POLITICS DocsThe Logical Consistency 2024-08-21

Onto The Discussions about The Frameworks for Making Rational Decisions: Expected Utility.

In everyday of our lives, we are often faced with the risks of not knowing the outcomes of the decisions that we make. For example, we might go into a field or industry expecting that it might bring us abundant opportunities and profitable outcomes. However, in the end it might be the complete opposite where it brings us nothing but unemployment and debt. Therefore, something called the expected utility has been brought into conversations, and its trick is to pick the act with the highest expected utility.

I have gone through articles that talk about expected utility theory as a normative theory – that is, a theory of how people should make decisions. Now, let’s discuss about expected utility being used as a descriptive or predictive theory in economics.

In the subsequent section, we will go through some formulas and definitions of expected utility. Following general convention, I will make the following assumptions about the relationships between acts, states, and outcomes.

The general framework goes as below,

  • States, acts, and outcomes are propositions, i.e., sets of possibilities. There is a maximal set of possibilities.
  • The set of acts, the set of states, and the set of outcomes are all partitions on all possibilities.
  • Acts and states are logically independent, so that no state rules out the performance of any act.
  • I will assume for the moment that, given a state of the world, each act has exactly one possible outcome.
Acts / States It Rains It Does Not Rain
Take Umbrella Encumbered, Dry Encumbered, Dry
Leave Umbrella Wet Free, Dry

The expected utility formula depends on two parts: the probabilities of a set of outcomes conditioned on a certain act and the utility function over the set of outcomes.

Let’s break down the expected utility formula in a super simple way!

Understanding the Expected Utility Formula

The formula you gave is:

$
EU(A) = \sum_{o \in O} P_A(o) \cdot U(o)
$

This formula might look complicated, but it’s really just a way to decide which choice is the best, based on how good the results are and how likely they are to happen.

Let’s use an example to make sense of it.

Imagine You Are Choosing a Snack

Think of expected utility like deciding which snack to pick:

  • A is the choice you are making. Let’s say it’s the choice between eating a chocolate bar or an apple.
  • O is all the different outcomes (results) that could happen after you pick a snack. For example, if you pick the chocolate, the outcomes might be “Yummy!” or “Too sweet!” If you pick the apple, the outcomes might be “Crispy and juicy!” or “Too sour!”

Now, the formula helps you decide which snack to pick by thinking about:

  1. $U(o)$: This is how much you like each outcome. For example:

    • “Yummy!” might be worth 10 points.
    • “Too sweet!” might be worth 3 points.
    • “Crispy and juicy!” might be worth 8 points.
    • “Too sour!” might be worth 2 points.

  2. $P_A(o)$: This is how likely each outcome is to happen. It’s like guessing:

    • The chocolate being “Yummy!” might happen 70% of the time (or 0.7 probability).
    • The chocolate being “Too sweet!” might happen 30% of the time (or 0.3 probability).
    • The apple being “Crispy and juicy!” might happen 60% of the time (or 0.6 probability).
    • The apple being “Too sour!” might happen 40% of the time (or 0.4 probability).

Putting It All Together

To find out which snack to choose, you use the formula:

  1. Multiply: For each possible outcome, you multiply how much you like it ($U(o)$) by how likely it is to happen ($P_A(o)$). This tells you the “expected value” of each outcome.

    • For chocolate:

      • “Yummy!” = 10 points × 0.7 (70% chance) = 7
      • “Too sweet!” = 3 points × 0.3 (30% chance) = 0.9

    • For apple:

      • “Crispy and juicy!” = 8 points × 0.6 (60% chance) = 4.8
      • “Too sour!” = 2 points × 0.4 (40% chance) = 0.8

  2. Add Up: Add these numbers together for each snack to get the expected utility.

    • Chocolate’s Expected Utility: 7 (Yummy) + 0.9 (Too Sweet) = 7.9
    • Apple’s Expected Utility: 4.8 (Crispy) + 0.8 (Too Sour) = 5.6

Deciding Which Choice Is Better

  • Higher Expected Utility: The snack with the higher number (expected utility) is the better choice based on how much you like the outcomes and how likely they are to happen.
  • Chocolate Wins: In this case, chocolate has a higher expected utility (7.9) compared to the apple (5.6), so, according to the formula, picking the chocolate is the better choice!

