Theorie Part 2

• A consistent and coherent social welfare function that is optimized by a social planner or a benevolent dictator does not exist.

• Therefore, different sets of preferences have to be traded off against each other and heterogeneities need to be taken into account.

• Abstracting from dictatorship or oligarchy, a democratic decision making process has to find mechanisms how different preferences are taken into account and how conflicts are (peacefully) resolved.

• This usually entails voting, but voting is not unproblematic either.

  • Voting is (usually) a binary procedure ( “Yes” or “No”). As a consequence, neither the motive nor the intensity of preferences is taken into account.

  • Outcomes are unstable or can be manipulated

• Methodological individualism: individuals are decisive actors, not collectives. Individuals are heterogeneous and have different preferences.

  • There are conflicts of interest.

• Utility maximization: economic actors are interested in maximizing their personal benefit or utility, given their preferences.

  • Utility can be defined over many things and include the interest of others.

• Rationality: individuals’ behavior and decisions are rational and goal-oriented.

  • Rationality can be bounded: information is incomplete, situations are too complex, mistakes are possible.

Basic requirements of voting rules:

• Universality: can be applied to all pairwise alternatives.

• Nonnegative Reaction: a change of an individual’s preferences toward an alternative A never changes the collective preferences against alternative A.

• Anonymity: it does not matter for the collective preferences who supports or denies an alternative; this is even more than non-dictatorship (“one-person-one-vote”).

• Weighted or un-weighted voting. We usually assume unweighted voting (“one person-one vote”).

Summarized:

Under the unanimity rule, a policy can only be approved if every single voter supports it, giving each individual veto power. This rule ensures that no individual or minority is exploited. Unanimity is chosen at the "constitutional stage" when individuals decide on basic rules without knowledge of their future preferences or situation. This hypothetical stage considers unanimity as optimal, as it guarantees Pareto efficiency.

Difficulties and problems in practice at the “operational stage”:

• Difficult to realize in large groups (costly in terms of time, negotiations).

• Individual participants can block decisions (crucial role of participants’ bargaining power).

• Incentives for strategic behavior under asymmetric information.

Nevertheless, unanimity rule is an important benchmark for evaluating outcomes of decision processes.

• Democracies typically apply the simple majority rule with 𝑞 ≥ 1/2.

• Buchanan/Tullock emphasize that each less-than-unanimity rule (𝑞 < 1) imposes costs on those who are outvoted.

• These are labeled as external costs (EC). The lower 𝑞, the higher the external costs of the quorum.

• The highest external costs are caused by dictatorship; they are zero for unanimity

• The higher the quorum q, the higher the cost of negotiations and finding a compromise. These cost are labeled decision costs (DC).

• Therefore, there is a trade-off between external and decision costs

Summarize:

The costs of decision-making vary based on the complexity of the issue and the number of people involved. There is no one-size-fits-all optimal majority rule. Important issues may need a higher majority (supermajority), while less critical ones may require a lower majority (submajority). Indirect democracy is seen as an improvement as it allows for flexibility in decision-making based on the importance of the issue.

• In democracy, the simple majority rule (𝑞=𝑛/2+1) is used very widely.

• the option with the most votes, regardless of the percentage, is declared the winner.

• It only requires a proposal to receive more votes than any other single option, even if it falls short of obtaining more than 50% of the total votes.

• For example, if there are 100 people voting, the option that receives 40 votes would win under the simple majority rule, even though it represents less than half (40%) of the total votes.

• Condorcet Jury Theorem:

  • The Condorcet Jury Theorem says that if each person in the group is more likely than not to make the correct decision, then as the group gets larger, the chances of making the right decision also get higher.

  • This assumption is based on voters making independent judgments, voting honestly, and each member having a probability of 𝑝>1/2 to make the correct decision. If the probability is less than 1/2, it would be better to randomly choose an option (e.g., flip a coin) instead.

