ࡱ> 58234 bjbj 8rr"t+ ZZ...BBB8ztBgKl  t O!O!O!bJdJdJdJdJdJdJ$WM PNJ.O!O!O!O!O!JZ|X pt !KO$O$O$O!d.t .t bJO$O!bJO$O$R>hAt ^V!`?NJ7K0gK@bWP#<WP<hAhAWP.RGO!O!O$O!O!O!O!O!JJO$O!O!O!gKO!O!O!O!WPO!O!O!O!O!O!O!O!O! : Quantifying Health Part One: Introduction Ranking the health level of populations is helpful in making a variety of decisions. Health spending for some purposes (one type of disease) has to be traded off against other health-related purposes, such as prevention and treatment of other diseases. Consider, for example, whether priority should be given to the deadliest cancers or most common ones. The big loser in the cancer funding race is lung cancer. It is the biggest cancer killer in the country, yet on a per-death basis receives the least [National Cancer Institute] N.C.I. funding among major cancers. In 2006, the N.C.I. spent $1,518 for each new case of lung cancer and $1,630 for each lung cancer death, according to data from the institute and the American Cancer Society. Among the big cancers, breast cancer receives the most funding per new case, $2,596 and by far the most money relative to each death, $13,452. Notably, prostate cancer, the most common cancer, receives the least funding per new case at just $1,318. But on a per-death basis it ranks second, with $11,298 in N.C.I. funds. Heres a look at the N.C.I. cancer funding based on 2006 death rates and incidence rates for some of the most common and deadliest cancers. Cancer (Deaths)N.C.I. Funding per DeathLung (162,460)$1,630Colon (55,170)$4,566Breast (41,430)$13,452Pancreas (32,300 )$2,297Prostate (27,350)$11,298Cancer (New cases)N.C.I. Funding per New CaseProstate (234,460)$1,318Breast (214,640)$2,596Lung (174,470)$1,518Colon (106,680)$2,361Pancreas (33,730)$2,200 Next, consider how funding should be allocated between prevention and treatment. A 2010 study in the journal Health Affairs, for instance, calculated that if 90 percent of the U.S. population used proven preventive services, more than do now, it would save only 0.2 percent of healthcare spending. One big reason why preventive care does not save money, say health economists, is that some of the best-known forms don't actually improve someone's health. These low- or no-benefit measures include annual physicals for healthy adults. A 2012 analysis of 14 large studies found they do not lower the risk of serious illness or premature death. But about one-third of U.S. adults get them, said Dr. Ateev Mehrota, a primary-care physician and healthcare analyst at RAND, for a cost of about $8 billion a year. Similarly, some cancer screenings -- including for ovarian cancer and testicular cancer, and for prostate cancer via PSA tests -- produce essentially no health benefits, causing the U.S. Preventive Services Task Force to recommend against their routine use. The task force bases its recommendations on medical benefits alone, not costs. The second reason preventive care brings so few cost savings is the large number of people who need to receive a particular preventive service in order to avert a single expensive illness. "It seems counterintuitive: If you provide care to prevent all these expensive diseases, it should save money," said Peter Neumann, an expert on health policy and professor of medicine at Tufts University School of Medicine. "But prevention itself costs money, and some preventive measures can be very expensive, especially if you give them to a lot of people who won't benefit." A better gauge of the value of preventive medicine is bang for the buck; that is, not whether it reduces healthcare spending but whether it buys more health than treating the disease does. "We don't ask whether cancer treatment or heart disease treatment saves money," said Dr. Steven Woolf, professor of family medicine at Virginia Commonwealth University Medical Center in Richmond. "But it is reasonable to ask how to make our healthcare dollar go further." On that score, screening for hypertension and for some cancers (such as colorectal and breast) are good investments, he said, at less than $25,000 per year of healthy life. In contrast, such common treatments as angioplasty cost $100,000 or more per healthy year of life. Health also has to be traded off for other non-health concerns. One 2012 study found that given budget constraints, the following are the sixteen charitable programs worthy of investment in descending order of desirability.  