Talk:Mere addition paradox

"He does not have a solution"??? Before I read the last two paragraphs, I thought "gee, that's easy to explain, hardly worth being called a paradox." It's a typical apples-and-oranges thing. By saying A+ is no worse than A, he just considers the total amount of happiness (because the average person's happiness in the population is in fact reduced). And if you just want to maximize the total amount of happiness, then of course B is better than A (and so is Z). Nothing paradoxical about it. But if you want to maximize the average happiness, then A+ is already worse than A. --Wik 23:33, Sep 6, 2003 (UTC)

But this is where the mere addition comes in. The mere addition of people to group A, to get A Plus, can't be bad, since the people in the 1st group are still just as happy - the addition of a second group can't possibly make things worse, surely? This is a reason for rejecting the principle of average happiness, if nothing else... Evercat 23:37, 6 Sep 2003 (UTC)

It may not make things worse for the first group, but why just consider them? Considered as a whole, A+ is definitely worse than A. The average happiness of the population decreases. If that doesn't matter, and you want to maximize the total sum of happiness instead, then Z is indeed best. Whether you prefer one goal or the other (or some weighted combination of the two) is a subjective matter, but in this "paradox" the goals are incoherently mixed. First it is assumed that an increase in total happiness (despite a decrease in the average) is preferable, and in the end the opposite is suggested. --Wik 23:55, Sep 6, 2003 (UTC)

Well, if you're happy believing that a huge population of only slightly happy people is better than a small population of really happy people, be my guest. :-)

Or, if you're happy believing that a world with a very happy group and a moderately happy group is worse than a world with only the very happy group, be my guest.

But I (as well as most people, I'd have thought) am not happy believing either... Evercat 23:59, 6 Sep 2003 (UTC)

Well, if you're happy with your paradoxical beliefs, be my guest. But if you set coherent goals, which may of course be more complex than just one of the two extremes, you won't have a paradox. --Wik 00:10, Sep 7, 2003 (UTC)

Heh. I'm not trying to set goals - all I'm doing is accepting that:

1. The mere addition of people whose lives are worth living cannot make things worse (or "is not a bad thing")
2. Increasing average happiness (by "redistribution" of happiness) cannot make things worse (or "is not a bad thing")

I think both these claims are reasonable; but they do lead to the Repugnant Conclusion. Evercat 00:16, 7 Sep 2003 (UTC)

Well, I for one don't think it's reasonable at all. It is flat out contradictory. The first thing makes things worse for the population as a whole, and the second makes things worse for those individuals who lose in the redistribution. If you consistently apply either an individual or a global view, one of the two will be a bad thing. --Wik 00:49, Sep 7, 2003 (UTC)

To the first case - suppose there exists just one person in the world, but he is absurdly happy. Is it actually a bad thing for God to create a trillion more people, all of whom will be slightly less happy (but nevertheless extremely happy)? I really can't accept this.

To the second case - while the redistribution does make some people worse off, this is more than offset by the gain to the others. So I don't see how this can be a bad thing either.

We can of course just accept the Repugnant Conclusion. Evercat 01:03, 7 Sep 2003 (UTC)

The Repugnant Conclusion is only repugnant if you incorrectly apply addition and substraction. In math it is true that:

A-B+B=A

But that is not the case if we are talking about levels of population and -B = "X people killed", +B = "X people born". Therefore you can argue that one should maximise average happyness instead of the sum of happyness without advocating killing sad people. --Xeeron 17:13, 2 December 2005 (UTC)

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Note also that you can increase the average happiness of a group by killing all the sad people, as practiced by Monty Python's King Otto. -- The Anome 00:19, 7 Sep 2003 (UTC)

Another reason to reject the idea that average happiness is all that matters. Evercat 01:03, 7 Sep 2003 (UTC)

Why? lysdexia 07:56, 13 Oct 2004 (UTC)

This assumes that happiness is a scalar quantity, that is, that it'd make sense to say things like "Person A is twice as happy as Person B", or "People A and B summed together are as happy as people C and D". My belief is that this makes no sense.

Why not? And since when was it about good or bad instead of better or worse? Why are right and wrong not mentioned? Someone please write a section on happiness vampires and zombies, with illustrations. :) lysdexia 07:56, 13 Oct 2004 (UTC)

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This is a strange statement: "However, this position does involve the claim that it is actually bad for people of less-than-average happiness to be born, even if their lives are worth living."

