. Studies on votes are difficult since the vote is secret. Research is made mainly based on exit pools. It is not rare to find a discrepancy between exit pool results and actual results. Turnout is positively correlated with: • Age (the higher, the more participation) • Income (higher voting participation since high income people are taxed and policies can be highly influential) • Education (more informed on benefits of voting) • Campaign spending • Being contacted by canvassers • Trust in the role of government (higher trust in public institutions makes people more willing to vote) • Lower requirements for registration (in the US, there might be limits on the way registration for voting has to occur, if steps for voting are lower, more participation can be expected). • Media coverage: the influence of media on turnout can be spotted. Social Incentives and Voter Turnout: Evidence from the Swiss Mail Ballot System Mail voting in Swiss was introduced, we should have expected an increase in turnover, due to the reduction of costs. Instead, there was a reduction in turnout, this because of the reduction in the social pressure: with mail voting, less check on actual participation of individuals, which could claim to have voted by email, rather than going physically to the pools. Electoral competition From direct democracy (citizens vote policies) to representative democracy (citizens vote candidates), citizens delegate the vote. It allows to reduce the dimensionality problem. In direct democracy, more than three policy options could lead to a stuck situation, representative democracy reduces the dimensionality problem. Factors for going towards representative democracy are dimensionality and turnout. Running a country with direct democracy would be difficult to be pursued. 5 stars movement pushed for this (populist party, more focused on short term benefits) The Downsian model From direct democracy (citizens vote policies) to representative democracy (citizens vote candidates) Representative democracy reduces the dimensionality problem (number of voters and policies). Turnout is the key variable; in fact it happens that people do not always show up to vote. Here there are the made assumptions. - The denominator is negative, and it expresses the change in income mean with taxes. High level fo taxes can generate two effects: substitution and income effect. Higher taxes push wages down. High level of taxes makes people earn more, up to the point people prefer leisure, with substitution effect winning. It is the elasticity of labour supply. If on average higher level of taxes are implemented, society is working less, because of this, income mean would reduce. Hence, the denominator is negative. There are two opposing forces. High inequality pushes for higher levels of taxes, especially if median is skewed to the left, so that income is redistributed. It is convenient to tax more, BUT on the same note, high taxes might lead people to stop working, reduce the amount of taxes collected. The numerator pushes for an increase in taxation, at denominator we have a negative effect of high taxes on income mean. Example of exam question: assume median is lower than mean, and labour supply is negative to taxation. What if new billionaires leave the country? Mean is going down; median is also moving to the left. Reduce taxation, the distance between mean and median reduces. The conclusion is that, in general, when the distance between the income of the median and the mean is negative, when we divide it for the change in income when taxes increase, since both are negative, we get a positive rate of taxation. This is subject to the assumptions which are made, in particular on the fact that the substitution effect prevails. It could be, instead, that the income effect prevails, in the sense that as taxation becomes larger, we work more. In more unequal societies, taxation tends to be higher with more redistribution, on average. Probabilistic voting model Main hypotheses of the Downsian model • Office-seeking politicians: Politicians are primarily motivated by their desire to attain and retain political office. Their actions, including policy positions and campaign strategies, are driven by this goal. • Full commitment to platforms: Politicians commit fully to specific policy platforms or positions during election campaigns. Once elected, they are expected to implement the policies they promised to the electorate. Theory demonstrates that they will converge to the median • Majoritarian election: The candidate who receives the most votes wins the election. This contrasts with proportional representation systems where seats are allocated based on the proportion of votes received. • Two candidates: The model focuses on elections with only two viable candidates. This simplification allows for clearer analysis of strategic behavior by candidates and voters. • Perfect Information: Voters have perfect information about the policies and positions of the candidates. This means that voters are fully aware of the candidates' platforms and can accurately assess which candidate aligns best with their preferences. • Unidimensional policy space over which voters have single-peaked preferences (to have the median voter result) Attempts were made to deviate from some of such assumptions, in particular from the assumption of perfect information, which in reality might not be feasible. In real-world elections, voters often do not have perfect information about the candidates and their platforms. This means that they may not be fully aware of the details of each candidate's policies, their track record, or their personal characteristics. Similarly, candidates may not have perfect information about the distribution of voter preferences. While they may have some understanding of the general demographics and concerns of the electorate, they cannot accurately predict the specific preferences of individual voters and where the median is. Hence, a probabilistic voting model is introduced, with the introduction of uncertainty and the conclusion that not all politicians converge to the median voter. Parties do not exactly propose the same. In a deterministic model, voters