HYPERLINK "http://www.copenhagenconsensus.com/publication/hunger-and-malnutrition" Bundled micronutrient interventions to fight hunger and improve education  HYPERLINK "http://www.copenhagenconsensus.com/publication/infectious-disease" Expanding the Subsidy for Malaria Combination Treatment  HYPERLINK "http://www.copenhagenconsensus.com/publication/infectious-disease" Expanded Childhood Immunization Coverage  HYPERLINK "http://www.copenhagenconsensus.com/publication/infectious-disease" Deworming of Schoolchildren, to improve educational and health outcomes  HYPERLINK "http://www.copenhagenconsensus.com/publication/infectious-disease" Expanding Tuberculosis Treatment  HYPERLINK "http://www.copenhagenconsensus.com/publication/hunger-and-malnutrition" R&D to Increase Yield Enhancements, to decrease hunger, fight biodiversity destruction, and lessen the effects of climate change  HYPERLINK "http://www.copenhagenconsensus.com/publication/natural-disasters" Investing in Effective Early Warning Systems to protect populations against natural disaster  HYPERLINK "http://www.copenhagenconsensus.com/publication/infectious-disease" Strengthening Surgical Capacity  HYPERLINK "http://www.copenhagenconsensus.com/publication/chronic-disease" Hepatitis B Immunization  HYPERLINK "http://www.copenhagenconsensus.com/publication/chronic-disease" Using Low Cost Drugs in the case of Acute Heart Attacks in poorer nations (these are already available in developed countries)  HYPERLINK "http://www.copenhagenconsensus.com/publication/chronic-disease" Salt Reduction Campaign to reduce chronic disease  HYPERLINK "http://www.copenhagenconsensus.com/publication/climate-change-climate-engineering" Geo Engineering R&D into the feasibility of solar radiation management  HYPERLINK "http://www.copenhagenconsensus.com/publication/education" Conditional Cash Transfers for School Attendance  HYPERLINK "http://www.copenhagenconsensus.com/publication/infectious-disease" Accelerated HIV Vaccine R&D  HYPERLINK "http://www.copenhagenconsensus.com/publication/education" Extended Field Trial of Information Campaigns on the Benefits From Schooling  HYPERLINK "http://www.copenhagenconsensus.com/publication/water-and-sanitation" Borehole and Public Hand Pump Intervention An earlier study by this ground found that three projects addressing climate change ( HYPERLINK "http://en.wikipedia.org/wiki/Optimal_carbon_tax" \o "Optimal carbon tax" optimal carbon tax, the HYPERLINK "http://en.wikipedia.org/wiki/Kyoto_Protocol" \o "Kyoto Protocol" Kyoto Protocoland HYPERLINK "http://en.wikipedia.org/wiki/Value-at-risk_carbon_tax" \o "Value-at-risk carbon tax" value-at-risk carbon tax) are the least cost-efficient of the proposals. The Copenhagen Consensus 2008 panel found that all three climate policies have "costs that were likely to exceed the benefits". It further stated "global warming must be addressed, but agreed that approaches based on too abrupt a shift toward lower emissions of carbon are needlessly expensive." Part of weighing different types of health benefits for a population against one another and against other benefits involves quantifying health. Such quantification is part of assessing a health measures costs and benefits. My theses address how health should be quantified. Thesis #1: Theoretical Thesis. Theoretical population health-levels are best quantified via totalism. The method of quantifying health has been taken from the population ethics because it is best framework by which to quantify value across a collection. Totalism about health is the notion that we add the health-level of every member of the relevant population and the sum is the health of a population. This sum allows us to compare the health of populations via ordinal and cardinal rankings. Thesis #2: Practical Thesis. Practical population health-levels are best quantified via totalism. Two assumptions underlie my approach. First, individuals can have positive, neutral, and negative health. This might be a function of the bio-statistical norm or the degree to which a person has a harmful dysfunction (Boorse 1975, 1977, 1997; Wakefield 1992, 1997). Both focus on a part, process, or system relative to a reference class. On this account, function below the norm is negative, at the norm is neutral, and above the norm is positive. Second, individual health can be quantified in real-world units that allow for precise measurement. Specifically, there is a true zero point (for example, average function) and equally sized units of measurement that correspond to the degree to which an individual exemplifies a property. There are standard economic measures of health, the most influential being quality-adjusted life-year (QALY) (Klarman 1968; Farnsel and Bush 1970; Torrance 1972). A QALY is a measure of disease burden including both the quality and the quantity of life lived. It is often used incost-benefit analysis to calculate the ratio of cost to QALYs saved for a particular procedure. This is then used to allocate HYPERLINK "http://en.wikipedia.org/wiki/Health_care" \o "Health care" healthcare resources in an efficient manner. By themselves, QALYs do not tell us how healthy a population is. This is in part because QALYs measure the marginal contribution of a health-related procedure (and an operational one at that) and this is distinct issue from what is an individuals lifetime health-level. By analogy, the cost-benefit method by which we determine the marginal value of an additional acre of land for a farmer cannot be used, at least in a straightforward manner, to determine the economic value of his farm before the addition (Sen), let alone the degree to which the farm actually makes his life go better. This is also in part because we still need to know in theory how individuals lifetime QALY-values should be combined to determine a populations health-level. Even if it could do so in economic terms (and QALYs are in life-years, not dollars), we