Distributional issues can lead to majorities forming to benefit the majority at the expense of the minority. Even when efficient allocations are achieved, distribution remains crucial. For example, investments in public goods like infrastructure or education can increase overall welfare, but conflicting groups (e.g., rich and poor) in the voting population may have different interests and preferences.

Individuals have an incentive to strategize and form coalitions (majorities) to their advantage, anticipating the possibility of being exploited by other majorities. For example, Group A may support a decision important to Group B in exchange for support from Group B on a different decision important to Group A. This process, known as logrolling, can lead to both efficient and inefficient outcomes, depending on individual preferences and the feasibility of creating credible coalitions.

• However, Voters B and C could agree to vote in favor of both projects. Both realize an individual profit of 3, gaining overall 6.

• The agreement between B and C improves “welfare” but individual A incurs a loss of 4 units.

• Note that the overall gain depends on the sufficiently strong divergence between gains and losses. If gains change from 5 to 3 units, log rolling leads to a net loss for society.

• Moreover, the considered logrolling solution is not necessarily stable. The losing party may try to break up the initial coalition.

• Log-rolling may lead to a cycle:

  • Coalition between B and C for (X, Y): Payoff is (-4, 3, 3).

  • A convinces B to build a coalition for (X, ~Y): Payoff is (-2, 5, -2).

  • Now C convinces A of a coalition of (~X, ~Y): Payoff is (0, 0, 0).

  • Now B may form again a coalition with C.

• In reality, we do not observe that much instability in the political process, because of reputation and reliability of parties, formal coalitions with contracts, compensating behavior and limited voting alternatives to minimize deviations

Example: If Z should win, the chairman starts with X vs.  Y, so that X wins, which will lose against Z in the second pairwise voting

• chairpersons and procedural rules are extremely influential & important to avoid manipulation of voting processes.

• bildet einen “cycle” ab, kann geändeert werden, wenn z.B. Voter B. seine preference ändert zu Y lieber statt X Ranking. Clear: Y>Z>X

• Majority rule can produce an intransitive preference order for the group.

• But if preferences are all single-peaked, there will be a Condorcet winner that will dominate all alternative positions in a pair-wise comparison.

• Let policy positions be distributed on a one-dimensional scale.

• Each voter ranks all alternatives in a pair-wise comparison.

• Each voter is utility maximizing.

Both in Graphics:

Conocret Winner:

Der Condorcet-Gewinner bezieht sich auf einen Kandidaten in einer Wahl, der in einem Kopf-an-Kopf-Vergleich gegen jeden anderen Kandidaten gewinnen würde.

In einem Wahlsystem mit mehreren Kandidaten tritt jeder Kandidat in einem direkten Vergleich gegen jeden anderen an. Wenn es einen Kandidaten gibt, der in jedem dieser Vergleiche gewinnt, wird er als Condorcet-Gewinner bezeichnet. Mit anderen Worten, der Condorcet-Gewinner ist derjenige Kandidat, der die größte Unterstützung hat und von einer Mehrheit der Wählerinnen und Wähler bevorzugt wird, wenn er gegen jeden anderen Kandidaten einzeln antritt.

Es ist jedoch wichtig zu beachten, dass in realen Wahlsystemen, insbesondere bei Wahlen mit mehreren Kandidaten, nicht immer ein eindeutiger Condorcet-Gewinner existiert. Dies liegt daran, dass es zu Zyklen oder Inkonsistenzen in den Präferenzen der Wählerinnen und Wähler kommen kann, sodass es keinen Kandidaten gibt, der in jedem Vergleich gewinnt.

• If a Condorcet winner exists, there is an elegant and simple solution to the voting problem. There is a decisive voter whose preferences on one issue will dominate all others. There is no possibility for manipulation or logrolling and no cycling.

• The Median-Voter concept is widely used in economic and political debates to explain and predict voting outcomes. But:

  • It doesn’t guarantee an efficient, fair or just outcome.

  • Its applicability is severely restricted.