Summary

Expected utility helps you choose by:

  • Guessing how much you will like each possible outcome.
  • Figuring out how likely each outcome is to happen.
  • Multiplying and adding these to see which choice is the most “valuable” overall.

Why Is It Important To Bring Up The Above here?

To understand the connection between logical consistency, expected utility theory, and outcomes, let’s break down each concept and how they relate to each other when making decisions.

1. Logical Consistency:

  • Logical consistency means that your beliefs, choices, and actions do not contradict each other.
  • For example, if you believe that rain makes you wet and you want to stay dry, it would be logically inconsistent to not use an umbrella when you know it’s going to rain.

2. Expected Utility Theory:

  • Expected Utility Theory is a mathematical framework used to make decisions under uncertainty. It helps you evaluate which action to take by calculating the “expected utility” (a measure of satisfaction or benefit) for each possible action.

  • The idea is to choose the action with the highest expected utility — meaning, the action that gives you the most benefit or satisfaction on average over the long term.

    The formula for expected utility is:
    $
    \text{EU(A)} = \sum \text{Probability of Outcome} \times \text{Utility of Outcome}
    $
    where:

    • EU(A) is the expected utility of choosing action A.
    • Probability of Outcome is how likely each outcome is if you choose action A.
    • Utility of Outcome is how good or valuable each outcome is to you.

3. Outcomes:

  • Outcomes are the possible results that happen based on the actions you take. Each outcome has a certain probability of happening and a certain utility or value to you.

Connecting Logical Consistency, Expected Utility, and Outcomes:

  1. Maintaining Logical Consistency with Expected Utility:

    • To make rational decisions, you should choose actions that are consistent with your beliefs and values. Expected Utility Theory provides a formal way to do this by making sure that the choices you make align with your goals and the probabilities you assign to different outcomes.
    • For example, if you believe it will rain (high probability of getting wet without an umbrella) and you want to stay dry, it is logically consistent to take an umbrella because this action has a higher expected utility (you stay dry) than not taking an umbrella (high risk of getting wet).

  2. Expected Utility Helps Ensure the Best Outcome:

    • By calculating the expected utility, you are making a choice that maximizes your satisfaction based on what you believe will happen. This means you’re not just hoping for the best; you are strategically planning for the most beneficial outcome based on logic and evidence.
    • It aligns your decision-making process with your goals, so you consistently make choices that lead to the best possible results given the uncertainty.

  3. Avoiding Inconsistent Decisions:

    • Without a framework like Expected Utility Theory, you might make decisions that contradict each other or your beliefs. For example, if you sometimes take an umbrella when you believe it will rain and sometimes don’t without any logical reason, your decisions are inconsistent.
    • Logical consistency helps prevent errors or irrational decisions by providing a clear rationale for every action, ensuring that your choices align with your beliefs and the actual probabilities of outcomes.

Why This Connection Matters:

  • Decision Quality: Logical consistency and expected utility theory help ensure that your decisions are rational, structured, and grounded in evidence, leading to better outcomes over time.
  • Predictability and Planning: When decisions are consistent and based on calculated expectations, you can better predict outcomes and plan effectively.
  • Reducing Cognitive Biases: Using a structured approach like Expected Utility Theory minimizes the influence of cognitive biases (like overconfidence or loss aversion) that might lead to poor decision-making.

Summary:

By understanding the logical consistency between your beliefs, actions, and desired outcomes, and applying Expected Utility Theory, you can make rational, well-founded decisions that maximize your chances of achieving the best possible outcomes.