compare the utilities (𝑉) associated with the platforms of each candidate, where "platforms" refer to the set of policies or positions that each candidate (denoted as A and B) proposes or advocates for during an election campaign. These platforms outline what the candidates stand for and what they intend to do if elected to office. The utility of each voter for each policy is computed (with certainty) hence 𝑎 and 𝑎 are determined, and the vote will go for the candidate whose platform offers them the highest utility. Mathematically, if 𝑉(𝑎 ) > 𝑉(𝑎 ), the voter will vote for candidate A; otherwise, they will vote for candidate B. In the probabilistic model, instead of making a strict determination based on utility, voters introduce a probabilistic element into their decision-making process. This probabilistic element is represented by the probability (𝜋) of voting for candidate A, denoted as 𝜋 = 𝑓[𝑉(𝑎 ) − 𝑉(𝑎 )]. The function 𝑓() determines how the difference in utilities between the two candidates' platforms influences the probability of voting for candidate A. This function captures the uncertainty or noise in voter decision-making due to imperfect information. Essentially, the voter calculates the difference in utilities between the platforms of candidate A and candidate B. This difference serves as a signal of preference. For example, if the difference in utilities is large (indicating a strong preference for one candidate over the other), the probability of voting for candidate A would be high. Conversely, if the difference is small, the probability of voting for candidate A would be lower. The probabilistic nature of this model acknowledges that even if one candidate's platform seems slightly better, there's still a chance that the voter might choose the other candidate due to uncertainty or other factors influencing their decision. Candidates still do not care of the policies they propose, and they remain office-seeking, with the aim of maximising the probability of winning. Noise is introduced, such that the voting decision will be dependent on the following formula: The equation states that voter 𝑖 will vote for candidate A if the difference in utility between candidate A's platform and candidate B's platform, plus the noise term 𝜀 is greater than 0. Otherwise, voter 𝑖 will vote for candidate B. The noise term 𝜀 represents uncertainty or randomness in the voter's decision-making process. This noise could arise from various sources such as incomplete information, personal biases, or external factors influencing the voter's decision. The noise term 𝜀 is assumed to be distributed according to the density function 𝑓(𝜀) with cumulative distribution function 𝐹(𝜀). The properties of this noise are as follows: - Symmetric: The density function 𝑓(𝜀) is symmetric, meaning that the probability of positive and negative noise values is the same. - Zero Expected Value: The noise has a zero expected value, indicating that on average, the noise does not systematically favor one candidate over the other. - Uncorrelated with 𝑽𝒊(. ): The noise term 𝜀 is assumed to be uncorrelated with the utility values 𝑉(𝑎 ), 𝑉(𝑎 ). This means that the noise is independent of the voter's preferences and does not systematically influence the utility values assigned to the candidates' platforms. For the error, we are assuming a uniform distribution, a probability distribution where all outcomes within a certain range are equally likely to occur. In other words, each value within the range has the same probability of being chosen. This distribution is often represented graphically as a flat, constant line over the interval of possible values. The expression 𝑝 (𝑎 , 𝑎 ) represents the probability that agent 𝑖 votes for party A. As seen, voter 𝑖 will vote for candidate A if the difference in utility between candidate A's platform and candidate B's platform, plus the noise term 𝜀 is greater than 0. Otherwise, voter 𝑖 will vote for candidate B. Hence, A will be chosen if 𝑃𝑟{𝑉 (𝑎 ) − 𝑉 (𝑎 ) + 𝜀 > 0}, which can be rewritten as if 𝑃𝑟{𝑉 (𝑎 ) − 𝑉 (𝑎 ) > −𝜀 }. Again, by multiplying both sides for -1, we obtain the equivalent definition 𝑃𝑟{𝑉 (𝑎 ) − 𝑉 (𝑎 ) < 𝜀 }. This part of the equation 𝑃𝑟{𝑉 (𝑎 ) − 𝑉 (𝑎 ) < 𝜀 } = 𝐹(𝑉 (𝑎 ) − 𝑉 (𝑎 )) states that the probability that the difference in utility between candidate B's platform and candidate A's platform is less than the noise term 𝜀 is equal to the cumulative distribution function (CDF) evaluated at the difference in utility 𝑉(𝑎 ) − 𝑉(𝑎 ). In probability theory, when we say 𝑃𝑟{𝑋 < 𝑥}, we’re asking for the probability that a random variable 𝑋 is less than a particular value 𝑥. Now, considering 𝑉 (𝑎 ) − 𝑉 (𝑎 ) as a random variable, we’re essentially asking for the probability that this difference is less than 𝜀 The CDF 𝐹(𝑥) of a random variable 𝑋 gives the probability that 𝑋 is less than or equal to a particular value 𝑥. So, 𝐹(𝑉 (𝑎 ) − 𝑉 (𝑎 )) gives the probability that 𝑉 (𝑎 ) − 𝑉 (𝑎 ) is less than or equal to some value, in this case 𝑒 . Before it was assumed that the noise term 𝑒 is distributed symmetrically around zero. This means that positive and negative values of 𝑒 are equally likely. Because of this, the probability of 𝐹(𝑥) being less than a certain value is equal to 1 minus the probability of it being greater than the negative of that value. Mathematically: 𝐹(𝑥) = 1 − 𝐹(−𝑥), which applied to our case gives: This has an important intuition: the probability of one candidate being preferred over the other due to noise is the same as the probability of the other candidate being preferred over the first candidate due to noise, because of the symmetric nature of the distribution of the noise term. Example: the swing voter model The swing voter model is a concept used in political science to describe the behavior of voters who are not firmly committed to one political party or candidate and may switch their support between different options, swinging the outcome of an election. Think of representative elections in the USA. Consider a population 𝐽 which is made of 3 groups: 𝑅, 𝑀, 𝑃. Each of them has a given size, measures as a share 𝛼 , the sum of all shares is equal to 1. There are two office seeking candidates 𝐴 and 