  • It works only for an at maximum two-dimensional issue.

  • It does not apply to representative democracy.

• One should be aware of its limitations when using it

If all voters have single-peaked preferences over a one-dimensional policy space 𝑥, the position of the median voter (𝑥𝑚) cannot be defeated by any other position in pairwise comparisons. This applies when policy positions are defined along one-dimensional issues, and voters' preferences are single-peaked in that dimension.

When voters act rationally and vote according to their preferences to maximize their utility, the simple majority rule yields a stable and unique solution.

Example:

• doesn’t work in a two-dimensional space

If there is a policy position that most people prefer over all others, it will also affect how political parties compete. Only parties that adopt this preferred position have a chance to win. This creates a political equilibrium where both parties' positions converge at the preferred policy of the majority of voters.

In representative democracy, this means the median voter is the decisive voter, and parties cannot afford to stray from that position if they want to win elections. This is often used to explain why political parties tend to become similar over time.

However, it's essential to remember that these conclusions rely on strict assumptions, and real-world situations may not always align with these ideas.

Assumptions:

• One-dimensional policy space.

• Single-peaked preferences in that dimension.

• The number of voters approaches infinity.

• Voters vote rational for parties according to their preferences.

• No costs of voting and no possibility for strategic voting.

• Parties maximize their election chances. Party utility is equal to the number of supporting voters.

• Perfect information about preferences, policy positions and their implications

The conditions for an equilibrium are:

1. No party has a vote share that is less than one-half of the interval to any other position. If this is not the case, one party can increase its voting share by moving. This can be no equilibrium.

2. The left-most and right-most positions on the interval are shared by two parties. Assume party 1 has position Q1 and party 2 has position Q2. Party 1 can increase its vote share by moving right. Again, this can be no equilibrium.

3. There is no equilibrium for three parties

Problematic Assumptions

In reality, the assumptions are not always fulfilled:

• There exist partisan candidates and voters (ideology, loyalty).

• Parties follow further objectives.

• Parties’ positions are constrained due to party members or people who finance the party.

• Parties are threatened by potential entry of a new party.

• The information distribution among voters and parties is incomplete and/or asymmetric.

• There is a multidimensional policy space.

• Not everyone votes.

• Although there is a decline in the share of voters who actually vote, there is nevertheless a surprisingly high turn-out at elections.

• In fact, rational behavior would dictate not to vote. Even though costs of voting might be (usually) small, the probability of being decisive is close to zero. So why bother?

• The „Paradox of Voting“ (Anthony Downs).

  • Irrational behavior.

  • Taste for voting („expressive voting“).

  • Altruism.

  • Voting as a game of cat and mouse

• Under the Median-Voter assumption, political parties do not really play a role. They choose positions opportunistically and implement the (median-) voter‘s position.

• There is no role for ideology (or political convictions), self-interest, corruption, the influence of interest groups, or deviance between political decisions and their implementation.

• But of course, voters do not fully control politicians and „bureaucrats“, and neither do politicians fully control bureaucrats.

• What are alternative explanations of the political process, taking these factors into account?

The Median-Voter assumption suggests that political parties opportunistically choose positions that align with the preferences of the median voter and implement those positions. This assumption disregards the role of ideology, self-interest, corruption, interest groups, and any deviation between political decisions and their implementation. However, it acknowledges that voters do not have full control over politicians and bureaucrats, and likewise, politicians do not have complete control over bureaucrats and other governmental institutions.

The deterministic voting approach assumes that each voter always votes for the candidate or party closest to their preferred position. This suggests that minor changes in party platforms can have dramatic effects on voting outcomes, which seems unrealistic.

In contrast, the probabilistic voting approach offers a more realistic model by considering the probabilities of voter support and addressing some of the limitations of the deterministic approach.

• Voters are not perfectly informed about the parties positions.

• The parties do not perfectly know the voters’ bliss points and preferences.

• There are random events that might change preferences or the votes, or the voter turn-out.

