by After a comment on this post, it was found that the idea expressed has a deep flaw. Because of this, I no longer recommend reading it.
In this post we construct a variant of utilitarianism by modifying the expected utility formula. We aim for this variant to differ from total, hedonistic utilitarianism in a few ways.
Intended differences. This variant aims to beat the repugnant conclusion and choose the same as a prioritarian (not the utilitarian) in a "tie-breaker" situation. How can these differences come about?
Motivation. It might be that we do not just want pleasure to beat out pain; we might also want our well-being to be distant from pain for its own sake. We try to formulate this idea mathematically.
Formulation. Define the utility of an action as before,
Before getting to the definition of the variant, but we first define a concept. Begin by calling the red curve f(w).
The scale of this depends on how one defines utilon quantities. Let w = 0 be where pleasure balances pain with no excess. Also, for example, a positive w implies a positive well-being of an individual. Last, at any time, each person has exactly one w.
Let's use this curve to arrive at the variant definition. First imagine an action that causes a person's well-being to shift from w_0 to w_1, and this shift could be in any horizontal direction. Now define D as f(w_0) - f(w_1). If w_0 < w_1, then D > 0. Now, all of these definitions culminate in what makes the utilitarianism variant:
V_v(O) := V(O) + ΣD_i,
where D_i is the D for the ith individual considered. (Maybe it should be an average of D and not the sum; we will explore this only if it seems worthwhile.) Thus the expected utility variant U_v(A) only differs in that the value function is defined differently.
Examples.
In this post we construct a variant of utilitarianism by modifying the expected utility formula. We aim for this variant to differ from total, hedonistic utilitarianism in a few ways.
Intended differences. This variant aims to beat the repugnant conclusion and choose the same as a prioritarian (not the utilitarian) in a "tie-breaker" situation. How can these differences come about?
Motivation. It might be that we do not just want pleasure to beat out pain; we might also want our well-being to be distant from pain for its own sake. We try to formulate this idea mathematically.
Formulation. Define the utility of an action as before,
Before getting to the definition of the variant, but we first define a concept. Begin by calling the red curve f(w).
The scale of this depends on how one defines utilon quantities. Let w = 0 be where pleasure balances pain with no excess. Also, for example, a positive w implies a positive well-being of an individual. Last, at any time, each person has exactly one w.
Let's use this curve to arrive at the variant definition. First imagine an action that causes a person's well-being to shift from w_0 to w_1, and this shift could be in any horizontal direction. Now define D as f(w_0) - f(w_1). If w_0 < w_1, then D > 0. Now, all of these definitions culminate in what makes the utilitarianism variant:
V_v(O) := V(O) + ΣD_i,
where D_i is the D for the ith individual considered. (Maybe it should be an average of D and not the sum; we will explore this only if it seems worthwhile.) Thus the expected utility variant U_v(A) only differs in that the value function is defined differently.
Examples.
- With this new definition at hand, let's explore the prioritarianism/utilitarianism tie-breaker example.
The increase in well-being from the $10,000 is equal for Jim and Pam (w_{1, Pam} - w_{0, Pam} = w_{1, Jim} - w_{0, Jim}). However,
U_v($10,000 to Pam) = V($10,000 to Pam) + D_Pam > U_v($10,000 to Jim)
only because D_Pam > D_Jim. Then the variant's expected utility is greater for Pam, and the $10,000 should then go to Pam. This agrees with the prioritarian decision. How does this variant perform in other situations? - Next, consider a world demanded by the repugnant conclusion. Now consider an action applied to this repugnant world that would generate a smaller population with the same total utility as the current world. With the variant, we would not be indifferent between the two possible worlds because ΣD is positive, so
U_v(keeping repugnant world) < U_v(repugnant world -> smaller population where the nonvariant utility of the two worlds are equal).
For any repugnant world, any action that keeps the total pleasure over pain the same but increases the well-being of people by reducing the population is preferable to inaction. This safeguards us against the repugnant conclusion. - What's more is that this variant implies utility monsters must derive much more satisfaction from the efforts of enslaved groups than before. Fortunately, we don't think utility monsters are a problem with normal utilitarianism anyway.
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