It seems to me that I can reject it merely by claiming that averagely happy people's lives aren't worth living since the suffering they go through isn't worth their happiness. This sets a simple floor on the minimum level of happiness which is needed per person.

Well I think the idea that people of average happiness don't have lives worth living is the stranger claim! :-) But yes, if you believe that the threshold for a life worth living is actually very high, this might provide a way out of the problem. Evercat 22:45, 15 August 2005 (UTC)

Or put another way, there is a simple way to go around this; define happiness = x - y/p where x is a negative number (intrinsic suffering), y is a larger positive number (the available happiness) and p is the population. As soon as you a large popluation (defined as p > y/x, the (negative) x dominates the positive y.

It seems to me that it's the assumption that happiness is something which is simply divided by population which is the main stupidity of this whole theory.

But the Mere Addition Paradox is a theoretical matter. It's a thought experiment. You're meant to just accept the assumptions that happiness can be measured and can be equal for everyone in a population, to see what conclusions follow. Evercat 22:45, 15 August 2005 (UTC)

In this case, to maximise total happiness we have to minimise population. With more realistic happiness equation (there's only so much happiness a single person can gather in a lifetime, for example) then we can probably select any population size we wish.

Azikala 19:33, 3 Jan 2005 (UTC)

comments

(First, a joke: Hey, I wouldn't be terribly happy either if my existence were described as a "mere addition" to the existence of some absurdly happy individual.) I found the article to be a bit lacking in its explanation. It seems that, for the purpose of this paradox, amounts of happiness can be compared and averaged, and that they are measured in reference to some "zero". (As Lysdexia pointed out, they appear to be scalar quantities.) Is it reasonable to replace or supplement the graphs with numerical examples? Or would that give the happiness quantities additional properties that are undesirable/distracting? Actually, I only just realized that in the graphs, the x axis does not represent population size, as stated. Instead, the sizes of the rectangles along the x axis represents population size, if I understand correctly. At any rate, I find the graphs confusing. -- Wmarkham

A couple other comments: Would links to utility and social welfare function be appropriate? Also, are there any relevent papers or other references that discuss this topic? -- Wmarkham

Dear Wmarkham, I organized an ample bibliography on the repugnant conclusion in my blog. The blog is in Portuguese, but the bibliography is there, and it's all in English with links to the PDF files. Anyone is welcome. It's right here. -- Kripkenstein (talk) 03:11, 4 May 2008 (UTC)

Perhaps morality is not defined by the states, but only by the transitions: some transitions are moral and some are not, without regard to the before and after states. This does open a whole new can of worms.

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The article suggests "Some say that this paradox can be defeated by simply denying its first axiom: that adding people of less-than-average happiness into the world doesn't make the overall situation worse." and points out that that implies it would be bad for people with less than average happiness to be born.

However, it seems like there's a third alternative: adding people of less than average happiness *sometimes* makes the overall situation worse. In this view, creating A+ does not reduce the total happiness, but similar steps in further iterations of the argument might.

Well it's up to the critics to specify when and why mere addition can be bad, or when and why increasing the average happiness (at the cost of the highest level of happiness attained) is bad... Evercat 22:36, 15 August 2005 (UTC)

There's also a related answer which in some ways is equivalent: The first step involves adding some people who are moderately happy--i.e. who are less happy than A, but not too much less happy. This requires some kind of threshhold for what "moderate" is and how much less happy the people may be. Depending on how this threshhold is related to the current degree of happiness, repeating the steps may cause convergence; if so, the average happiness, while it decreases each iteration, woukd never get below a certain value. Ken Arromdee 20:12, 15 August 2005 (UTC)

Well, not really: it works as long as we agree that creating people whose lives are worth living is never bad. But Parfit considers this very argument in section 147 of his book (well worth reading, by the way, or at least the second half is). You're right that there would be a certain level that we could not go below and still say that things were as good or better than they were before, but that level is going to be fairly low. Do we really want to believe that a huge population of people who are somewhat happy, is better than a relatively small population that is very very happy? Maybe we do, I don't know. Evercat 22:36, 15 August 2005 (UTC)

There's no paradox here, just the illusion of one due to semantics and perceptions skewed by trying to quantify happiness. The biggest bias is in the wording "barely worth living." There's a lot of inference implicit in this phrase, considering that we're trying to make a somewhat objective judgement. When people consider their lives to be barely worth living, it usually implies that they have a lot of unhappiness.

