HL5Eq&Future PDF

Equality of Well-Being, Future People Erasmus School for Philosophy Erasmus Institute for Philosophy and Economics (EIPE) Last Time + This Time Social Welfare Functions....... The Utilitarian SWF.......... This lecture: I + II........... Structure of this lecture........ Equality of well-being and P...

Equality of Well-Being, Future People Erasmus School for Philosophy Erasmus Institute for Philosophy and Economics (EIPE) Last Time + This Time Social Welfare Functions....... The Utilitarian SWF.......... This lecture: I + II........... Structure of this lecture........ Equality of well-being and P5.... 1. Egalitarianism............. Simple Egalitarian SWF illustrated. Equality: Well-being vs Resources. Egalitarianism and Levelling Down. Levelling Down: definition...... Levelling down and Strong Pareto. Levelling Down further illustrated. Equality Respecting SWFs...... Levelling down, equality respecting 2. Prioritarianism............ Simple Prioritarian SWF illustrated Concavity & Priority.......... Prioritarian SWFs............ 3. Difference principle......... MaxMin SWF illustrated....... Levelling down, equality............................. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Summary + Reflection Part I Four SWFs and their properties................................................. Caring about Equality....................................................... Caring about Well-Being..................................................... 24 25 26 27....................................................................................................................................................................................................................................... 1.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................... II. Future People Who’s in a society?......... Variable vs Fixed Populations.. Problem for Fixed Population.. Problem for Variable Population Revised Fixed Population..... Problem 1 for Revised F-Pop.. Problem 2 for Revised F-Pop.................................................................................................................................................................................................................................................................................................................................................. 28 29 30 31 32 33 34 35 Summary + Reflection Part II 36 Problems for future people.................................................... 37 Literature 38 Further Reading part I....................................................... 39 Further Reading part II...................................................... 40 2 Last Time + This Time 2 / 40 Social Welfare Functions A social welfare function (SWF) for (N, A) is a function which, when given any profile for (N, A) as input, outputs a weak ordering of the alternatives. The output of a SWF ranks alternatives / outcomes from best to worst. Lecture 3: SWFs that take profiles of well-being orderings as input. This lecture: we study SWFs that take utility profiles as input. P= Ann: Bob: P B B P T T U = uA uB P 10 4 B 7 7 T 6 2 Lecture 4: We discussed utility functions & utility profiles and how they can represent well-being (ordinal / cardinal / comparable). This lecture: we assume that the well-being that is represented by all our utility profiles is cardinal and comparable (i.e. we assume that P4 is true). 3 / 40 The Utilitarian SWF The Utilitarian SWF is determined by Sum-ranking Welfarism which, as you may recall from Lecture 1, is equivalent to P2, P3, P4 and P5 together: Utilitarian SWF (Sum-Ranking Welfarism) x is better than y iff the sum-total of well-being in x is greater than in y. In terms of utility profiles: x ≻ y iff ∑i ui (x) > ∑i ui (y) uA uB P 10 4 B 7 7 T 6 2 Utilitarianism: P is just as good as B. Utilitarianism does not care about “equality of well-being”. Some say: this shows that utilitarianism is wrong! Intuition: a society in which everyone is moderately well-off is better than a society in which an elite are very well-off and the masses are badly off. 4 / 40 3 This lecture: I + II P5. Transitional Equity If outcome x is obtained from outcome y by: increasing the well-being value of person i by amount k, and by decreasing the well-being value of person j with k, then x and y are equally good. P5 readily implies that the Utilitarian SWF does not “care about equality” I. We will examine three alternatives to P5 and the Utlitarian SWF which somehow do care about equality of well-being. We do so by considering 2 person utility profiles only, but everything generalizes to profiles with more people. A SWF