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If one is a consequentialist, one at least implicitly makes decisions based on how good or bad the consequences are. As such, you must implicitly have a function f that maps from the set of attainable potential futures into a totally ordered set (let's say real numbers) so you can pick the best one(s) and avoid the worst.

Coming up with such a function is fraught with difficulty, however.

  • Functions that depend on instantaneous state recommend nonsensical courses of action like binging on chocolate because you're enjoying it while you're eating it.
  • Functions that consider all time with equal weight don't converge to a finite value when taken arbitrarily far into the future, allowing arbitrarily bad conditions now as long as they are expected to lead to the tiniest long-term improvement (plus these are impossible to evaluate due to uncertainty)
  • Functions that decrease exponentially have nice self-similarity properties (you maintain your relative quantitative judgments of actions whether they occur now or in the future), but you end up with highly counterintuitive results that any tiny thing that improves value now is worth committing everyone to torture and/or destroying the universe as long as it happens far enough in the future
  • It's much easier to define functions on individuals than to know how to combine results from individuals, but even if you know how to combine results it's made even trickier because individuals don't even stay stable over time (new ones are born, old ones die, etc.) and the existence/non-existence of individuals may depend on your actions.

What strategies are there to deal robustly with these problems? Alternatively, if the solutions are too elaborate to be done justice in an answer, where can I find a good resource that discusses these issues and/or proposes solutions?

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Consider your first scenario. You question if an instantaneous state can lead to good outcomes. The answer a Consequentialist will tell you is no. There are no good outcomes where time for reasoning is not allowed.

Consider your second and third scenario (which are inverse propositions). A consequentialist will tell you it depends. The length of time do not affect the amount of possible outcomes, because the possible inputs are infinite at any point of time. Thus, at any point of time, use the greatest possible information that are relevant to the consideration in mind.

Keep in mind the difference between 2 things. There is the point of time in which you choose as your 'function'. And there is the amount of inputs, which ranges. However, at any one point of time, you are given only one set of inputs and a specific evaluative criteria, taken from the point of view of an actor.

If in that shorter period of time leads to worser outcomes than the longer period of time, both using the same set of criteria to evaluate the value of outcomes, then a Consequentialst will not go ahead with that action. Again, it depends on what criteria you use to evaluate the outcomes. Some consequentialists will say it is greater happiness, some will say it is greater security. Your outcome will depend on this evaluative criteria. If the consequences in the longer period of time justifies and overrides the negative consequences in the shorter period of time, then the consequentialist will go ahead with it.

Consider your fourth scenario. You consider groups. You cannot simply add the inputs together because the evaluative criteria (the equation) changes. How would a consequentialist deal with this? Ignore the individual actors totally and consider the group. Determine the evaluative criteria and inputs possible for this group that you choose, and draw the function. You will get the answer.

The questions you raise are not new to Consequentialism as a moral theory. There are mainly two types: 'Act' and 'Rule'. Act consequentialism says that the rightness of the act depends on what the individual knows at that point of time, and choose optimally upon. Rule consequentialism says that it is the group's, or more complete information, that should determine the rightness of acts. This is the subjectivist vs. objectivist concern.

  • There are other concerns, namely:
    • How much information should be included?
    • Do the evaluative process matter?
    • What would be considered complete information for decision making?
    • What should the evaluative criteria be?

In order to answer the question and find a satisfactory solution, it is not possible to consider only disparate problematic scenarios. You have to get down to comparing and ask linearly for instance, why a group's impression of a scenario should triumph over the individual's. Or why the greatest happiness principle should take precedence over other principles. It will lead you to other moral questions, and you have to argue for why they are so, positively, not why they should not be, negatively.

  • Relevant Books (taken from Oxford Companion to Philosophy):
    • John Stuart Mill, Utilitarianism
    • Brad Hooker, Ideal Code, Real World
    • Derek Parfit, Reason and Persons (Part 2)
    • Samuel Scheffler, Consequentialism and its critics

Update: Regarding the first scenario, there is a school of thought, 'Intuitionists', who will say that instantaneous states do not lead to worser outcomes because one can consider past experiences as helpful to making decisions.

  • These are interesting comments (+1), but you have mostly just restated my questions. In most every case, I presented both a basic-level question and a more advanced question that arises from the most straightforward attempt to solve the basic question. For instance, you say that the consequentialist should take the longest possible temporal view; but I already raised the problem of longer outlooks being inherently less certain...so how are you to balance those? Also, with group vs. single, you say it's a different function, but you don't provide much guidance on how one could do it. – Rex Kerr Dec 20 '13 at 23:39
  • Yes that is true, I haven't answered your question because there is no one or even a satisfactory group of answers. It is not mathematics where the impression of a function will give you an answer. You cannot answer the question without familiarizing yourself with the other moral theories (Deontology, Virtue and Feminist ethics), and problems such as Epistemological theories. I cannot state them all here, there is no space - it also requires work on your part. – Aloysius Dec 21 '13 at 3:07
  • Also, how do your weigh values such as Greatest Happiness, Liberty or Good? If you use a function which denotes a mathematical input, how would you assign a value say 10, or 20 or 50 as an input, to a particular value? Not only will a consequentialist run into improbable outcomes, the questions of what are the correct inputs for evaluation are there as well. But these are abstract generalities. If you want an answer read all the books. Separate the theoretical and practical realm tentatively so that a less than complete answer can allow you to move forward later on. – Aloysius Dec 21 '13 at 3:16
  • The question is specifically about how to get a function with the correct mathematical properties--and for consequentialism to be workable, you do need to have the right properties even if you don't normally spend much time thinking about them as such. So saying "it is not mathematics" is basically just saying that you're not answering the central part of the question. Fair enough--maybe no-one has thought about this in enough depth, or the thinking is not easily summarized. I'll have a look at the books (I've already read Mill); maybe they contain part or all of an answer. – Rex Kerr Dec 21 '13 at 17:26
  • Rex, interestingly, I don't actually disagree with you that you could actually use actual values to determine outcomes. Consider how we are doing it already know through the use of monetary value. I'm not saying that it cannot be mathematically workable or have anything against it. I'm just saying you got to be careful when you use an idea such as a function to determine its outcome. This is because drawing it up in itself is fraught with problems and you really have to restrict yourself only certain cases and scenarios, which a more linguistic approach can clarify. – Aloysius Dec 22 '13 at 20:18

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