𝐵, maximising their number of votes in order to be elected. In such model, voter 𝑖 prefers candidate 𝐴 if 𝑉 (𝑎 ) > 𝑉 (𝑎 ) + 𝜎 + 𝛿. We notice the introduction of two error components: 𝝈𝒊𝑱 is specific to any individual in a group J, and it is a measure of ideological bias, in this case, against B. Individual ideological bias represents how strongly a voter leans towards one candidate over another based on their personal beliefs, values, or ideological preferences. For example, a voter with a higher bias towards candidate B might be more inclined to support candidate B's policies, even if candidate A's policies are objectively more favourable. The bias is uniformly distributed over a range which is specific to the group J. This means that the bias could take on any value within this range with equal probability. It is centred around zero and has the following distribution, which is specific for each region: 𝜹 is a measure of the relative popularity of candidate B, not specific to any individual voter. It is related to the candidate. For instance, it is related to charisma. It is an overall variable, which has the following distribution: . Charisma might be so strong that perhaps candidate A has an overall positive policy, but charisma is such that it makes the final vote different. The formula of the probability of A winning is The candidate A cannot change the ideology of the population and only to some extent they can change popularity. During a campaign, they need to decide what to promise and decide on 𝑎 . To maximise, they would like to choose a policy which favours more or less all groups, in particular, it should be better to give higher weight to larger groups, and so the largest regions. Besides the size of region, focus should be given to the homogeneity of the group, meaning that the ideological distribution is compressed and there are not a lot of differences. Hence, largest and more homogeneous groups are preferred. Remember that 𝑝 describes the probability of candidate A winning the election. are a constant and cannot be maximised. They are two constant parameters which cannot be affected that much. What instead can be maximised is the summation across groups of the difference in utilities for each group. A policy is made and we know it provides a certain level of utility to a group, then the utility derived from the other policy is subtracted too. All utilities for the groups are summed and weighted for the size of the group 𝛼 and the homogeneity 𝜙 . The probability of winning for candidate A being larger than ½ depends on the utilities that the groups obtain from policy A compared to B, summed and scaled for the size and the homogeneity for each group. The larger the group, the larger the support. Homogeneous groups might also be a positive element, in the sense that the set of preferences are similar. Heterogeneity is such that within a region, the same policy grants different levels of utility. The policy is equal for all the groups, but each of them will perceive them differently. Another example. Suppose groups divided for income level. A policy proposed by the Right candidate might favour rich people. The group of rich people with higher level of income might be homogeneous, but small. The Poor group might be large and homogeneous, such policy from the R candidate will lead them to a negative policy. A politician therefore needs to decide which group to address. Ideally, the best solution is a large and homogeneous region, but it might not always occur at the same time. When targeting a group, a politician chooses to focus on the homogenous and largest group, which however might imply that other groups, perhaps smaller and more heterogeneous, have a negative utility. The size of a group is obvious and can be easily measured, the concept of homogeneity is more sophisticated. The measure of 𝜙 tells how much a group is homogeneous. A smaller 𝜙 means that the distribution of preferences is dispersed, instead if 𝜙 is large, it means that there is a concentration of preferences around 0. This follows from the uniform distribution This model explains what a politician should do in order to win, and it does not provide with certainty who is going to win, although over time parties will converge to the same policy, targeting the same group. The only difference is given by the level of popularity. Policy oriented (partisans) candidates In the realm of political behaviour and electoral strategies, the concept of policy-oriented (partisan) candidates plays a significant role. These candidates align themselves with specific political parties or ideologies, shaping their policy positions accordingly. Within the theoretical framework of the Policy Voting Model (PVM), politicians have the ability to credibly pre-commit to a particular set of policies. In this context, full convergence on the proposed policy can occur, abstracting from considerations like popularity. The partisan paradigm dictates that candidates must balance their policy preferences with the desire to win elections. This involves trading off their personal beliefs with the need to appeal to voters and secure victory. In a one-shot game, where elections are considered as singular events, the outcome depends on how closely candidates' policy positions align with the preferences of the median voter. However, the dynamics change in repeated interactions. Over time, candidates have the opportunity to build credibility by consistently proposing policies closer to the median voter's preferences, rather than their own ideal positions. Alberto Alesina's research in 1988 sheds light on this phenomenon. He demonstrates that even partisan candidates, initially driven by their own policy preferences, may converge towards the preferences of the median voter over time. This convergence is facilitated by repeated interactions, as candidates learn to propose policies that are more credible and appealing to a broader base of voters. Alesina made an argument against the Downsian model: parties are not just office-seeking and have their own ideology. Parties do not just want to win; they also have their set of preferences. The assumption of winning only is relaxed. A