takes well-being information for each individual in a society as its input, and it outputs a ranking of the alternatives from best to worst. II. We will ask: who should count as a member of society, for this purpose? Only currently existing or future people as well? 5 / 40 Structure of this lecture I. Equality of well-being Summary + reflection Part I II. Future people Summary + reflection Part II 6 / 40 4 Equality of well-being and P5 P5. Transitional Equity If x is obtained from y by: increasing the well-being value of person i by k, and by decreasing the well-being value of person j with k, then x and y are equally good. We discuss three alternatives to P5 according to which transferring k “units of well-being value” from Ann to Bob may yield a better outcome: 1. Egalitarianism 2. Prioritarianism 3. The Difference Principle We formulate SWFs which capture the spirit of these three ideas. Each of them cares, in some sense, about “equality of well-being”. We will explain the different senses in which they do. 7 / 40 1. Egalitarianism Egalitarianism. If x is obtained from y by: increasing the well-being value of person i by k, and by decreasing the well-being value of person j with k, then x is better than y when the distribution of wellbeing in x is more equal than in y. Egalitarianism does not define a specific SWF. But we can illustrate the main idea of Egalitarianism via: Simple Egalitarian SWF x ≻ y iff uA + uB − 2⋅ ∣ uA − uB ∣ is greater for x than for y. ∣uA − uB ∣ describes (in)equality (how close Bob’s well-being is to Ann’s). −2 ⋅ ∣uA − uB ∣ describes inequality’s contribution to overall goodness. Indeed, it’s a (deliberately) simple Egalitarian SWF. 8 / 40 5 Simple Egalitarian SWF illustrated Simple Egalitarian SWF x ≻ y iff uA + uB − 2⋅ ∣ uA − uB ∣ is greater for x than for y. uA uB x 5 5 y 1 9 x y uA + uB 10 10 uA + uB − 2⋅ ∣ uA − uB ∣ 10 −6 Utilitarianism: x is just as good as y as 10 = 10 Simple Egalitarianism: x is better than y as 10 > −6 9 / 40 Equality: Well-being vs Resources Making everyone’s well-being equal does not entail giving everyone the same resources. For example, people with impaired mobility will need (expensive) mobility aids to get the same level of well-being as abled bodied people (who can walk unaided). Although utilitarians do not care about “equality of well-being”, they may very well argue that e.g. wealth has to be distributed equally as doing so maximizes the sum-total of well-being. At any rate, keep in mind that SWFs talk about how best to distribute well-being, rather than how best to distribute resources. 10 / 40 6 Egalitarianism and Levelling Down uA uB L 10 15 M 10 16 R 9.9 15 Simple Egalitarianism says: L(eft) is better than M (middle), as 15 > 14 R(right) is better than M (iddle), as 14.7 > 14 So according to Simple Egalitarianism, if we’re in situation M : We can make the situation better (realize L) by making Bob worse off! We can make the situation better (realize R) by making everyone worse off! Thus, we can improve situation M by “levelling down”. 11 / 40 Levelling Down: definition Levelling Down A SWF allows for levelling down iff there are situations x and y such that: x is obtained from y by making one or more persons worse off than in y, while the SWF says that x is better than y. Many philosophers think: a SWF that allows for levelling down is incorrect. So Simple Egalitarianism is incorrect. The Utilitarian SWF does not allow for levelling down: Say that we make Ann worse off, i.e. say that we decrease uA , then we make the situation worse, as uA + uB will then decrease. 12 / 40 7 Levelling down and Strong Pareto Strong Pareto If everyone is at least as well-off in y as in x and at least someone is better off in y than in x, then y is better than x. If an SWF allows for levelling down, then there are situations x, y where (i) x is obtained from y by “levelling down” e.g. uA uB x 5 6 y 5 7 , while (ii) the SWF says that x is better than y About situations that respect (i), Strong Pareto says: y is better than x. So, if an SWF allows for levelling down then it violates Strong Pareto. Ad (i): note that Weak Pareto (P3) does not imply that y is better than x. 13 / 40 Levelling Down further illustrated Consider a situation in which well-being is very unequally distributed: a small fraction (the elite) has much more well-being than others (the masses). Imagine that there is some policy that would take away some of the well-being of the elite. Does this policy increase the well-being of at least one person (from the masses for example)? If yes, then this policy is not subject to the levelling down objection. One might still think the policy is bad: perhaps the policy involves a small benefit to the masses, but imposes a huge cost on the elite, and this trade-off is bad. But this is not the levelling down objection. If no, then this policy is subject to the levelling down objection. And so this policy faces the levelling down objection, as does any SWF that says this policy is makes things better. 