would still want to know whether the economic terms are tracking the relevant quantity. Part Two: Thesis #1 [Theoretical population health is best quantified via totalism] Argument Here is the argument for the first thesis. (P1) In theory, totalism is better than its competitors as a theory of population health. (P2) If, in theory, totalism is better than its competitors as a theory of population health, then theoretical population health is best quantified via totalism. (C1) Hence, theoretical population health is best quantified via totalism. [(P1), (P2)] The competitor theories concern the ways in which members health-levels determine a populations health-level. Here are the competitors. TheoryAssertionTotalismThe health of a population is the sum of individuals health-levels.Critical Level TotalismThe health of a population is the sum of each individuals health-level level minus a positive critical level.AveragismThe health of a population is the average health-level per individual.Diminishing Value FunctionThe health of a population is a function that in effect has a diminishing marginal value per individuals health-level. Here are the theories in more precise form. Theory #1: Totalism. The health of a population is the sum of individuals health. Here Q is a populations health-level. It can be seen as a quantity of health. h1 is the health-level of the first individual, h2 is the health-level of the second, and so on. Q = h1 + h2 + h3 + Here is an example of how the totalist function converts a collections health-levels into a populations health-level. PersonWell-Being (utils)1100280360440Total280Average70 Theory #2: Critical Level Totalism. The health of a population is the sum of each individuals health level minus a positive critical level (Kavka 1982, Parfit 1984; Locke 1984; Blackorbyet al. 1997, 2004, 2005; Broome 2004). Here Q is the populations health-level, C is the critical level of health, and h1 is the health-level of the first individual, h2 is the health-level of the second, and so on. Q = (h1 C) + (h2 C) + (h3 C) + Not every critical-level theory is totalist, but this is how it has been developed in the literature. In the context of population ethics, this function avoids the repugnant conclusion because a very large population with a positive but very low level of well-being makes the world worse. This theory entails that lives that are worth living still make the world worse. In addition, there is an issue as to whether the critical level is arbitrary. If it is too low, then a watered down version of the repugnant conclusion is true. If it is too high, then the critical level theorist ends up having to assert that quite good lives make the world worse. Here is an example of critical-level-totalist function converts individuals health-levels into a populations health-level. PersonHealth-LevelCritical LevelHealth-Level Contribution to Population11006040280602036060044060-20Total28040Average7010 Theory #3: Averagism. The health of a population is the average health per individual. The average can be per individual, per time, or some combination of these. Here n is the number of individuals in the population. The average might a matter of health-level per individual, health-level per time, health-level per individual per time, or health-level per time per individual. These measures differ and a concern is that averagism cannot provide a principled reason to prefer one average over the others. Q1 = (h1 + h2 + h3 + ) / n Q2 = (h1 + h2 + h3 + ) / t Q3 = [(h1 + h2 + h3 + ) / n] / t Q4 = [(h1 + h2 + h3 + ) / t] / n Here Q is the populations health-level, n is the number of members of a population, t is a time, h1 is the health-level of the first individual, h2 is the health-level of the second, and so on. Here is an example of how an averagist function converts a collections health-levels into a populations health-level. PersonHealth-Level1100280360440Total280Average (well-being/individual)70 The theory avoids the repugnant conclusion because a very large population with a very low health-level has a very low average and thus is not a very healthy. There is a concern in that whether an individuals health-level makes a population more or less healthy depends on how healthy others are and were. So, for example, whether Frank Sinatras health-level makes humanity more or less healthy depends on how healthy the Egyptians were. This is odd. Unless there is a boundary on the population over which averaging occurs, the function is arbitrary in another way. This concern is shared by the other theories and thus not a distinct problem for averagism. It is also a feature of all theories that use a reference class to determine an individuals health-level. Theory #4: Diminishing Value Function. The health of a population is a function that in effect has a diminishing marginal value per individuals health (Hurka 1983, Ng 1989; Sider 1991). On one version, Ngs theory, Q is the populations health-level, f(n) is the diminishing marginal function, and A is the populations average health-level. . Q = f(n) x A n f(n) = " k i - 1 = k0 + k1 + k2 & kn-1 1 > k > 0 i=1 On a second version, Ted Sider s theory, the first