Happiness can't be quantified. If we try, we come up with something like this: in scenario A, 1000 people each experience 1000 moments of happiness, resulting in a million total moments of happiness. Each further scenario increases the total moments of happiness. Z might include a billion people each experiencing one moment of happiness. If the rest of life is neutral (so that, outside the moment of happiness, the people's lives are ordinary, though not distressing; about as worth living as not), then the one moment of happiness does indeed make each of their lives worth living. This is hardly repugnant (a neutral life is not repugnant, just neutral. We just perceive it to be repugnant because we expect happiness). It is better for there to be a billion moments of happiness than a million. We've spread the happiness out; nothing wrong with that.

If this seems a bit reductive, well, that's what you get when you try to quantify happiness. It's not valid, you just end up with words filled with innuendo such as "repugnant." It only seems repugnant because my goodness, all those years of working at a job, raising kids, conflict etc. and just for a single moment of happiness! But you can't do that -- the tireless effort of work can be seen as unhappiness, which changes everything. The only way to address the 'paradox' is to avoid all of these things and try to quantify happiness as I've done above, and then the paradox disappears.24.64.223.203 23:32, 27 October 2005 (UTC)

A solution, I think

I think the solution to the paradox is that the transition from A to A+ is practically impossible. Since the world has limited resources, we cannot just add moderately happy people without making the old group less happy. With more effective farming and such, there is room for more people, and that is just what happened through history. If the earth was infinitely big, then I would suggest increasing the population.

I know this is a thought example. But in unrealistic though example, we cannot use out ethical intuition. It seems like a "Repugnant Conclusion", but that's because out sense of ethics is made for real situation. --Apoc2400 10:37, 22 March 2006 (UTC)

mistaken resolution section

The resolution section requires significant amendment.

There is a fairly substantial literature on the mere addition paradox and the related repugnant conclusion (there is a recent book devoted entirely to writings on the repugnant conclusion). The resolutions presented in this article are not represented in the literature on this topic (they appear to be original to Wikipedia) because they are misguided. The resolutions offered appeal to extrinsic characteristics of overpopulation - it tends to make things worse for people by stretching resources thin, spreading disease, causing empathetic sorrow, and so forth. Parfit is aware of the negative effects of overpopulation. His examples intentionally appeal to populations that are isolated from one another (R&P 419-20: "A+ contains another group, whom I call the extra people. These people have lives that are worth living, and they affect no one else . . . assume, for simplicity, that the two groups in A+ are not aware of each other's existence, and could not communicate."). This is because Parfit is interested in the question of mere addition - extrinsic factors aside, is the universe better with more people in it? It is no answer to this question to say that population growth in a given setting would be detrimental. Such population growth would not be a mere addition.

Perhaps the author of this entry does not intend to resolve the paradox but rather to challenge its relevance. If that is the case, he or she should say so. Let me suggest, though, at least one reason why the more theoretical question is relevant: If there is intrinsic value in adding more people whose lives are worth living, then we should be willing to bear the extrinsic costs of a certain degree of overpopulation in exchange for the added value of more people. Alternatively, if there is no intrinsic value, or if producing more people with lives worth living can be intrinsically bad, we should be much more concerned with the costs of overpopulation. Alecbings 16:56, 21 April 2006 (UTC)

For this reason, I amended the intro to make explicit that the two groups are totally separate, and I deleted the following, which seems to presuppose some interaction between the two groups:

The latter can be resolved by stating that for this person it is not bad be born at all, but bad to be born at the given time, simultaneously with many other persons in the same situation. If more and more people live at the same time at a given place, life gets miserable for all.

The paradox is also weak in one of its assumptions: Adding people of much less-than-average happiness into the world makes life more miserable for the formerly happy people (group A) as well, because they are confronted with poverty and diseases in people they know, possibly friends or even loved ones -- One might be inclined to help only the friends, but this will make them dependent on you and this dependency usually destroys a friendship after a while and reduces it to a mere façade.

The knowledge and sight of outrageous injustice is quite incompatible with true happiness for most people on both sides, see also the results about the "Tit for Tat" strategy on iterated prisoner's dilemma. One might argue that the groups could be isolated from each other and the rich ones could just ignore the others. But this means that society falls apart and that life is based on ignorance and lies. Knowing and facing the truth about reality constitutes an important part of happiness, particularly but not exclusively for scientists and artists.