14 / 40 8 Equality Respecting SWFs Simple Egalitarianism is equality respecting: Equality Respecting SWFs Consider all possible distributions of a given amount of well-being value. An SWF is equality respecting if it says that the best distribution is the one in which well-being is equally distributed. Three distributions of 10 ∶ uA uB x 5 5 y 6 4 z 9 1 (5, 5) is the distribution of 10 which maximizes uA + uB + 2⋅ ∣ uA − uB ∣ This illustrates that Simple Egalitarianism is equality respecting. 15 / 40 Levelling down, equality respecting Egalitarian SWFs A SWF is egalitarian if and only if the function that it uses to evaluate alternatives is of the form f (uA ) + f (uB )+EQ(uA , uB ) where f is some increasing function and where EQ specifies how equality of well-being contributes to the evaluation. Simple Egalitarianism faces the levelling down objection. The levelling down objection threatens all Egalitarian SWFs Whether or not such an SWF faces the objection depends on its details. Simple Egalitarianism (as any Egalitarian SWF) is equality respecting. Let us now look at another alternative to Transitional Equity (P5). This alternative, Prioritarianism, gives rise to SWFs that are equality respecting but that do not face the levelling down objection. 16 / 40 9 2. Prioritarianism Prioritarianism. If x is obtained from y by: increasing the well-being value of person i by amount k, and by decreasing the well-being value of person j with k, then x is better than y when i was worse-off than j in y. Prioritarianism is not specific enough to define a SWF. But we can illustrate the main idea of Prioritarianism via: Simple Prioritarian SWF x ≻ y iff √ √ uA + uB is greater for x than for y. 17 / 40 Simple Prioritarian SWF illustrated U x y uA 0 1 uB 10 9 √ √ x: 0 + 10 = 3.16 √ √ y: 1 + 9 = 4 V a b c uA 4 5 4 uB 6 6 7 √ √ b: 5 + 6 = 4.69 √ √ c: 4 + 7 = 4.65 The two utility profiles illustrate that according to (Simple) Prioritarianism: Transferring well-being from a better-off to a worse-off person is better overall: y is better than x When an additional unit of well-being becomes available (in a), it is better overall to benefit a worse-off person: b is better than c. In a nutshell, Prioritarianism gives priority to the worse-off. This feature is due to the fact that the square root function is concave. 18 / 40 10 Concavity & Priority Concavity of √ u: each additional unit of u leads to an ever-smaller increase in √ u 3 √ u 2 1 0 0 2 4 u 6 8 10 Say that we’re in a situation where uA = 0 and uB = 10. Transferring 1 unit of well-being from Bob to Ann yields an increase in overall goodness. An additional unit of well-being does more good when given to Ann than when given to Bob. This can be observed by simply looking at the shape of the graph of the square root or from the graph of any strictly increasing, concave function. 19 / 40 Prioritarian SWFs Prioritarian SWFs A SWF is prioritarian if and only if the function that it uses to evaluate alternatives is of the form f (uA ) + f (uB ) where f is some strictly increasing concave function. Prioritarian SWFs do not allow for levelling-down. That’s because f (uA ) + f (uB ) is strictly increasing in both uA and uB : making someone worse-off (e.g. decreasing uA ) decreases f (uA ) + f (uB ) and so can never make the situation better. Prioritarian SWFs are equality respecting. That’s because any unequal distribution of well-being can be improved upon by transferring well-being from a better-off to a worse-off person. Prioritarian SWFs are attractive to many philosophers. That’s because they do not allow for levelling down and are equality respecting. 20 / 40 11 3. Difference principle Difference principle. If x is obtained from y by: increasing the well-being value of person i by k, and by decreasing the well-being value of person j with k, then x is better than y if and only if the worst-off person in x is better off than the worst-off person in y The difference principle gives rise to a unique SW F : MaxMin SWF x is better than y if and only if the worst-off person in x is better off than the worst-off person in y. 21 / 40 MaxMin SWF illustrated The worst-off person’s well-being is given by min(uA , uB ), so according to the MaxMin SWF: x is better than y if and only if min(uA , uB ) is greater in x than in y. The best overall situation is the one for which min(uA , uB ) is maximized. Example: b is best, a and c equally good according to MaxMin. uA uB a 10 15 b 11 12 c 10 18 The above example also shows that MaxMin violates Strong Pareto: In c, everyone is as least as well-off in as in a and at least someone is better off in c than in a. Strong Pareto then says that c is better than a. MaxMin says that c and a are equally good, so MaxMin violates Strong Pareto. 