function concerns individuals with positive or neutral health arranged form most to least healthy. The second concerns individuals with negative health arranged from least to most healthy. Q = f(n) n m f(n) = " hi x k i - 1 + " ui x k j - 1 + 1 > k > 0 i=1 j=1 h1, h2, h3, & are the health-levels of people of people with positive or zero health in descending order. u1, u2, u3, & are the health-levels of people with negative health (unhealthy) in ascending order. This theory is a compromise between totalism and averagism. It functions like totalism for small populations and like averagism with large populations. Here is an example of how Siders diminishing-value function converts a collections health-levels into a populations health-level. PersonWell-Being (utils)Value-Function (k = 0.5)Net Addition110011002800.5403600.25154400.1255Total280160 This avoids the repugnant conclusion because each successive person with minimal positive health adds less and less to the population health-level. The contribution of each individual depends on how his level relates to others rather than merely his own health-level. Similar to averagism, then, this theory is an externalist account. In addition, there are concerns for arbitrariness in terms of the value of the diminishing-value-function (that is, the value of k) and also the seemingly arbitrary ordering of people with positive from most to least health and people with negative health with the opposite (see Sider 1991). One might wonder whether the theories need to be adjusted for justice. For example, perhaps the contribution of an individuals health-level to the health-level of a population depend in part on what individuals deserve, whether in general or in terms of heath. Alternatively, the most unhealthy peoples health-levels might count more toward others health-levels. The problem with this is that this is relative to the rightness or goodness of a populations health-level, not the level itself. If addition, if justice (for example, desert) is a matter of the right, and I think it is, rather than the good, then this issue might be relevant to what governments and charities should prioritize, but not to what makes one populations healthier than another. The criteria by which these functions are to be evaluated are the following. Principle #1: Repugnant Principle. For a large population that is very healthy (10 billion), there is a much larger population (100,000 billion) every member of which has barely positive health that is healthier than the first population (Parfit 1984). For example, a massive population whose members are barely alive intuitively seems less healthy and a much smaller population all of whom are in the peak of health. Principle #2: Mere Addition Principle. If one adds an individual with positive health to the population without affecting the health of the original population, then the new population is at least as healthy as the original population (Parfit 1984; Arrhenius 2000; Tannsjo 2002; Rachels 2004). Intuitively, adding healthy people to the population cannot make it less healthy. Principle #3: Intrinsic Property. Whether an individuals health adds or subtracts from population health, and the degree to which it does so, depends on his health-level and not that of others (Parfit 1984). Consider, for example, ancient Egyptians (Parfit 1984). Whether an individual with positive health makes a population more or less healthy does not intuitively depend on how healthy the ancient Egyptians were. Principle #4: Arbitrary Principle. A populations health cannot depend on arbitrary facts. The idea is that neither an individuals nor a populations health-level cannot depend on an arbitrary fact. Principle #5: Across Board/Different Number Principle. If one population has greater total and average level of health relative to a second population and is more equal, then the first has greater health (Arrehenius 2000). This principle intuitively seems obvious, especially if total, average, and equality are the only ways by which to compare different populations level of health. Principle #6: Sadistic Principle. When adding people to a population without affecting its level of health, it is always better to add people with positive health than negative health (Arrhenius 2000a, 2000b). Adding individuals who are unhealthy should make a population less healthy than adding individuals who are healthy. Premise (P1) rests on the following. RepugnantMere AdditionIntrinsicArbitraryAcross BoardSadisticTotalismFailsCritical Level TotalismFailsFailsFailsFailsAveragismFailsFailsFails?FailsDiminishing Value FunctionFails (Ng)FailsFailsFails (Sider)Fails (Ng) Premise (P2) is trivially true. Let us turn to objections to this argument. Objections Here are some objections to totalism as a measure of a populations health-level. First, an objector might claim that we cannot rank individual health-levels in the way needed for the arithmetic function involved in totalism because there is no true zero point or no metric tracking a real property. This might be based on the property itself, boundary problems with the reference class, or arbitrary threshold for dysfunction or harm. If