compromise needs to be found between the willingness of parties to win and their ideal policy. Parties will try to converge to the median, but not necessarily. The political landscape is simplified to one dimension, meaning policies are represented along a single spectrum. There are two major political parties involved, often referred to as the left (L) and the right (R). The policy preferences of the two parties are characterized by quadratic loss functions, where the aim is to minimise the loss in which parties might incur. In this graph the loss functions of left and right candidate are depicted. Their bliss points are normalised at zero and represent the point at which losses are minimised. Suppose the candidates’ loss functions are 𝑢(𝑙) = −( )𝑙 and 𝑣(𝑙) = −( )(𝑙 − 𝑐) ., with 0 and 𝑐 being the bliss point. When the policies go beyond the bliss points of each party, the loss increases. There exists a median policy 𝜆 , which is located between 0 and 1. Prior to the election, voters anticipate the policy positions of each party. Party L is expected to adopt a policy position represented by '𝑥 ', which is less than 𝜆 , while party R is expected to adopt a position represented by '𝑦 ', which is greater than 𝜆 . The likelihood of party L winning the election, denoted as 𝑃 (𝑥 , 𝑦 ), depends on the relative positions of the expected policies (𝑥 , 𝑦 ) with respect to the median policy (𝜆 ). Specifically, the probability of winning increases for party L as (𝑥 approaches 𝜆 and 𝑦 moves away from 𝜆 . Similarly, the probability of party R winning (denoted as PR) decreases as 𝑥 approaches 𝜆 and 𝑦 moves away from 𝜆 . By moderating the proposed policy the change of winning increases. This passage outlines three potential outcomes or Nash equilibria within a political framework where policies are influenced by both voter preferences and strategic decisions by political parties: 1. Complete Convergence: In this scenario, both parties converge on implementing optimal policies represented by 𝑥 ∗ = 𝑦 ∗ = 𝜆𝑐, where λ ranges between 0 and 1. This outcome resembles the situation described by Downs, where voters' preferences significantly influence policies adopted by parties. 2. Partial Convergence: Here, policies implemented by the parties may partially converge, with 0 ≤ x* ≤ y* ≤ c. This indicates that while some alignment occurs between the parties' policies, there are still differences. Parties are close to the median but not equal to it. 3. Complete Divergence: This outcome sees the parties implementing completely divergent policies, where x* = 0 and y*=c. In this case, parties’ preferences are such that they focus on their bliss points. The passage also highlights the consequences of parties deviating from the expected policy positions after an election. Such deviations result in a loss of reputation and a return to the scenario of complete policy divergence. This underscores the importance of credibility in maintaining stable relationships with voters over the long term. Parties are willing to trade their ideology to get closer to the median voter, according to their own bliss point and loss function to minimise. Citizen-candidate model The citizen-candidate model, as developed by Osborne and Slivinski in 1996 and Besley and Coate in 1997, is a theoretical framework used to study political competition and decision-making in democratic societies. It assumes a polity with N citizens, each having their own policy preferences. In this model, elected officials are chosen from among the citizens who decide to run as candidates in an election. 1. Citizens as Potential Candidates: In this model, every citizen is a potential candidate for political office. This means that individuals from the general population can choose to stand for election if they wish. 2. Integration of Preferences: Because politicians are drawn from the citizenry, their policy preferences cannot be considered separately from those of the voters. In other words, politicians' preferences are not independent of the broader preferences of the electorate. Three Stages: - Entry (at a cost c): Individuals decide whether or not to become candidates for political office. This decision to enter the political arena comes at a certain cost, denoted as 'c'. This cost could represent various factors such as time, effort, or financial resources required to run a campaign. Costs are broadly defined. - Voting: The citizenry votes to select their representatives from among the pool of candidates who have entered the race. This stage represents the democratic process where citizens express their preferences through voting. - Policy Implementation (no commitment): Once elected, officials implement policies without any pre-commitment. This means that elected officials are not bound to specific policy platforms or promises made during the campaign, and they have the flexibility to enact policies based on the prevailing circumstances. Stage 3: Policy Implementation This stage involves the implementation of policies by the winning candidate. The lack of commitment means that the winning candidate implements their own policy preference, referred to as their "bliss point." In other words, the elected official enacts policies that maximize their own utility, rather than being bound by pre-election promises or commitments. decide whether or not to run for office by trading off the probability of being elected (and getting to implement their favorite outcomes) against a fixed cost of running for election. Women have a higher fixed cost of running for elections, in terms of money and time. Everyone is eligible to vote and to stand as a candidate. The village elects an individual who will implement a policy, chosen in the interval [0 1]. Each citizen has a preferred policy option ωi, and women and men have different policy preferences. Specifically, we assume that women’s preferences are distributed over the interval [0 W], and men’s preferences are distributed over the interval [M 1]. the political game has three stages. Citizens first decide whether or not to run. The cost of running for women, δw, is greater than the cost of running for men, δm. Then a candidate is elected which finally implements