22 / 40 12 Levelling down, equality So MaxMin violates Strong Pareto. However: The MaxMin SWF does not allow for levelling-down. That’s because making someone worse-off (e.g. decreasing uA ) can never make the situation better, i.e. increase min(uA , uB ) The MaxMin SWF is equality respecting. That’s because any unequal distribution of well-being can be improved upon by transferring well-being from person who is not worst-off to a person that is worst off. MaxMin embodies a rather extreme emphasis on the well-being of the worst-off person: it’s worth making a million people considerably worse-off, just to make the worst-off person ever-so-slightly better off. 23 / 40 Summary + Reflection Part I 24 / 40 Four SWFs and their properties We have discussed 4 SWFs and their evaluation functions: Utilitarianism (Ut): uA + uB Simple Egalitarianism (SE): uA + uB − 2⋅ ∣ uA − uB ∣ √ √ Simple Prioritarianism (SP): uA + uB MaxMin: min(uA , uB ) We’ve seen that they have the following properties: Avoid levelling down? Satisfy Strong Pareto? Equality respecting? Ut yes yes no SE no no yes SP yes yes yes MaxMin yes no yes 25 / 40 13 Caring about Equality So SE, SP and MaxMin are all equality respecting. Simple Egalitarianism (SE): uA + uB − 2⋅ ∣ uA − uB ∣ √ √ Simple Prioritarianism (SP): uA + uB MaxMin: min(uA , uB ) But they “care about equality” in different ways: Only Egalitarian SWFs such as SE care about equality itself. According to Egalitarians, equality of well-being is “intrinsically good”. This is revealed by the EQ(uA , uB ) term in their SWF. SP and MaxMin are equality respecting in virtue of something else: Priority for the worse-off (SP) The fate of the worst-off person (MaxMin) 26 / 40 14 Caring about Well-Being Ut, SE, SP and MaxMin all satisfy: P2. Welfarism Only well-being determines how good an outcome is. Indeed, these SWFs are, ultimately, functions of uA and uB only, i.e. of representations of Ann’s and Bob’s well-being. (Remember: another name for the Utilitarian SWF is “Sum-Ranking Welfarism”) Next week: How should policy-makers ought to take fairness into account? We’ll explain that fairness is determined by claims (/= well-being). We’ll discuss: does this mean that Welfarism (P2) needs to go? If so, bye bye to the Utilitarian Principle (UP), which presupposes P2. But before next week, there’s the present: 27 / 40 15 II. Future People 28 / 40 Who’s in a society? Utilitarian Principle (UP) You should perform an action which, of all actions that are available to you, results in the greatest sum-total of individual well-being. So UP requires that you maximize individual well-being. But of which individuals? That is, who are the members of the“ societies” (N, A) that we studied? That question will receive further attention in Lecture 7. In this lecture, we assume that the Alternatives of our society are different policies and that its iN dividuals are “people affected by the policy”. This still raises the question whether we mean: All people currently alive. All people currently alive or who will/would be alive in the future. 29 / 40 Variable vs Fixed Populations Fixed Population (interpretation of) Utilitarianism The members of society means all the people who are currently alive. Variable Population (interpretation of) Utilitarianism The members of society means all the people who are currently alive or who will/would be alive in the future Different alternatives (i.e. policies) can result in different people being alive, so the members of society vary from alternative to alternative. Hence the name “variable” population utilitarianism We could also discuss other SWFs in terms of the fixed / variable population distinction. But we will only do so for the Utilitarian one. 30 / 40 16 Problem for Fixed Population Energy policy in 1990s to mitigate climate change Policy A (Business as usual), will lead to: Flooding + drought + heat-waves starting in 21st century. Policy B (Cap Annual Carbon Emissions), will lead to: Flooding + drought + heat-waves starting in 22nd century. Policy C (Sustainable Energy), will lead to: Impact of climate change averted. Fixed Population Utilitarianism says: only the well-being of people alive in 1990s matters (for policymaking in 1990s). So nothing that happens in 22nd century matters. But then policy C is no better than B. But intuitively that’s false, some would say. So Fixed Population Utilitarianism is incorrect, one might argue. 