the antecedent is correct, then the consequent follows. It is not clear to me that the antecedent is correct, but a discussion of it will take us too far afield. A second objector might claim that the way in which we quantify health is relative to the quantifiers purpose. For instance, we might quantify health differently if we are deciding where to allocate resources or, alternatively, which population can better handle a blockade of food and medicine. The assumptions underlying the argument conflict with this objection. If disease is a real property that can be cardinally ranked for individuals and aggregation does not interfere with this type of ranking, then it follows than ranking populations health-levels does not depend on the purpose for the ranking. A third objector might claim that that intuitively it seems that you cannot make a population healthier merely by adding to it. Contra the objector, though, if the totalist account is correct, then this is a counterintuitive result entailed by the failure of rival theories. A fourth objector might assert that totalism entails the repugnant conclusion. Because this conclusion is obviously false, whether in the context of health, population well-being, or overall good, so is totalism, including totalism about health. As argued above, however, the repugnant conclusion follows from some very plausible conclusions, especially, the Modal Pareto Principle and transitivity. For any possible worlds x and y, if, from the standpoint of self-interest, x would rationally bepreferredto y by every being who would exist in eitherx or y, then x is better than y with respect to utility. See Huemer 2008. If one rejects the repugnant conclusion and the intrinsic, arbitrary, and sadistic principles, then population health cannot be ranked. This would make many public health decisions arbitrary and unprincipled. A fifth objector might assert that totalism treats individuals as are mere vessels for health (and, also, well-being). This objection is unclear but, in some sense, all the theories do this in that they treat individuals as having a health-level that feeds into a function and generates a population health-level. It is unclear why this is truer of totalism than other theories. A sixth objection is that averagism is an intuitively better model. Intuitively, when comparing two different-sized populations, the one with the higher average is healthier. This fails if one thinks that the above objections to averagism are fatal. A seventh objection is that totalism cannot handle infinite values. However, it is not clear that averagism can handle it either (average = total/population) given that division works differently for finite and infinite sums. For example, 1/3 of " is not smaller than ", whereas 1/3 of 9 is smaller than 9. In any case, this is a general problem for ethics in the context of the infinite and not a distinct problem for totalism. An eighth objection is that a ranking of populations health-levels should take into account actualism. Actualism is the theory that something is good only if it is good for someone and something is good for someone only if that person exists (that is, is actual). Actualism does not preserve transitivity and thus is implausible. For example, consider the following worlds. A blank box indicates that the relevant individual does not exist in that world. AliceBobCharlesWorld A21World B12World C21 Here A > B and B > C, yet C > A because in the two-world comparisons, the superior world has one person doing better and no one doing worse. Actualism also fails to properly rank worlds, one of which is clearly better than the other. Consider, for example, the following. AliceBethCathyAlBobCharley"World A111World B1100100100100 Actualism holds that A = B, but it intuitively is not. In any case, totalism can be combined with an actualist system as can the other theories, so this is not an objection to totalism, merely to a modal version of totalism. Here is a summary of the objections and my responses. ObjectionResponseIndividual health-levels cannot be ranked in the way needed for totalisms arithmetic function. This issue is too far afield.Health-quantification is relative to purpose. This is false if we can (1) quantify individuals health-levels and (2) aggregate them.Totalism entails that a population becomes healthier merely by adding individuals with positive health.This is an implication of totalism. Totalism entails the repugnant conclusionThis conclusion is made more plausible by the Modal Pareto Principle.Totalism treats individuals as are mere vessels for healthThis is not a distinct problem for totalism. Averagism is an intuitively better modelThis is false.Totalism cannot handle infinite valuesThis is not a distinct problem for totalism.Totalism conflicts with actualism. Totalism is consistent with actualism. In any case, actualism is false. Part Three: Thesis #2 Argument Here is the argument for Thesis #2 (Practical population health is best quantified via totalism). (P1) In practice, totalism about population-health is better than its competitors. (P2) If, in practice, totalism about population-health is better than its