In addition, the formerly happy people may contract diseases from the miserable ones. They might also live in fear of a revolution, so they need weapons, again isolation and protection against them, making life miserable for themselves, too.

Human history is a source of many examples of the points mentioned above.

The reasoning is similar to the discussion about the reintroduction of torture: On a very hypothetical basis and remote of the real experiences history taught us, abstract subtleties are discussed in order to question established principles of civilization.

-Dan 03:00, 23 May 2006 (UTC)

I think you're right that many of the resolutions offered presuppose tidbits that aren't directly related to the thought experiment. Best I can tell there is no way out of it as it is set up. I think the interesting thing about it is that in trying to work it out individually a number of different ethical considerations must be made & that seems to be what people were up to in the above comments.

However, I thought I should add something to these considerations based on lessons learned from the social sciences. According to much research of late, the appropriate conclusion to draw is that one population is not better/worse than any other b/c happiness is far more subjective & individuals actually assess their happiness based on those around them. If there are deviants it messes with everyone but in each of the three populations this is not the case - in population A+ the two different levels of happiness are completely separate & distinct populations. Thus, there is no 'gold standard' for happiness; rather, the key is equality. 66.57.13.12 14:00, 14 July 2006 (UTC)

Barely Worth Living - a clarification and resolution?

The Repugnant Conclusion includes the loaded phrase 'barely worth living'. What does this mean?

Suppose we add a dotted horizontal line to the original diagram, at a height somewhere lower than that of the shortest column, and label this 'Worth Living'. Then columns whose height's are above this line consist of people whose lives are worth living.

This is assumed, but not explicitly, stated by the original 'paradox'.

Now presumably The Repugnant Conclusion describes a situation represented by a column as wide as possible, whose height is just over this dotted line. So everyone in this population has a life that is worth living. Therefore we accept the so-called Repugnant conclusion, and the paradox is gone. —The preceding unsigned comment was added by Deglog (talk • contribs) 14:30, 3 December 2006 (UTC).

Other opinions

There is John Rawl's A Theory of Justice, where he considers a minimax way of choosing the world where it has the best worst case scenario.

In addition, Average vs. Total Utility should be discussed. --70.111.218.254 14:55, 3 December 2006 (UTC)

Yes, the key is the average utility vs total utility. The mere addition phrase for some reason made me think of families. World A could be some rich bachelor. World A+ could the rich bachelor getting married and this relationship with its pros and cons nets out to zero but brings great happiness to his wife (like the Pretty Woman movie or something). World B is them having children and becoming slightly less happy but bringing much happiness and existence to the children. The repugnant conclusion becomes a "large family". Not a perfect match of course. 64.42.233.61 17:10, 4 December 2006 (UTC)

Why must B be higher than A+

I'm struggling to follow the logical argument given in this article. It looks to me like some crucial part is missing. When population B is introduced it is said to have the same population as A+ but a higher average happiness. The article doesn't state why it must be higher. If it is not higher the Repugnant Conclusion does not follow. Can someone who has read more around this subject please elaborate the article on this point, since at the moment it makes no sense. Thanks. Pseudospin 14:31, 3 April 2007 (UTC)

It has also been observed that nowhere in Parfit's many works on this subject does he explain why doubling the size of the population is guaranteed to always produce a population where each person has a level of happiness at least half that of the original population... [1]

• Erm, well, basically, it is so by hypothesis, to see where such an assumption leads. Parfit also gives the "divided B" example. I think I shall add this to the article at some point. But I am also curious as to who has made this observation, and what precisely they did actually say, as it seems to me that Parfit has thoroughly discussed various possibilities. --74.100.225.24 01:52, 16 July 2007 (UTC)

Well, I couldn't find anything. It seems to me that all assumptions should be justified in the first section, and then criticised in the second. Having unwritten assumptions smells of dishonesty, particularly when there is no obvious justification for it and removing it kills the paradox.

As it stands the paradox simply observes that there is a sequence of possible population/average happiness pairs where each successive one is better than the previous (on a total happiness basis). Without a justified constraint for the average happiness for a given population (or the change in the average happiness for a given change in the population) the conclusion that the infinite limit of this sequence is "the best" is erroneous. At each stage I could just as easily have plucked a different population B out of thin air and come to a completely different conclusion.

