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Do percentages of negative things in a given sample matter more or less than the quantity of negative things? And is there a name for this concept? Is it some sort of fallacy to appeal to percentages?

Consider the argument that the issue of human slavery is better today than in the past because the percentage of people in slavery relative to the human population has gone down over time. However the total number of human individuals who are slaves has increased over time. This has happened because of population growth, such that there are more slaves today than there have ever been in human history even though the percentage of people who are slaves is lower than previously.

My feeling is that if you see the decline in the percentage of slavery as a positive while at the same time ignoring the increase in the number of slaves you are missing something in the moral equation but I can't point to what that specific logic is. Does this have some connection to and change based on what moral framework it is seen through?

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    Yes and No. The use of statistics is very broad and I would say is more often tied to a wanted perception of an issue, rather than the morality of a subject. For example, you could argue that slaves are morally wrong. But depending on which statistic you present, you can sway the opinion of readers to show that there has been a great amount of work reducing slavery, or that slavery is running more rampant than ever before. Neither of these statistics justify the morality of owning a slave.
    – Shadowzee
    Aug 14, 2019 at 5:34
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    What "matters more" begs the question: matters to whom? to what purpose? Basing ethical considerations on statistics is derided by some authors as "moral arithmetic", while others see it as a valid basis for arriving at unbiased conclusions. Selecting evidence that favors one's point of view, while overlooking contrary evidence, is called cherry picking, but it is not specific to what you describe. Clearly, we should aim at complete eradication of slavery (or racism, or measles, etc.), but percentage decrease is still an indication of progress.
    – Conifold
    Aug 14, 2019 at 7:42
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    Is a percentage decrease an indication of progress when the total quantity increases? I guess that is the question I am trying to get at. If we are trying to assess whether we have made progress in something or gone backwards what are we to make of a percentage decrease but a quantity increase? What tools can philosophy provide to understand this and make an assessment? Obviously the goal is to reach zero quantity and if percentage decreases and total quantity decreases everyone would agree that progress has been made.
    – Roy
    Aug 14, 2019 at 9:39
  • However in the other case I feel like there is a mixed opinion. Some people would say a percentage decrease is obviously progress and others might say "but more people than before are suffering now, this is not progress". How does the birth of more humans (increasing the sample size) change the perception of progress?
    – Roy
    Aug 14, 2019 at 9:39
  • Yes. In fact, the mistake is more often made the other way: people look at absolute numbers in a vacuum, without contextualizing them or relating them to anything. Improvement can not happen on every possible measure, people you mention do not disagree, they just interpret "progress" differently and talk past each other. Opposition to births is called anti-natalism, and is a small minority position. Taken to its logical conclusion, the surest way to get rid of slavery is to have the humanity go extinct.
    – Conifold
    Aug 14, 2019 at 20:24

6 Answers 6

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To enlarge perhaps on @shadowzee's comment:

Statistics is a mathematical tool which allows for example valid conclusions to be drawn from small samples drawn from large populations, while offering measures of confidence in those conclusions based on the relative size of the sample.

As such it is value-neutral in the sense that it is silent on the ethicality or desirability of the outcomes it lets us quantify and/or predict.

In other words, there are statistical tools which let us accurately quantify the relative prevalence of slavery in the world at different points in our history, while at the same time furnishing us with no guidance on the ethicality of this practice.

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    The question I wish to ask is not whether statistical tools can provide us with ethics guidance. It is also not about the ethicality of a practice which in this case is assumed to be agreed upon by all (that slavery is wrong). If all parties agree that the aim is to reduce slavery how might they interpret their progress after doing some work (changes to society, economics, laws etc) if the percentage of slaves goes down but the total number goes up? Sorry if I wasn't clearer.
    – Roy
    Aug 14, 2019 at 9:54
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There are various ways to misuse statistics. People listening to arguments using statistics as evidence need to be cautious. Wikipedia describes this misuse as follows:

Statistics are supposed to make something easier to understand but when used in a misleading fashion can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy.

Using a percentage rather than the actual data is for convenience. It is easier to view a ratio (percentage) than both numbers making up that ratio. However, the actual numbers may be what is important in an argument. If that is the case then relying on the ratio is deceptive.


Wikipedia contributors. (2019, August 7). Misuse of statistics. In Wikipedia, The Free Encyclopedia. Retrieved 13:32, August 14, 2019, from https://en.wikipedia.org/w/index.php?title=Misuse_of_statistics&oldid=909781441

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For an individual, yes, the percentage matters more. For the world, maybe not. And which of these two is more important can indeed depend on your moral framework.

The reduced percentage speaks to the fact that an arbitrary individual is less likely to be affected by the problem. In a utilitarian sense, that is what matters -- the affect of the problem on the happiness of an arbitrarily chosen individual.

In a more absolute sense, just reducing something truly awful to a very small percentage does not mean it is dealt with. While one person still had smallpox, it could still grow back to a real threat to public health. The percentage mattered a lot to a lot of people, but it was not ultimately what mattered. Only once the problem was solved, was it solved.

More absolute forms of ethics, like deontology sometimes think this way. You have a duty to find ways to eliminate reasons for anyone to meet with certain kinds of violation, and make them stick. In this case, we can't just be happy when there are zero slaves, but we need to keep pressing until we have made it virtually impossible that it should ever arise again. Ideally, we would continue reshaping society closer and closer to the point where slavery would not extend anyone a usable advantage (as long as we could do so in line with other rights, protections and duties.)

(This is one of the reasons everyone needs both of these ethical perspectives and should not choose between them, in my own opinion. I think there are real biological drives underlying both of these approaches to ethics.)