competitors, then practical population health is best quantified via totalism. (C1) Hence, practical population health is best quantified via totalism. [(P1), (P2)] Premise (P1) rests on the two assumptions. First, a cost-benefit analysis best allows for health-tradeoffs. The underlying idea here is that a cost-benefit analysis uses market valuation (price) to value things and the market valuation tends to track a goods or services contribution to individuals lives. This makes a cost-benefit analysis well-suited for tradeoffs. Cost-benefit analysis (CBA) does not fit as cleanly with the other theories. First, CBA values health above and below critical threshold in the same way, whereas critical-level totalism does not. Second, CBA values total health as well as average health. Consider, for example, that a demand curve in economics looks at the goods that will be purchased at a given price in a way that takes into account aggregate purchases at a continuum of prices. This aggregate purchases takes into account a populations size, preferences, and resources. CBA also values individuals higher (earlier) health-levels in the same way it values lower (later) health-levels. Note I assume here that any discounting (for example, discounting for present value) is epistemic. Even if it were not epistemic, CBA does not discount in a way similar to how diminishing-marginal-value theories do so. The critical-level and diminishing-value theorists might respond that CBA tracks what makes peoples lives healthier (or go well), but that the critical level theory instead tracks what makes a population healthier (or what makes the world a better place). If this is correct, then, on these accounts, CBA is not reliably tracking population-health. This might be correct, but it is true only CBA is an unreliable measure of population health. Premise (P2) is trivially true. Part Three: Implications Totalism in the context of quantifying health has some interesting implications. First, if one rejects the repugnant conclusion and the intrinsic, arbitrary, and sadistic principles, then population health cannot be ranked at all. This is truly repellant in that it makes it impossible for there to be a way to optimize the distribution of health-related benefits. Second, other things being equal (specifically, average health being equal), a larger population is healthier. Third, other things being equal (average and total health being equal), the health of a population is not affected by the degree to which individuals health-levels are unequal. Specifically, very healthy peoples health-level can counterbalance very unhealthy peoples health-level. Fourth, if totalism should reject actualism, future and possible individuals health-levels count as much as present and actual ones. Part Four: Conclusion In this paper, I argued that as a theoretical matter, population health-levels are best quantified via totalism. I argued that this model was better because it had less crippling objections. I also argued as a practical matter, population health-levels are best quantified via totalism. I then considered some objections to this theory. I argued that totalism fit better with cost-benefit analysis and that such an analysis was the best way to handle tradeoff issues in the real world.      PAGE \* MERGEFORMAT 1  See Tara Parker-Pope, Cancer Funding: Does It Add Up? New York Times, March 6, 2008,  HYPERLINK "http://well.blogs.nytimes.com/2008/03/06/cancer-funding-does-it-add-up/?_php=true&_type=blogs&_r=0" http://well.blogs.nytimes.com/2008/03/06/cancer-funding-does-it-add-up/?_php=true&_type=blogs&_r=0.  Sharon Begley, Think preventive medicine will save money? Think again, Reuters, January 29, 2013,  HYPERLINK "http://www.reuters.com/article/2013/01/29/us-preventive-economics-idUSBRE90S05M20130129" http://www.reuters.com/article/2013/01/29/us-preventive-economics-idUSBRE90S05M20130129. See, also,  HYPERLINK "http://content.healthaffairs.org/search?author1=Michael+V.+Maciosek&sortspec=date&submit=Submit" Michael V. Maciosek et al., Greater Use Of Preventive Services In U.S. Health Care Could Save Lives At Little Or No Cost, Health Affairs 29:9 (2010): 1656-1660.  See Copenhagen Consensus Center, Copenhagen Consensus 2012,  HYPERLINK "http://www.copenhagenconsensus.com/copenhagen-consensus-iii/outcome" http://www.copenhagenconsensus.com/copenhagen-consensus-iii/outcome, accessed )7/22/14.  Here is an explanation of how QALYs work. The QALY is a measure of the value of health outcomes. Since health is a function of length of life and quality of life, the QALY was developed as an attempt to combine the value of these attributes into a single index number. The basic idea underlying the QALY is simple: it assumes that a year of life lived in perfect health is worth 1 QALY (1 Year of Life 1 Utility value = 1 QALY) and that a year of life lived in a state of less than this perfect health is worth less than 1. In order to determine the exact QALY value, it is sufficient to multiply the HYPERLINK "http://en.wikipedia.org/wiki/Utility" \o "Utility" utilityvalue associated with a given state of health by the years lived in that state. QALYs are therefore expressed in terms of "years lived in perfect health": half a year lived in perfect health is equivalent to 0.5 QALYs (0.5 years 1 Utility), the same as 1 year of life lived in a situation with utility 0.5 (e.g. bedridden) (1 year 0.5 Utility). QALYs can then be incorporated with medical costs to arrive at a final common denominator of cost/QALY. This parameter can be used to develop a HYPERLINK "http://en.wikipedia.org/wiki/Cost-effectiveness_analysis" \o "Cost-effectiveness analysis" cost-effectiveness analysisof any treatment.  