Coming Back To The Discussions on Politics

The concepts of logical consistency, expected utility theory, and outcome analysis are highly important in the field of politics because they help political actors—such as policymakers, politicians, strategists, and voters—make more rational and effective decisions in an environment that is often filled with uncertainty, complexity, and conflicting interests. Here’s why these concepts matter in politics:

1. Logical Consistency in Political Decision-Making:

  • Building Credibility and Trust: Politicians and policymakers need to maintain logical consistency to build credibility and trust with their constituents, allies, and stakeholders. When their decisions align with their stated beliefs, values, and policies, they are seen as reliable and principled. Inconsistent actions (e.g., saying one thing and doing another) can damage trust and reduce political capital.
  • Strategic Clarity: Logical consistency helps political actors maintain a clear strategic direction. For example, if a government’s stated goal is to reduce carbon emissions, logically consistent policies would involve supporting renewable energy and taxing carbon-heavy industries. Inconsistent actions, such as simultaneously subsidizing fossil fuels, would undermine the strategy.

2. Expected Utility Theory in Political Strategy:

  • Choosing the Best Course of Action: Politics often involves making decisions under uncertainty (like whether to support a controversial policy, form a coalition, or enter negotiations). Expected Utility Theory helps political actors assess the potential outcomes of different choices and select the one that offers the greatest expected benefit.
    • For example, a politician deciding whether to support a risky but popular policy might calculate the expected utility by considering the probability of success, the benefits of success (increased support, reelection chances), and the costs of failure (public backlash, loss of credibility).
  • Balancing Risks and Rewards: Expected Utility Theory allows politicians to weigh risks and rewards systematically. This can help them make decisions that align with their objectives, like maximizing voter support or achieving policy goals, while minimizing potential downsides.

3. Outcomes Analysis in Political Contexts:

  • Evaluating Policies and Campaigns: Understanding the potential outcomes of different actions helps political actors evaluate which policies to promote or which campaign strategies to adopt. For instance, they might analyze past election outcomes to see which strategies worked and adjust their approach accordingly.
  • Adapting to Uncertainty: In politics, many factors are unpredictable (like voter behavior, economic changes, or international events). By using frameworks like expected utility, politicians can prepare for multiple possible outcomes and make flexible decisions that adapt to changing circumstances.

4. Reducing Cognitive Biases and Improving Rationality:

  • Counteracting Biases in Decision-Making: Political decisions are often subject to cognitive biases like overconfidence, confirmation bias, or fear of loss. Expected Utility Theory helps counter these biases by forcing decision-makers to base their choices on a structured analysis of probabilities and outcomes, rather than gut feelings or partisan loyalties.
  • Improving Negotiation Outcomes: In negotiations (whether between political parties, countries, or interest groups), understanding logical consistency and expected utility helps negotiators identify their own and others’ best alternatives and make offers that are most likely to be accepted. It enhances their ability to secure better outcomes by anticipating responses and planning strategically.

5. Framing Political Debates and Public Opinion:

  • Crafting Persuasive Arguments: Politicians and campaigners can use these concepts to frame their arguments in ways that appear more logically consistent and rational to the public. For instance, by presenting a policy choice in terms of expected benefits and probabilities, they can persuade voters of its merits.
  • Engaging with Rational Voters: As some voters base their decisions on rational analysis (weighing risks, benefits, and policy impacts), politicians who understand expected utility can craft messages that appeal to these voters’ desire for logical consistency and sound decision-making.

6. Designing Effective Institutions and Policies:

  • Policy Design and Evaluation: Governments use concepts like expected utility to design policies that maximize social welfare or achieve specific objectives (like reducing crime or increasing economic growth). Policymakers might use these principles to evaluate the effectiveness of different policy options, considering the expected benefits and costs to various groups in society.
  • Institutional Decision-Making: In democratic systems, institutions (such as parliaments, courts, and bureaucracies) need to make decisions that are fair, transparent, and aligned with public interest. Understanding logical consistency and expected utility helps ensure that these institutions are designed to function rationally and effectively.

Conclusion:

Understanding logical consistency, expected utility theory, and outcomes analysis is vital in politics because it equips political actors to make rational, strategic, and effective decisions. These concepts help in aligning actions with goals, maximizing benefits while minimizing risks, counteracting biases, and framing arguments in ways that are compelling to the public and other stakeholders. In a field where the stakes are high and uncertainty is pervasive, such tools are essential for achieving desired political objectives.

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