Anyway, you caught me sticking my OR in. Feel free to revert my edit if you wish. I'm just disappointed that, given the size of the literature on this, no-one else seems to have noticed this obvious point. Pseudospin 03:05, 16 July 2007 (UTC)

I deleted this proposed solution from the main page of the article because it also seems to be a Wikipedia original that is not found anywhere in the published literature. It's great that people are brain storming on solutions in the discussion section, but the main page is not the place for this. If you think you've solved the paradox, think to yourself, is this an idea so original that it would likely get me tenure in a philosophy department? If not, you are *probably* missing something. There does, however, seem to be enough confusion regarding what Parfit is trying to show that it may be worth adding a sentence or two at the start about what the paradox is and isn't about - i.e. it *is not* making any empirical claims or assumptions about population growth, it *is* highlighting an apparent contradiction in common moral intuitions about different population scenarios. —Preceding unsigned comment added by Alecbings (talk • contribs) 17:36, 18 September 2007 (UTC)

I stand by my comment above. I understand that this is not supposed to be "about making any empirical claims or assumptions about population growth". My point is that it is making such assumptions.

In the article a sequence of population/average happiness pairs is identified and compared based on their total happiness, but why choose this linear sequence? There is a whole 2d plane of possible pairs! He can only be choosing this sequence based on some assumptions or constraints about happiness and population growth.

For instance I could construct a sequence which was just like the one in the article (I.e. where the happiness level in B is somewhere between the two levels in A+, and in C is somewhere between the two levels in B+, etc.) which didn't culminate in an extremely large population with lives barely worth living, but in an extremely large population with any finite level of happiness you desired.

You could attempt to discredit this based on the idea that it seems wrong to have an infinite population with finite happiness, but you would have to appeal to the notion a finite level of resources or some such assumption about population growth.

This idea of Parfit's is the first inkling towards a proper mathematical model of population ethics. He demonstrates (by comparing A and A+) that maximising average happiness is not the criteria we use to decide the relative merits of two populations. He then attempts to demonstrate that we do not try to maximise total happiness either. He fails at this, as I just explained, but I believe he is correct - we don't exclusively try to maximize total happiness either. There is a simple modification, though, which would result in a population ethics which fits much more closely to what we actually see in the real world.

Simply put, we try to maximize total happiness in our communities but we have a certain minimum threshold of happiness that we are willing to abide. We welcome outsiders and newcomers even though it reduces our individual happiness, but only up to a certain point. This means in the sequence A->B->C->... there is a point, S say, where we would stop. We are a mixture of charitibility and (S)elfishness. —Preceding unsigned comment added by Pseudospin (talk • contribs) 09:26, 14 October 2007 (UTC)

Not repugnant, but absurd

You can't take an absurdity, arrive at an absurdity and claim to have proven anything. If you accept the initial scenario of a population of individuals of IDENTICAL happiness then whatever absurdity results is your own fault.

A population of individuals of the exact same instantaneous happiness, is just as absurd as a population of particles with the exact same quantum states.

If happiness is taken to be the ONLY important characteristic of life, and the origin of all moral value, then a persons specific level of happiness defines them completely.

At best this merely shows that in the most extreme of situations (populations of infinite number, of infinitessimal happiness, or when comparing happiness levels of virtually identical quantities) normal rules of addition no longer can be relied on as valid APPROXIMATIONS. It doesn't show a defect in utilitarianism applied to real moral problems, any more than the discovery that the universe doesn't follow euclydean geometry has deterred people from successfully treating parallel lines as never meeting for real problems. Moral philosophies do not need to concern themselves with morally absurd hypotheticals.

This appeal to repugnancy also fails on another basis. It assumes that you dont already find population A to be repugnant, but it is. If I was identical to everyone else, no matter how large or small the population was, I would find my life barely worth living anyway (and so would they, since they are the same as me).. so consequently the only difference between A and Z is the population count itself, any difference in happiness is an illusion in the mind of the external observer. All these populations are repugnant. TheDarknessVisible 20:11, 28 May 2007 (UTC)

Not really. The total uniformity of each group is not essential to the argument. "...[assume] there is neither social nor natural inequality; no one is worse off than anyone else. This would never in fact be true. But it cannot distort our reasoning, on the questions I shall ask, if we imagine that it would be true..." (page 385 in my edition) --74.100.225.24 01:37, 16 July 2007 (UTC)