a policy. The utility of citizen i if outcome xj is implemented is −|xj − ωi| if citizen i was not a candidate. This basically reflects the utility each voter obtains given its ideal policy. −|xj − ωi| − δi if citizen i was a candidate, meaning we also account for the cost of running for the campaign. This shape is due to fact that we are measuring the loss function, and every distance from the ideal policy is squared in order to obtain a positive value. The outcome which is finally implemented may not reflect the preference of the median voter, for several reasons. there may be an equilibrium with two candidates who, if elected, will implement decisions that are symmetric around the median voter, but relatively far away from the median voter’s preferred position. Second, and specific to this model, parameters may be such that, without reservation, there is no equilibrium where a woman is a candidate. In this case, the outcome that will be implemented in equilibrium will be to the right of M, the most “pro-female” outcome preferred by a man. By inducing women to run, the reservation policy moves to the left of the range of outcomes that can be implemented in equilibrium. This will tend to improve women’s utility, and, because the median voter’s policy may now be included in the range of policies that can be implemented in equilibrium, this may also improve the utility of the median voter. The model predicts that there is difference in policy outcomes for male and women. Preferences of men and women might be different. Randomisation, actually means that reserved and unreserved should in principle be identical. From data, it is shown that on several parameters, such as literacy, reserved and unreserved cities performed similarly and the statistical difference was not significant. Expected outcome for certain policies is considered. Both in West Bengal and in Rajasthan, the gender of the Pradhan affects the provision of public goods. In both places, there are significantly more investments in drinking water in GPs reserved for women. This is what we expected, since in both places, women complain more often than men about water. POLITICAL AGENCY Theories of microeconomics, with incentives and misbehaves. So far, politicians did not cheat and committed to their platform. Assume a winner, which does not commit to its promise. This new model looks at the implementation phase, looking at agency theory: personnel economics. The firms is the principal and the personnel, workers, are delegated to do something. There is imperfect information, the personnel does not know whether the personnel is doing his best and cannot perfect monitor on the activity of workers. Citizens (the Principal) delegate authority to policy-makers (the Agent). Asymmetric information occurs between citizens and polocy-makers. For instance, politicians might have better access to information, to which voters cannot have access. Politicians might also misbehave but voters would not know. Consider a representative citizen (say the median voter): • Pre-election: citizen wants to select politicians with certain characteristics, like competence and honesty (unobserved). Both of them are parameter which are difficult to be determined and observed. • Post-election: citizen has less info on state of the world (unobserved), policy-makers may act opportunistically, and moral hazard arises (politicians do something in their favour since they cannot be observed. Selection and incentive mechanisms in politics are harder, such as a pay-benefit system. Main instrument which can be used are elections! The only way of disciplining politicians! 13-03-2024 In the Political-Agency model, it is assumed that an optimal policy exists, but uncertainty exist on the nature of the politicians. Asymmetric information exists, meaning that voters (principal) and agent (politicians) have different levels of information. Uncertainty arises in two stages: - At selection phase, principal is uncertainty on competence and honesty of the agent (politicians) - After elected, the voter can only know the utility coming from the choice of the politicians, but it cannot directly know whether the right policy has been implemented. This ex-post utility is the only parameter the voter has to check on the policy outcome. Basic Model (Barro) The main discipline device for agents, that the principal can use, are elections. To model uncertainty, probabilities are introduced to formalise the model, which assumes: - 2 time periods t, there is no other period; - In each period a policy-maker is elected to take an action a ∈ {0,1}. It can be just one of them, for instance, deciding whether to go to war or not. - The utility for voters in each comes from the policy which is implemented by the politicians. When the policy adopted is the optimal one, a positive utility is obtained, otherwise no utility. Example of interest rate: with inflation, there should be an increase in the interest rate. Politicians know it should be made, but at the end they might not do it. Voters only check on the effect of the policy which is implemented. Only after receiving the policy and the consequence, voters can check on whether the ideal policy has been implemented. The politician knows what the optimal policy is (𝑠 , stands for state of the world), the voter doesn’t and only observes the utility which obtains from the implemented policy. Utility in period 2 is discounted: with multiple periods, it is necessary to discount, especially future values. They need to be discounted at the present value. For instance, think of 100 euros today: they can be invested and become 103. It is not the same of 100 dollars tomorrow. Hence, they are discounted at the present value. In general, the discount rate 𝛽 < 1, meaning that it is preferred to receive money today rather than in the future. Two kinds of politicians are assumed based on honesty: congruent (good) and dissonant (bad) denoted by 𝑖 ∈ {𝑐, 𝑑}. The probability of a politician being congruent is 𝜋, the probability of the politician being dissonant is 1 − 𝜋. • congruent politicians always choose 𝑎 = 𝑠 and obtain utility ∆+W, since they care about the optimal policy being implemented. This