• Hence, parties cannot choose platforms and predict deterministically their corresponding number of votes, but are uncertain.

• They thus maximize their expected votes

Thus, optimizing behavior of parties implies that:

• Only people expected to vote are taken into account.

• Only voters who are expected to react to a particular party‘s platform are taken into account.

• Those whose expected reaction is stronger receive a higher attention.

• As long as voters are not expected to react, parties have leeway to pursue their self-interest.

• Different target groups and/or information sets lead to different policy platforms.

• As politicians are not fully controlled by voters, there is also room for interest groups to influence politicians and their policy platforms.

• As voters cannot fully control politicians, so can politicians not fully control the implementation of policy decisions. There is room for self-interested behavior of „bureaucracy “.

• From the point of view of voters, there is a two-stage principal agent problem.

• The probabilistic voting model highlights that certain groups hold more influence in the political process while others are disregarded. Non-voters have no impact, but well-organized and vocal groups can exert significant influence.

• Preconditions for the existence of interest groups: Legal permissions to organize

• Larger groups have more influence

• Smaller groups are usually more influential than larger groups

  • Financial support:

    • Campaign contributions (legal).

    • Corruption (illegal).

Summarized:

In politics, some businesses seek to redistribute benefits in their favor. They do this through regulations set by the government, which can raise the price of certain goods, leading to higher profits for those businesses. However, the rest of society loses out in this situation.

The businesses that benefit from the regulations support the government, while those who lose support may withdraw their political support. This support can be in the form of votes or other means, and both winners and losers don't necessarily try to optimize how much support they give.

• In politics, there is a trade-off between marginal gains and losses in support. The optimal policy may not fully align with the preferences of either industries or consumers.

• The influence of groups on political decisions is crucial. Uninformed or large groups with weak reactions are often overlooked.

• Regulation and intervention in markets can lead to efficiency losses, resulting in overall negative effects on society.

Summarized:

Interest groups invest resources and efforts to influence politicians in order to implement policies that benefit them, resulting in rents. However, part of these rents are spent by interest groups, reducing overall net benefits. This process of influencing policy through resource expenditure is known as lobbying. If the expenditures are redistributed to politicians, there are no additional costs for society. However, "unproductive" expenditures increase the social loss beyond the initial costs (L), considering the opportunity costs of such expenditures.

Summarized:

The responsibility for policy implementation is often delegated to government agencies or bureaucracy. Governments frequently entrust decision-making power to bureaucrats in areas such as monetary policy and competition policy. As a result, numerous specialized agencies exist, often with overlapping and conflicting responsibilities. It is important to note that bureaucrats themselves can function as interest groups and act in their own self-interest, which may impact policy outcomes.

Bureaucrats are assumed to be utility maximizers with the following objectives:

1. Budget maximization.

2. Slack maximization / workload minimization.

3. Risk minimization.

• Asymmetric information; bureaus are specialized and “experts” in ministries and other bureaucracies have informational advantages about the effects and costs of policies.

• Cost functions of bureaucracies are hard to observe.

• Output is hard to measure; in many cases, this leads to input control.

• Often non-market goods (e.g., national defense) are produced that have no market price.

• There is no competitor and bureaucrats are often monopolists in production of their services.

—> Efficiency is hard to measure.

—> Bureaucrats cannot be controlled completely.

—> Therefore, bureaucrats have the opportunity to follow and realize their own interest.

Summarized:

While democratic policy-making relies on voting, it does not guarantee efficient outcomes that accurately reflect the preferences of the population. Voting can yield inconsistent results and be susceptible to manipulation. In theory, under certain assumptions, direct democracy can lead to consistent policies based on the preferences of the median voter. However, in representative democracies, transaction costs and factors like uncertainty and asymmetric information create principal-agent problems, allowing for political self-interest, the influence of interest groups, and distortive behavior of bureaucracies. As a result, depending on the political system, there is a high probability of inefficient and distorted policies.