Misunderstanding happiness

The paradox is fun at first glance. The reason it is not a paradox lies in a misconception of Human happiness. Happiness is not an absolute and the human mind does not have an agreed upon scale nor do humans have the ability to measure happiness outside of their own. By way of example consider the case of a person living with a physical or mental deviation from the norm. Nearly every normally configured person would with extreme certitude claim that the un-norm has sub-norm happiness but this conclusion is entirely unfounded. There is extensive data demonstrating that a human can be extremely happy (or sad) within the scales they individually establish based on their own experiences and there can be no substitute nor projection of valuation of happiness beyond the individual's. The point here being that it is virtually impossible to assign relative levels of happiness across individuals as there is no way to agree upon an absolute scale (how do you compare a deaf individuals appreciation of a kaleidoscope to a blind individual's appreciation of techno-trance music? Can it not be the case that a sighted person enjoys music and other non-vision senses less such that the blind person en total breaks even for happiness? Ram A M 22:07, 11 October 2007 (UTC)

Interpersonal comparisons of happiness are certainly tricky, but the paradox requires only that some people can be happier than others - not that we be able to tell who is happier and by how much. —Preceding unsigned comment added by 209.6.110.68 (talk) 16:49, 11 November 2007 (UTC)

Isn't happiness a tricky word to use when discussing these issues? I'm prone to think of welfare or well-being, conditions that are obviously dependent on external factors, contrary to many conceptions of happiness, such as the Buddhist one. (One could say running water and electricity aren't conditions of happiness, but I don't see how one could say they aren't conditions for some level of well-being.) -- Kripkenstein (talk) 03:20, 4 May 2008 (UTC)

Problems with the average happiness of A

Why the non-existence (zero happiness) of the missing population of A doesn't count in the average happiness ? (A country of 1 man is no way better than a country of 1 000 000) Frigo (talk) 17:54, 12 December 2007 (UTC)

Because they don't exist. If you are going to count non-existent people, how many of them are there? How would you know when to stop counting? Richard001 (talk) 06:59, 31 March 2008 (UTC)

Yeah, this paradox is full of unclarified variables :) Comparing the average happiness of two population with different sizes is a little like comparing apples and oranges. By doing so, we assume that the (non-)existence of the surplus population has no effect on the happiness of the other part of the population. Considering the possible attitude of a population of 1 against a newcomer of 1, and the attitude of 1 000 000 000 000 against a newcomer of 1, it's not hard to see they aren't necessarily indifferent to him. Similarly in the case of a loss of 1. I believe that if we take into account the non-linear relation between happiness and the (inverse of the) population size, this problem is solvable. Frigo (talk) 22:42, 27 April 2008 (UTC)

What if the newcomers are, say, on a different planet, so that the old-times aren't even aware of them? Would you still agree that it's better for the newcomers not to be born? That's what A+ versus A is trying to get across. --192.75.48.150 (talk) 20:01, 13 May 2008 (UTC)

Relationship between this article and average and total utilitarianism

Does anyone have any ideas how the above article should be differentiated from this one? We obviously don't want to have too much repetition. I suppose that one could provide a quick summary of this one, but they seem to be basically the same subject. This is just an article about the dilemma of the utilitarian when it comes to average or total. What else is there to talk about besides the dilemma? Richard001 (talk) 07:03, 31 March 2008 (UTC)

This paradox seems to be more general, and applies to anyone who thinks that situations such as A, A+ and B can be meaningfully compared. As a side note, that other article implies that it is not a problem for average utilitarians, when clearly it is: they are forced to conclude that A+ is worse than A, when it is a mere addition and so cannot be. --192.75.48.150 (talk) 19:51, 13 May 2008 (UTC)

It's not a Paradox. It's a simple mistake in understanding arithmetic.

I'm writing this to show you how absurdly silly this graph coupled with the explanation is. Intelligent people have thought this is a paradox which blows my mind, because these intelligent people have missed some very simple things.

First you have a graph of QUANTITY. If you can't quantify happiness, DON'T MAKE A GRAPH! A graph ONLY SHOWS QUANTITY. A graph of something unquantifiable is not a graph, it's just a picture of bars. There's no meaning because there's no number, a.k.a. quantity behind it.

If you look at the quantity as actual numbers, you see how absurd this idea is. IT'S NOT A PARADOX.