means that in any period, they will choose to apply the optimal policy congruent to the state of the world. They also get a wage, beyond ∆ which is obtained when the right policy is chosen. • dissonant politicians don’t care about realizing the optimal policy, no ∆ is obtained. When they deviate from the optimal policy, they obtain the” dissonance rent” 𝑟 ∈ [0, 𝑅], such that 𝑎 ≠ 𝑠 . r is a random variable extracted from a distribution with cumulative distributive function G(r), with 𝐸(𝑟) = µ, and 𝑅 > 𝛽(µ + 𝑊) (i.e., the largest possible rent today is higher than the average return you could get tomorrow). This is influenced by the state of the world and the possibilities for bribing. The condition tells that the highest bribe which can potentially be obtained today, should be larger than the average income tomorrow (given by the wage which can be obtained after being re-elected) Bribe can occur, and it usually occurs when the politician gets a rent, and voters are going to have utility equal to zero. When they decide to be dissonant, they do not care of the potential impact this can have on society, in the sense that they do not care of the decision being implemented, they just care of the rent which can be obtained. As mentioned, the model is built on two periods. In period 1, nature selects the optimal policy (being defined by 𝑠 ), there is the definition of rent (what can be obtained by being dissonant, 𝑟 ), and a politician 𝑖 is chosen. A random draw from the population of politicians occurs. None of such factors are observed by voters. The elected politician implements 𝑎 . Voters and politician receive their period 1 payoff. Voters observe 𝑉 (they can either get ∆ or zero), instead politicians can either obtain the wage (if congruent) or the rent (dissonant). Then, an election occurs. Voters decide whether to confirm 𝑖 in office or to choose the challenger (randomly drawn). The first elected politician and the challenger, being randomly elected, have both a probability 𝜋 of being good. In period 2, Nature selects 𝑠 , 𝑟 and 𝑖 (if incumbent not re-elected, is randomly chosen among the population). Again, the politician will choose the policy and then voters and politicians will receive their payoffs. We want to know the optimal strategy for both voters and politicians in both periods: find the equilibrium by solving the game backward. The idea is: in order to achieve a given result, what should be the path to follow? Equilibrium In period 2, a congruent politician always chooses 𝑎 = 𝑠 (payoff for voters is ∆) and a dissonant politician always chooses 𝑎 ≠ 𝑠 (payoff for voters is zero), as there is no period 3. The dissonant will choose to bribe and obtain a rent. In period 1, voters would like to re-elect congruent politicians only, but not always clear how to separate congruent and dissonant politicians. Congruent politicians always choose the right policy, but it also occurs that a dissonant politician might choose to adopt the right policy and behave like a congruent politician. This can occur when rents for the given period, are lower than expected earnings in the future, given 𝜇 (expectations for bribing). When bribing is not convenient in period 1, the politician will choose the optimal policy, waiting for the following period to commit bribe. Since voters do not observe the nature of the politician, but they only observe outcomes and utilities, it can occur that they re-elect politicians which are actually dissonant, even if they adopted the optimal policy. Bayesian Equilibrium Bayesian equilibrium is used here to refer to a situation where both politicians and voters make decisions based on their beliefs and expectations about each other's behaviour, in order to address uncertainty. In period 1 the action of the politician is optimal given the re-election strategy of the voters. Voters’ re-election strategy in period 1 is optimal given the action of the politician and given their beliefs about the type of the politician. Both politicians and voters form their beliefs using Bayes' rule. This rule helps them update their beliefs when they observe new information or events. It calculates the probability of an event (Bj) being true after observing another related event (A). In our case, we want to determine the probability of receiving ∆ as an outcome, given that the politician is congruent. It states that the probability of event Bj being true after observing event A is equal to the probability of observing A given that Bj is true, multiplied by the prior probability of Bj, divided by the sum of similar products for all possible events Bi. Mathematically, it's represented as: So, the probability of the politician being congruent, after observing ∆ as utility, is equal to the probability of observing ∆ as utility, given that the politician is congruent, times the probability that the politician is congruent, divided for the sum of the different probabilities, in particular observing ∆ as utility even when the politician is dissonant. Voters have 3 possible strategies among which they can choose: - always re-elect the incumbent politician. - the incumbent is never re-elected. - re-elect a politician if voters observe ∆ as utility. When a voter wants to re-elect a politician if in period 1 the voter observed ∆ as utility, the voters will make their believes on the incumbent politician being congruent (𝑖 = 𝑐) after observing 𝑎 = 𝑠 The formula wants to compute the probability of the politician being congruent, given that utility ∆ is observed. It is equal to the probability of observing ∆, given that the politician is congruent Pr (𝑉 = ∆|𝑖 = 𝑐), multiplied for the probability of the politician being congruent Pr (𝑖 = 𝑐). In contrast, a parliamentary system often has less distinct separation between the executive and legislative branches. The head of government (prime minister) and their cabinet are drawn from the legislature, blurring the lines between the two branches. Presidents in presidential systems derive their mandate directly from the citizens through popular elections. They do not need the confidence of the legislature to remain in office or to carry out their duties. In parliamentary systems, the prime