If, instead, justice is part of the good and it is a feature of individuals (for example, what an individuals health-level contributes to the populations health-level depends on what he deserves), then we still need to combine the individual values (albeit desert-adjusted ones) to an overall value. This will return us to considering these four theories, albeit with the values to be combined being desert-adjusted health-level rather than just individual health-level. If the justice determines the value of a population independent of its effect on an individuals health-related contribution to the population value, then other theories are needed. For now, I will ignore such theories in so far as I think they are a feature of the right rather than the good. To the extent someone rejects this notion, I fail to canvass all of the plausible candidate theories. It is also worth noting that I ignore theories of population health that reject transitivity.  For a discussion of these and other objections to these theories, see Arrhenius 2000a.  This does not fail if three assumptions hold true: Transitivity, Non-anti-egalitarianism, and Benign Addition Principle. Betterness is transitive. Ifx and y have the same population, but x has a higher average utility, a higher total utility, and a more equal distribution of utility than y, then x is better than y with respect toutility. If worlds x and y are so related that x would be the result of increasing the well-being ofeveryone in y by some amount and adding some new people with worthwhile lives, then x isbetter than y with respect to utility The three can be captured by the Modal Pareto Principle. For any possible worlds x and y, if, from the standpoint of self-interest, x would rationally bepreferredto y by every being who would exist in eitherx or y, then x is better than y with respect to utility. See Huemer 2008; Tnnsj 2002.  The critical level is arbitrary.  Consider a critical level of 10 health-level. One population (100 people with all with health-values of 8) can be worse than a second (25 people with 6 and 25 people with 8) even though the former has a higher average and total and, also, is more equal. PopulationSize (people)Average [Health units (H)/person]TotalAdjusted critical-level factor (# people x critical level/person)Overall value11008 H/person800 H1,000 H-200 H2507 H/person350 H500 H-150 H  Consider a critical level of 10 health-level and a population of 100 people with all with health-value average of 10. The population is worse off health-wise if 5 people with -1 health-level are added to the population (55 health-units worse) than if 30 people at +5 health-level are added (150 health-units worse). Original population (OP) SizeOP AverageOP TotalNew Population (NP) SizeNP AverageNP TotalCritical-Level Baseline TotalNet ValueWorld A100 people20 H/person2,000 H5 people-1 H/person-5 H1,050 H1,995 HWorld B100 people20 H/person2,000 H30 people+5 H/person150 H1,300 H830 H  Arguably, the boundaries of the population are arbitrary. For example, consider whether one should average over all past and future human beings, all past human beings, all human beings for the last 2,000 years, and so on.  The negative health peoples effect on the average might be less than the effect of the healthy people. Consider the following. 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The diminishing-value function is arbitrary.  For small populations, a population with a very high health number and three low ones might generate a greater total than a population with four health numbers, even when the latter population has a higher average and total. PersonAs Well-Being (utils)Value-Function (k = 0.5)Net AdditionBs Well-Being1100110075752800.54075383600.251575194400.1255759Total280160300141Average7075EqualityUnequalEqual  Here the health-value of a population is equal to the product of the average and the sum of value-function outcomes. In cases in which the average is lowered less by a few negative-health people than by more positive-health people and in which the population is large enough so the value of the population is mQ. Where m is a constant and the sum of the k-function values.  For a discussion of utilitarianisms difficulties with infinite value, see Vallentyne 1993, 1994, 1995; Cain 1995; Liederkerke 1995; Kagan 1997.  Arguments for actualism are discussed in (Bigelow and Pargetter 1988; Warren 1978; Parson 2002. Critical discussions occur in Carlson 1995; Arrhenius 2000b; Bykvist 1998, 2007b; Hare 2007; Howard-Snyder 2008.  The slogan is filled out in Narveson 1967: Glover 1977; Temkin 1993.  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