HERE IS EXACTLY WHAT IS STATED IN THE GRAPH

Now in numerical format

A = 5 (average = 5)

A+ = 5 + 3 (average = 4)

B = average of 4.5 (5 + 5 + 4 + 4)

FIRST POINT) A+ is not less than A

(No... 8 is not less than 5. Bravo! First principle is a success) (We go on to point out that A = 5. And A+ is 5 and a little more. By mere addition we see that A+ is not less than A! Brilliant!)

SECOND POINT) The average of B (4.5) is MORE than the average of A+ (4).

(Yes, believe it or not, 4.5 is more than 4)

THIRD POINT) The average of B (4.5) is LESS than the average of A (5).

(Oh my God!!! What the hell is going on here!?!)

What IS going on here:

As most people beyond 5th grade math have probably realized by now looking at numbers instead of pictures, you are talking about a SUM in the first point and AVERAGES in point 2 and 3! It's not a question of these points being valid or not. They're all true, but THEY'RE NOT EVEN THE SAME EQUATION!

The 1st point DOESN'T TALK ABOUT A BLOODY AVERAGE. Everything else does. It's not a paradox people, it's 2 forms of elementary... ELEMENTARY mind you... 2 forms of elementary math. —Preceding unsigned comment added by Patrick Snyder (talk • contribs) 13:38, 13 May 2008 (UTC)

Well, that's sort of the idea. You can interpret it as averages, and then you're forced to deny point 1, and explain why A+ is actually a worse scenario than A, even though it is obviously a Mere Addition. You can interpret it as sums, and then you're forced into the Repugnant Conclusion. Almost all attempts to compare the three situations have some sort of problem. --192.75.48.150 (talk) 19:57, 13 May 2008 (UTC)

No you CANNOT COMPARE the three situations as you suggest. Just as you cannot compare kilometers and hours. They are TWO FORMS OF MEASUREMENT that CANNOT BE COMPARED. SUMS and AVERAGES are also 2 forms of measurement that cannot be compared. You don't have to deny point 1 or any point for that matter. They're ALL valid. But they're completely different things.

An example of trying to compare 2 completely different things: A violin is smaller than a piano, but a top-of-the-line violin is more expensive than a top-of-the-line piano. THIS IS NOT A PARADOX! The fact that a violin is smaller than a piano has no relation to how much someone will pay for it, just as a SUM has no relation to an AVERAGE.

An example of how we confuse ourselves: I like the number 100 better than 10. I also like the number 10 better than 1, but I like 1 better than 100. THIS IS A PARADOX ONLY IN A CONFUSED HUMAN MIND and NOT IN OBJECTIVE REALITY. This is me putting my own subjective value on random numbers when thinking about them individually, and if a sane person truly has these opinions then they have not thought about all 3 of their own opinions together. Humans do this all the time. It's not a paradox in reality, IT'S HUMAN CONFUSION. —Preceding comment added by Patrick Snyder (talk • contribs) 14 May 2008 —Preceding comment was added at 14:17, 14 May 2008 (UTC)

But what if I have good reasons for wanting to choose 100 over 10, good reasons for wanting to choose 10 over 1, and good reasons for wanting to choose 1 over 100? Yes, obviously my reasons are different in each case. That doesn't tell me which reason trumps which, does it. Yes, it's "just" human confusion. You may prefer to call it a "dilemma" rather than "paradox" then. However, this is a prefectly normal and acceptable use of the word "paradox", it is almost always called the "Mere Addition Paradox" in published sources, and in any case, relabeling it a "dilemma" doesn't really help with an answer, does it? Cheers, --EmbraceParadox (talk) 15:47, 14 May 2008 (UTC)

Dear taxpayer,

In order to combat the increasing energy crisis, your government has decided to give 1 and only 1 large cash reward to the group that can come up with the best combustable fuel. A fuel that burns hotter than another fuel is better. Also a fuel that burns for longer than another fuel is better. These criteria will be used to find the best fuel.