minister and their cabinet require the support of a majority in the legislature to remain in power. If the government loses the confidence of the legislature (typically through a vote of no confidence), it may lead to the resignation of the government and potentially new elections. Coalitions In a presidential democracy, the executive (the president) is directly elected by the citizens. The president does not derive their authority from the legislature. Therefore, the formation of the government is not dependent on negotiations among elected members of the legislature. The president selects their cabinet independently, typically without the need to form coalitions with other political parties. In contrast, in a parliamentary democracy, the executive (the cabinet) derives its mandate from and is accountable to the legislature. This means that the formation of the government is not solely determined by elections but is instead the result of negotiations among elected members of the legislature. Political parties or coalitions must form in order to secure a majority in the legislature and thus form a government. These negotiations are typically driven by rational decision-making, where parties seek to achieve objectives they would not be able to attain otherwise. Since several parties typically compete and win seats in parliamentary elections, single-party majority governments (where one party controls the majority of parliament and hence forms the government) are extremely rare, unless the party is made of factions. In general we have: • Minority Coalition (MC): a coalition that controls less than 50% of the parliamentary seats • Minimal Winning Coalition (MWC): a coalition that controls at least 50% of the parliamentary seats and is such that each party in the coalition is essential to retain majority status • Surplus Coalition (SC): a coalition that controls more than 50% of the parliamentary seats and is such that there is at least one party in the coalition which is not necessary to have majority status Person and Tabellini In parliamentary systems, coalitions are a common feature due to the proportional representation of multiple parties. In such systems, single parties within coalitions often wield significant bargaining power. This is because coalition governments need to accommodate the diverse interests of multiple parties, resulting in larger governments. The aim is to satisfy the preferences of all coalition partners, which can lead to policy compromises and larger public expenditures to cater to various interests. Parliamentary systems tend to induce stable majorities in the legislature due to the nature of coalition politics. With stable majorities, parliamentary systems can pass legislation more efficiently. No need for this in presidential systems where legislators are more independent. Presidential systems often feature more targeted spending as individual legislators have greater independence. In such systems, legislators may focus on securing benefits for their specific constituencies or interest groups, leading to more targeted allocations of resources. In contrast, parliamentary systems may prioritize the provision of public goods due to the need to satisfy coalition partners and maintain legislative cohesion. Public goods benefit society as a whole and are less likely to be focused on specific interest groups. In parliamentary systems, where there is typically less separation of powers between the executive and legislative branches, there may be fewer checks and balances compared to presidential systems. This can create an environment where the ruling coalition, which controls both the executive and legislative branches, has relatively more unchecked power. Due to the greater cohesion and control exerted by the ruling coalition in parliamentary systems, there may be fewer obstacles to prevent rent extraction. Without robust checks and balances, members of the ruling coalition may have greater opportunities to exploit public resources or influence government decisions for their own benefit without facing significant consequences. Presidential systems, on the other hand, often feature stronger separation of powers and more distinct checks and balances between the executive and legislative branches. This can make it more difficult for any single individual or group to engage in rent extraction. Legislatures Within legislatures, there's often a division of labour and specialization, much like in other areas of society. This means that different members or bodies within the legislature focus on different tasks or areas of expertise. The purpose of this division of labour is to enhance efficiency. By allowing different members or bodies to focus on specific tasks, legislatures can capitalize on the diverse talents, experiences, and interests of their members. This specialization enables legislators to develop expertise in particular policy areas and to handle complex issues more effectively. Specialization within legislatures brings several advantages. It allows legislators to delve deeply into specific policy domains, gaining a comprehensive understanding of the issues at hand. This expertise can lead to more informed decision-making and the development of well-crafted legislation. However, specialization also comes with its costs and potential drawbacks. One concern is whether the delegation of decision-making to specialized groups preserves collective objectives. In other words, while specialization may enhance efficiency and expertise, it raises questions about whether the broader interests and goals of the legislature as a whole are adequately represented and safeguarded. Ensuring that collective objectives are preserved when decisions are delegated to specialized groups is a fundamental challenge for legislative bodies. It requires mechanisms for accountability, transparency, and oversight to mitigate the risk of capture by narrow interests. Committees Committees have jurisdiction on particular policy areas. Legislators are assigned to different committees and affect different policies. Legislators want to focus on subjects of highest priority to them (i.e. of highest priority to their district, to