31 / 40 Problem for Variable Population Bringing People into Existence Policy A: Produce 1 trillion children in the next generation with lives that are barely worth living. (Each child’s well-being value is very low, say 1) Policy B: Produce 3 billion children in the next generation with lives that are going really well. (High well-being values, say 100 each) Variable Population Utilitarianism says: Goodness of A: 1 trillion x 1 = 1 trillion, of B: 3 billion x 100 =.3 trillion. So A is better than B. (“Repugnant Conclusion”) Many people, on the contrary, have the intuition that B is better than A. “You can’t compensate for the fact that the people in A have low well-being by brining trillions of new people in to existence. Quantity doesn’t trump quality” So Variable Population Utilitarianism is false, they’d argue. 32 / 40 17 Revised Fixed Population One might hope that there is a ”half way” position between these two interpretations of utilitarianism. This half-way position takes account of some future people e.g. the billions of people in the 22nd century who will suffer the effects of climate change. But it does not take account of all future people. For example, it doesn’t take account of the trillions of future people that we might bring into existence as the result of a “breeding” programme. Revised Fixed Population (interpretation of) Utilitarianism The members of society means all the people who are currently alive, plus those future people who will come into existence no matter what policy we choose. This sketchy interpretation (maybe!) gives the intuitively correct result in the last two cases. However,... 33 / 40 Problem 1 for Revised F-Pop Embryo Selection Policy A: Allow parents to use embryo selection during IVF. Results in A: Alex has a healthy baby. Policy B: Ban embryo selection. Results in B: Alex has an unhealthy baby. Arguably, the baby in A is not the same person as the baby B. That’s because baby A originates from a different embryo than baby B. So, baby A is brought into existence by our policy choices. Same for B. Revised F-Pop Utilitarianism then says: neither baby A nor B’s well-being should be taken into account for evaluating the goodness of these policies. Intuitively that feels incorrect to many people. Revised F-Pop Utilitarianism is false, they (e.g. Derek Parfit) argue. 34 / 40 18 Problem 2 for Revised F-Pop Ann: uA Bob: uB Chu: uC x 30 40 − y − 30 40 z 40 − 30 where “-” denotes non-existence. Comparing x with y according to Revised F-Pop Utilitarianism: Bob’s the only one whose existence doesn’t depend on the choice between x and y. So only Bob’s well-being should be taken into account for the x-y comparison. (i) And so: x is better than y as 40 > 30 (ii) Similarly, y is better than z as 40 > 30 (ii) Similarly, z is better than x as 40 > 30 So according to Revised F-Pop Utilitarianism, x is better than y, y is better than z and z is better than x, so that the betterness relation is intransitive which is, arguably, absurd! Thus Revised F-Pop Utilitarianism is false, you might argue. 35 / 40 19 Summary + Reflection Part II 36 / 40 Problems for future people We’ve interpreted the Utilitarian SWF in three ways. The society it talks about can either be: (i) all currently existing people, or (ii) all present people and future people or (iii) all people whose existence is not brought about by the policies in question. It looks like there are prima facie compelling arguments against all three interpretations of the Utilitarian SWF. It’s not clear how to respond to this! Hopefully, future people will lead the way. 37 / 40 20 Literature 38 / 40 Further Reading part I Equality and Prioritarianism (introduction): Michael Weber. Prioritarianism. Philosophy Compass 9 :756-768 (2014). Deeper explorations: Richard J. Arneson. Prioritarianism. Cambridge University Press (2022). Matthew D. Adler and Ole F. Norheim (eds.) Prioritarianism in Practice. Cambridge University Press (2022). 39 / 40 Further Reading part II Fixed vs variable population (introduction): Hilary Greaves, Population axiology, Philosophy Compass 12 (2017) Deeper explorations: John Broome, The Welfare Economics of Population, Oxford Economic Papers, 48 (1996), pp. 177-193 Michael Huemer In Defence of Repugnance, Mind 117,(2008) Yew-Kwang Ng, What should we do about future generations?, Economics and Philosophy 5 (1989), pp. 235 - 253 Derek Parfit, Can We Avoid the Repugnant Conclusion? Theoria 82 (2016): 110–27. 40 / 40 21