Do you see any flaw in this logic? Would you like your tax money to go to this contest? Or would you rather your money go to educating our youth on things like: what a valid comparison is, or what the difference between an opinion and a fact is? —Preceding unsigned comment added by Patrick Snyder (talk • contribs) 15:34, 15 May 2008 (UTC)

We can rephrase that as "the winner is the fuel that burns with the greatest heat for the longest time". Now consider that utilitarianism can be described by the phrase "the greatest good for the greatest number". The difference is that your fuel contest is something you just made up as something "obviously silly", whereas utilitarianism is something taken very seriously by lots of people, so the Mere Addition Paradox is soemthing they need to deal with. (But, as I say, the Mere Addition Paradox is a problem for other theories of ethics as well, not just utilitarianism). --EmbraceParadox (talk) 16:00, 15 May 2008 (UTC)

Points Rebutted:

• The rephrase, "the winner is the fuel that burns with the greatest heat for the longest time" still does not actually tell how the contest would be won. Are you taking the highest average heat, or are you taking the longest amount of time burning over a predetermined temperature. If a Utilitarian doesn't know which way they swing: highest average happiness, highest sum of happiness, or highest sum of happiness as long as everybody is over a certain threshold of happiness, then they are actually confused about their own opinion. You can not logically have more than one of these.
• Just because something is taken seriously by lots of people DOES NOT MEAN it's not silly. Just because many people believe something to be true, does not make it true. ...unless you buy into the whole, "There is no universe outside a connected human consciousness" hypothesis.
• Just because something is not "obviously silly" DOES NOT MEAN it's not silly. Just because something is not "obviously flawed" DOES NOT MEAN it's not flawed.
• I like the new pictures on the article. Adding a 4th graph and explanation adds extra obfuscation and makes it harder to realize the comparison is flawed. If you cannot now see how this is logically not even a comparison (because SUM & AVERAGE are 2 different things, both cannot be "the best" outcome), it is your psychology stopping you and not your intelligence. Open your mind to the possibility, and then let logic fill the rest in. —Preceding unsigned comment added by Patrick Snyder (talk • contribs) 13:01, 16 May 2008 (UTC)

"Highest average happiness, highest sum of happiness, or highest sum of happiness as long as everybody is over a certain threshold of happiness... You can not logically have more than one of these." And that's PART OF THE POINT of the paradox. If you apply more than one of these standards, you get a contradiction. I take it we are in agreement, because these are your own words.

Of course, if that were the whole point, it wouldn't be all that interesting. Is that what you're trying to say? If so, then you've missed the REST OF THE POINT: you cannot apply ANY of these standards!

(Well, I mean, you CAN, and you will be logically consistent. But of course, it's not enough to be logically consistent. In your fuel example, you can't just decide that the best fuel is the one which tastes nicest - sure, it's consistent, but when you announce the winner of your contest, you will have some major explaining to do. I wouldn't like my tax dollars to go to that either.)

If you consistently apply the "average" standard, your winner is A. You get to explain why it would be best if the extra people of A+, who are happy and don't affect anyone, had never lived. If you consistently apply the "total" standard, your winner is Z. You get to explain why it would be best for there to be lots and lots of miserable people. If you consistently apply the "total + threshold" standard (i.e. the "bad level" in the last section of the article), your winner is somewhere in between (say E). You get to explain what's really so terrible about the threshold that it would be better if the extra people of E+, who are at that threshold and don't affect anyone, had never lived. And then you get to explain why it would be best for there to be lots of people just slightly above this terrible threshold.

Cheers, --EmbraceParadox (talk) 16:57, 16 May 2008 (UTC)

2 Questions:

• What do you mean, "it's not enough to be logically consistent"? Do you mean, that if you ARE logically consistent then it can't be ethical because logical consistency will put humanity on the "bad level"?
• What's the reasoning behind the threshold having to be a "bad level"? Why: "such a threshold would be so low as to apply only to lives that are "gravely deficient" and which, "though worth living ... must be crimped and mean.""? Why can't the threshold be high, like: all humans have their basic needs met as well as various forms of leisure available and freedom to create or do anything that does not impose profoundly upon other people's freedoms? Why does the threshold have to be E and not A for example? —Preceding unsigned comment added by Patrick Snyder (talk • contribs) 14:44, 18 May 2008 (UTC)

No, I don't mean ALL logically consistent solutions are unacceptable, just that some are, including most utilitarian solutions. One solution that might be defensible is to set the threshold quite high, as you suggest. Now, not many people in the real world are above the threshold, and personally I can't buy it. But yes, it does provide and a way out, and some people do take that view. For instance a couple of days ago I added to the article a short mention of Torbjörn Tännsjö, who suggests something like that.

Cheers, --EmbraceParadox (talk) 17:59, 18 May 2008 (UTC)