enhance their re-election prospects). Distributive theories emphasize that legislators prioritize delivering tangible benefits to their constituents. These benefits can take various forms, including funding for infrastructure projects, grants for local organizations, or programs aimed at addressing community needs. Legislators often leverage their positions on committees to advocate for policies and projects that directly benefit their districts. By securing benefits for their constituents, legislators aim to strengthen their standing and popularity within their districts. Distributive theories suggest that legislators strategically allocate resources to maximize their electoral appeal. Legislators have different preferences and priorities (heterogeneity). The policy space is multidimensional. Main issue: Policy benefits are public within each district; policies are funded through national taxation. Diffuse costs, targeted benefits ⇒ potential gains from exchange. Logrolling Assume two bills, assume the agricultural committee, which has to discuss on sugar and corn bill. This table provides a representation of benefits and costs from sugar and corn bill, for three legislators representing three different regions. The total cost for the country for the sugar bill is 9, for the corn bill it is 12. Costs are diffused and divided among districts, benefits instead are targeted. Voting in a majoritarian way would not provide any outcome: there would be always only one vote for each bill. In a context of diffused costs and targeted benefits, there is the potential for logrolling: a political strategy or practice in which legislators or policymakers exchange favors or support for each other's proposals or projects. In logrolling, politicians negotiate and agree to support each other's initiatives, often unrelated or of differing importance, with the understanding that each will receive reciprocal support for their own interests or priorities. In this example, legislators 1 and 2 decide to exchange votes and mutually sustain their policies. Legislator 1 obtains a net benefit of 12 − 3 − 4 = 5 (from the benefit of the sugar bill, the cost of the sugar and corn bill are subtracted). Legislator 2 obtains a net benefit of 20 − 4 − 3 = 13. This specific case also represents a situation in which there is efficient trading, in the sense that surplus has been generated for society. In fact, su subtracting from the overall benefits, the overall costs, the surplus is positive (12 − 3 − 3 − 3) + (20 − 4 − 4 − 4) > 0). This is not always the case: it can be that, although logrolling is possible, overall the trading is inefficient for society. Voting occurs when considering NET gains. To see grounds for logrolling, sum by rows. Policy making is not necessarily Pareto improving (such that no one loses), i.e., some legislators may loose (e.g., legislator 3), still logrolling can be still done, even if there is not a positive gain for society. Informational theories Informational theories start with the premise that legislators operate in an environment of uncertainty. Legislators may not fully understand how various policy options will impact outcomes such as economic growth, or may not know the policy preferences of their colleagues, making it challenging to predict how others will vote or negotiate on specific issues. Committees are crucial within the legislative process as they provide incentives for a reduced number of legislators to acquire information and become specialists in specific policy areas. This solves a collective action problem, where individually, legislators may lack the motivation to invest in gathering information, but collectively, they benefit from having specialized knowledge available within the legislature. While informational gains from specialization can enhance legislative decision-making, they also come with a cost: more knowledgeable legislators have more influence. Partisan theories Partisan theories suggest that the main goal of the majority party in a legislature is to control how committees are organized and run. This is because politicians are primarily focused on getting re-elected, and being associated with a strong political party can help them win votes. The reputation of a party is like a valuable asset shared by all its members. However, individual lawmakers often prioritize the needs of their own districts over party interests. So, committees are used by the majority party to ensure that legislators work together to support the party's goals. They help enforce party discipline and coordinate actions to benefit the party as a whole, even though individual lawmakers may have their own priorities based on their constituents' needs. Bureaucracy From direct democracy, we moved to representative democracy, politicians’ behaviours, and then policies. Bureaucracy is important in implementation of policies. The political process needs to be addressed: the existence of optimal policies does not imply their effective implementation, there are processes which might prevent this. Politicians might be disciplined and adopt optimal policy, but the role of bureaucracy needs to be addressed. Bureaucracy needs to be addressed as much as politicians. It is helpful to understand where misbehaviours come from, and how to realign interests of politicians with those of bureaucracy. It might delay, change the optimal policy and even stop its implementation. Laws usually do not address technicalities, which might change. In case of errors in defining technicalities, a parliamentary amendment might be necessary. Specifying everything in laws is risky, but such approach was aimed at avoiding bureaucracy. Historically, papers focused on analysing whether interests of bureaucracy align with those of voters. Assumption: everything before bureaucracy has gone well, with positive selection. Delegation refers to the process of assigning the responsibility for policy implementation to specific agencies or bureaucrats within the government. Instead of legislators directly handling all aspects of policy execution, they delegate certain tasks to specialized agencies, known as bureaus, which are responsible for carrying out these policies.