LESSWRONGLW

Even changing "do" to "did", my counter example holds.

Event A: At 1pm I get a cookie and I'm happy. At 10pm, I reflect on my day and am happy for the cookie I ate.

Event (not) A: At 1pm I do not get a cookie. I am not sad, because I did not expect a cookie. At 10pm, I reflect on my day and I'm happy for having eaten so healthy the entire day.

In either case, I end up happy. Not getting a cookie doesn't make me unhappy. Happiness is not a zero sum game.

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Destroying the Utility Monster—An Alternative Formation of Utility

I am a rational egoist, but that is only because there is no existing political system/social construct I identify with. If there was one I identified with, I would be strongly utilitarian. In all moral thought experiments, I err on the side of utilitarianism, and I’m faithful in my devotion to its tenets. There are some criticisms against utilitarianism, and one of the most common—and most powerful—is the utility monster which allegedly proves “utilitarianism is not egalitarian’’. [1]

For those who may not understand the terms, I shall define them below:

Utilitarianism is an ethical theory that states that the best action is the one that maximizes utility. "Utility" is defined in various ways, usually in terms of the well-being of sentient entities. Jeremy Bentham, the founder of utilitarianism, described utility as the sum of all pleasure that results from an action, minus the suffering of anyone involved in the action. Utilitarianism is a version of consequentialism, which states that the consequences of any action are the only standard of right and wrong. Unlike other forms of consequentialism, such as egoism, utilitarianism considers all interests equally.

[2]

The utility monster is a thought experiment in the study of ethics created by philosopher Robert Nozick in 1974 as a criticism of utilitarianism
A hypothetical being, which Nozick calls the utility monster, receives much more utility from each unit of a resource they consume than anyone else does. For instance, eating a cookie might bring only one unit of pleasure to an ordinary person but could bring 100 units of pleasure to a utility monster. If the utility monster can get so much pleasure from each unit of resources, it follows from utilitarianism that the distribution of resources should acknowledge this. If the utility monster existed, it would justify the mistreatment and perhaps annihilation of everyone else, according to the mandates of utilitarianism, because, for the utility monster, the pleasure they receive outweighs the suffering they may cause.[1] Nozick writes:
“Utilitarian theory is embarrassed by the possibility of utility monsters who get enormously greater sums of utility from any sacrifice of others than these others lose ... the theory seems to require that we all be sacrificed in the monster's maw, in order to increase total utility.”

This thought experiment attempts to show that utilitarianism is not actually egalitarian, even though it appears to be at first glance.

[1]
I first found out about the utility monster a few months ago, and pondered on it for a while, before filing it away. Today, I formalised a system for reasoning about utility that would not only defeat the utility monster, but make utilitarianism more egalitarian. I shall state my system, and then explain each of the points in more detail below.

Dragon’s System:

1. All individuals have the same utility system.
2. $U: -1 <= U <= 1$.
3. The sum of the utility of an event and its negation is $0$.
4. Specifically, the sum total of all positive utilities an individual can derive (for unique events without double counting) is $1$.
5. Specifically, the sum total of all negative utilities an individual can derive (for unique events without double counting) is $-1$.
6. At any given time, the sum total of an individual's potential utility space is $0$.
7. To increase the utility of an event, you have to decrease the utility of its negation.
8. To decrease the utility of an event you have to increase the utility of its negation.
9. An event and its negation cannot have the same utility unless both are $0$.
10. If two events are independent then the utility of both events occurring is the sum of their individual utilities.

Explanation:

1. The same system for appropriating utility is applied to all individuals. This is for the purposes of consistency and to be more egalitarian.
2. The Utility an individual can get from an event is between $-1$ and $1$. To derive the Utility an individual gains from any event $E_i$, let the utility of $E_i$ under more traditional systems be $W_i$. $U_i = \frac{W_i}{\sum_{k = 1}^n} \forall E_i: W_i > 0$. In English:

Express the positive utility of each individual as a fraction of their total positive utility across all possible events (without double counting any utility).