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  • For the individual percentages don't matter, what matters is whether you are or aren't a slave.
    – haxor789
    Sep 28, 2022 at 9:52
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It kinda depends on the details of the statistics, your hypothesis on the issue and the ethical framework that you apply and your own position in that situation.

Assume you have a non-contagious disease and you're literally the only one in the entire observable universe that has that disease. Now if I conduct a study with 2 participants (you and someone else) then 50% are infected. If I ask 100 participants it's only 1% and so on. So despite the same number of people alive and the same number of people infected, depending on the sample size you'd get a different estimate of how many people are infected.

Likewise one should be careful with the actual distribution of cases, like just because something decreased moderately in one place doesn't mean it's a good thing if it massively increased in another, raising rather than lowering the sum total.

But even if we assume that this percentage is perfect information, the distribution would still matter in terms of the question how to react to something. Whether it's peaking in one place or is uniformly distributed. Because if you distribute mitigating means uniformly to a localized problem than most places will have resources they don't need while the place that needs it will end up being short on them. Or vice versa you obliterate a problem in one place but the rest is short on even the basics.

Also the sum total of cases determines as to whether it's feasible to deal with that on the level of the individual (person or case) or whether you're in need of painting with a broader brush. Like is it a single act of criminal conduct or is it some larger pattern or even an inherent problem of the system itself?

So if it is 50% of a group but only 5 people you could have a group discussion or 5 1on1 talks, if it's 50% of millions of people distributed all over the place that is way more difficult to accomplish and having other people that share your problem can itself have consequences that range from bettering to worsening the situation.

So statistics can be tremendously helpful when you're trying to get an overview and when you're free to choose the parameter that you want to look for. But they are estimations, they are often incomplete, you have to be vary careful to look at sample sizes, methodology and what they actually want to and are able to accomplish, and they can be interpreted in various ways so often enough one statistic just prompts you to conduct even more statistics to check the hypotheses that you had constructed after reading the statistic.

Now in terms of human slavery you could for example ask the question of "Is it necessary?". Meaning does any society rely on a subset of that society to do unfree and exploitative labor and is it only a matter of who ends up doing it? Like some sort of trolley problem, where you have a no win situation and someone is going to end up in a bad place. So in that regard reducing the percentage of slaves would be a positive because it means that the situation improved so much that fewer slaves are required to make a society work and that the increase just comes from the population growth.

However that comes with several caveats. First of all it would obviously only require work to be done it wouldn't require slavery. Like nothing in that scenario forces you to force people to do something without freedom, against their will and under exploitative conditions. You might as well ask politely. Like the existence of society often is a net benefit for it's members and it's not impossible for members of a society to personally cut back on luxury and instead invest in a collective improvement that pays out in the future. So even if we assume the "benevolent slave owner" who only does it for the greater good, that person would still not really be benevolent and there's a good chance he's still just doing it to enrich himself and his peer group.

So the argument that slavery is necessary doesn't really work and the decrease in percentage is less likely to be emblematic of a change in necessity and rather of a change in acceptance. Meaning the increasing absolute numbers are still more important and more concerning.

The other question is "did the other parameters remain the same?". Like how was that reduction of slavery in percentages accomplished? Did the conditions for the slaves improve, stay the same or became worse?

So is it more people but less brutal or is it fewer people and even more brutal? Or did the quality of torture remain the same? Is it better to sacrifice the few to save the many and is what they are saved from a minor inconvenience or an existential threat? Or should you place yourself in the role of that individual (categorical imperative) and argue that if that is unbearable for a human there should never be a universal law that mandates or even allows for that? Then the percentage just gives you a scope of the problem but every single one is one too many and a preventable problem. So an increase in absolute numbers is worse and more important than a decrease in percentage.

And there are probably a lot more perspective that you can take on that and ways how you can read such a statistic and what about it matters or matters more given a specific context.

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The answer to your question is not really a matter of philosophical outlook. Absolute and percentage figures are two complementary perspectives, and usually presenting one without the other leads to a partial and potentially misleading view of the subject.

Suppose I were to tell you that my darts playing has improved enormously overnight, as yesterday I scored only one bullseye, whereas today I scored fifteen. You cannot make any sense of my claim unless I tell you how many times I tried to hit the bull on each day. The absolute number of bullseyes is meaningless by itself.

There are cases, such as my darts example, in which percentages are more important, and cases in which the absolute numbers are more important, depending on what you are trying to assess.

In the case you mentioned, the two statements 'The number of people in slavery is higher than ever' and 'The percentage of people in slavery is lower than ever), are both true. Whether you stress one or the other depends upon what point you are trying to make. An increase in percentage shows that progress has been made relative to the overall size of the problem. The absolute number in slavery shows the size of the problem still to be addressed.

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Me two cents worth ...

Hypothetical Scenario

City: Los Angeles
Year: 1800
Population: 100,000
Slaves: 30,000
Percentage slave: 30%

City: Los Angeles
Year: 1900
Population: 10,000,000
Slaves: 300,000
Percentage slave: 3%

By absolute figures, the slave population has increased from 30,000 to 300,000, by a factor of 10.

By relative figures (percentage), slave population has decreased from 30% to 3%.

Conflicting figures.

Did the situation get better/worse?

  1. Use the 1800 percentage on the 1900 population
    30% of 10,000,000 = 3,000,000. By 1800 "standards" there should be 3,000,000 slaves in 1900. We have "only" 300,000.

  2. Use the 1900 percentage on the 1800 population 3% of 100,000 = 3,000. By 1900 "standards" there should be only 3,000 slaves. Compare that to 30,000 slaves observed in 1800.

The point to relativizing numbers (as with percentages) is to make the comparison legit. If Los Angeles were given 100 people in 1800 and exactly the same number of people, 100, in 1900, how many of them would Angelenos make slaves in each of those years.

That's the best I could do.

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