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I feel the phrase "more likely than not" is often seen or heard here and there, sometimes in a sentence, other times just the phrase alone like the following ones.

"More likely than not" a COVID-19 vaccine is possible, Fauci tells Senate
https://arstechnica.com/tech-policy/2020/05/fauci-adequate-response-needed-to-reduce-deaths-from-covid-19-rebound/

More Likely Than Not? This is Scientific?
https://www.econlib.org/archives/2013/12/more_likely_tha.html

I am now curious about:

  1. How likely is it for you in percentage terms? (My perception is somewhere between 51% and 55%)

  2. Is there any phrase describing exactly the opposite, which implies a probability level of around 46% to 49%, for example? Any such phrase especially in a similar word combination like "less likely than xxxxx", if any?

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"More likely than not" logically means with a probability greater than 50%. A probability of 50% would be "as likely as not".

But the user of the phrase is not making a mathematically precise estimate of probability. They are expressing what they think is likely in an intentionally vague way, and it's misplaced precision to try to assign a number to it.

As an opposite, one could simply say "unlikely" to mean a probability of less than 50%. Or, given a proposition A, one could say "It's more likely than not that A is false."

I guess you could say "less likely than not", but I've never heard that.

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  • Thanks, Jack. I'm now wondering if the intentional ambiguity leaves open a possibility of both 51% and 95%. Maybe 95% possibility is highly unlikely, don't you think? And this is the point of my question. A research paper that I found (1) says, "*it need not be much higher than 50%; the phrase is generally understood to import only a slight preponderance.", so I just wanted to confirm if it is the general understanding of many native English speakers, but I now feel I should stop digging into it. (*1) papers.ssrn.com/sol3/papers.cfm?abstract_id=3281040
    – Takashi
    Jul 28, 2020 at 10:48
  • Takashi, even the phrase "slight preponderance" is vague. If those using "likely" about legal outcomes meant "60 to 75%", they could say that; but they don't. Table 2.1 in the paper you mention shows "mean numerical probability range" associated with the use of particular words, that is, even from a study of uses of the words, they can't state an exact number. They say "Even experts interpret probability words differently". That's in a legal field where they say there is some importance to the question. Established meanings don't exist.
    – Jack O'Flaherty
    Jul 28, 2020 at 11:10

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