3. For every event that can occur, there’s a corresponding event that represents that event not occurring called its negation; every event has a negation. If an individual gains positive utility from an event happening, then they must gain equivalent negative utility from the event not happening. The utility they derive from an event and its negation must sum to $0$. Such is only logical. The positive utility you gain from an event happening, is proportional to the negative utility g

4. This follows from the method of deriving “2” explained above.

5. This follows from the method of deriving “2” explained above.

6. This follows from “2” and “3”.

7. This follows from “3”.

8. This follows from “3”.

9. This follows from “3”.

10. This is via intuition. Two events $A$ and $B$ are independent if the utility of $A$ does not depend on the occurrence of $B$ nor does $B$ in any way affect the utility of $A$ and vice versa. If such is true, then to calculate the utility of $A$ and $B$, we need only sum the individual utilities of $A$ and $B$.

It can be seen that my system can be reduced to postulates “1”, “2”, “3”, “6” and “10”. The ten point system is for the sake of clarity which always supersedes brevity and eloquence.

If any desire the concise version:

11. All individuals have the same utility system.

12. $U: -1 <= U <= 1$.

13. The sum of the utility of an event and its negation is $0$.

14. At any given time, the sum total of an individual's potential utility space is $0$.

15. If two events are independent then the utility of both events occurring is the sum of their individual utilities.

Glossary

Individual: This refers to any sapient entity; generally, this is restricted to humans, but if another conscious life-form (being aware of their own awareness, and capable of conceiving “dubito, ergo cogito, ergo sum—res cogitans”) decided to adopt this system, then it applies to them as well.
Event: Any well-defined outcome from which an individual can derive utility—positive or negative.
Negation: The negation of an event refers to the event not occurring. If event $A$ is the event that I die, then $\neg A$ is the event that I don’t die (i.e. live). If $B$ is the event that I win the lottery, then $\neg B$ is the event that I don’t win the lottery.
Utility Space: The set containing all events from which an individual can possibly derive utility from. This set is finite.
Utility Preferences: The mapping of each event in an individual’s utility space to the fractional utility they derive from the event, and the implicit ordering of events according to it.

Assumptions:

Each individual’s utility preferences are unique. No two individuals have the same utility space with the same values for all events therein.

We deal only with the utility space of an individual at a given point in time. For example, an immortal who values their continued existence does not value their existence for eternity with ~1.0 utility, but their existence for the next time period, and as such the immortal and mortal may derive same utility from their continued existence. Once an individual receives units of a resource, their utility space is re-evaluated in light of that. After each event, the utility space is re-evaluated.
The capacity to derive utility (CDU) of any individual is finite. No one is allowed to have infinite CDU. (It may be possible that an individual’s capacity to derive utility is vastly greater than several other individuals (utility monster) but the utility is normalised to deal specifically with such existences). No one has the right to have a greater capacity to derive utility than other individuals. We normalise the utility of every individuals, such that the maximum utility any individual can derive is 1. This makes the system egalitarian as every individual is given equal maximum (and minimum) utility regardless of their CDU.

The Utility space of an individual is finite. There are only so many events that you can possibly derive utility from. The death of an individual you do not know about is not an event you can derive utility from (assuming you don’t also find out about their death). Individuals can only be affected (positively or negatively) by a finite number of events.

Some Inferences:

A change in an individual’s CDU does not produce a change in normalised utility, unless there’s also a change in their utility preferences.
A change in an individual’s utility preferences is necessary and sufficient to produce a change in their normalised utility.

Conclusion

Any Utility system that conforms to these 5 axioms destroys the utility monster. I think the main problems of traditional utility systems, was unbounded utility, and as such they were indeed not egalitarian. My system destroys the concept of unbounded utility by considering the utility of an event to an individual as the fraction of their total utility from their utility space. This means no individual can have their total (positive or negative) utility space sum to more than any other. The sum total of the utility space for all individuals is equal. I believe this makes a utility system in which every individual is equally represented and is truly egalitarian.
This is a concept still in its infancy, so do critique, comment and make suggestions. I will listen to all feedback and use it to develop the system. This only intends to provide a different paradigm for reasoning about utility, especially in the context of egalitarianism. I did not attempt to formalise a mathematical system for calculating utility, and did not accept to do so due to lacking the mathematical acumen to do. I would especially welcome suggestions for calculating utility of dependent events, and other scenarios. This is not a system of utilitarianism and does not pretend to be such; this is only a paradigm for reasoning about utility. This system can however be applied to existing utilitarian systems.