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?

  • 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 '19 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 '19 at 7:42
  • 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 '19 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 '19 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 '19 at 20:24

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.

  • 1
    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 '19 at 9:54

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


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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