You never really beat the odds

or, The ineffect of "many worlds" on the felicific calculus

There may appear to be a quite significant effect on the felicific calculus from Hugh Everett's "many worlds" interpretation of quantum theory. That is, it may appear that many worlds requires a massive "discount rate" to account for the branching of the universe. For example, some twitch of pleasure experienced in a universe at a certain time may be, say, a million times more valuable than an otherwise identical twitch occuring in a single universe a short while later. Why? Because, in between, the universe may have branched substantially, so the later twitch occurs in much lower density - this density being analogous to extent in a typical felicific calculation (see Q22 of the Everett FAQ on the conservation of energy and the "thickness" of "slices").

However this problem does not emerge in practice for, though we can grant the claim made above (that a given amount is more valuable in one universe than in another universe shortly afterward), in any given situation in which we might be choosing between the two the decision will not affect just a single later universe. An illustration: imagine I can do something, just once, to cause pleasure of fixed intensity and duration to a given person. I could do it immediately, or I could wait a short while before doing it. In the normal course of things, we would assume that there is no significant difference between the options. But one line of (fallacious) thinking goes like this: since the density of one universe now might be a million times higher than the density of a universe then, it is a million times better for me to do it now than later.

The mistake made is that it forgets that the cause behind the massive reduction in density is the massive increase in the number of worlds which are all (that we need consider) descendents of "this" world. Therefore, of the worlds which branch from the world in which I have just decided to delay the pleasure, the vast majority contain a version of me who is intent on, and therefore shall, produce this pleasure at the appointed time. So while a single world is less dense, we are talking about enough worlds to almost make up the difference. There shall be some losses: in some branches I shall have a heart attack, a stroke, or have a sudden loss of good will or I shall spontaneously combust or whatever, preventing me from fulfilling the plan. However, these branches will represent only a small fraction of the density of the wave-function, and - we are obliged to admit - if I had performed my decision according to an accurate felicific calculus I would have accounted for the probability of having something coming up to interfere with the plan anyway. So while there is some non-zero density of worlds which are worse-off than the corresponding worlds in the instant-pleasure branch, these represent such a small fraction of the branch that they are not noticeable to the level of accuracy to which we would perform the calculus - just as we would normally regard the chance of having a heart attack in the next few seconds as negligeable. Yes, if we were being really accurate in our calculations, we would account for these "heart attack" worlds - but we should be accounting for the "heart attack" risk anyway.

The only real difference in the "many worlds", as compared to a "single world" calculation, is in the viewing of probability, and even this not in any way that affects the result. Another illustration: I have the option of doing some act, or not doing the act. I think that there is a 40% chance of the act leading to a (unit) good effect (as compared to inaction), and a 60% chance of it leading to a (unit) bad effect. Now suppose I say "Sod it, I'm feeling lucky!" and decide to do the action. As a single world believer, if I find out that the good effect and and not the bad effect has happened, I will be busy congratulating myself on how I have "beaten the odds". "I took a risk", I might think, "but it paid off". However, from the "many worlds" perspective, I have caused both good and bad effects, in various worlds. But in what proportion? If it was accurate, then exactly that proportion I was thinking of as being my chance of success! So in 60% of the worlds I have done the wrong thing, and in 40% the right. And this is the sole implication of "many worlds" interpretation - you never really beat the odds. But this makes absolutely no difference at all for, in the above situation where the loses and gains were of equal size but the loss more likely, the felicific calculus would never have prescribed doing the action anyway. It only prescribes those actions where the product of effect and likelihood yield the highest "expected" utility, which - under "many worlds" - is exactly the same as the utility in all sub-branches. Under "many worlds" interpretation, what is likely to be right and what is right are always the same thing - and given that we were to always (when uncertain as to what was really right) aiming to do what was likely right anyway, this matters not at all.