Is it valid to talk about a smaller amount by referring to it as a multiple less than another number? It always feels wrong when I read something like "ABC is 3 times less likely than DEF", when it would make more sense to just say "ABC is a third as likely as DEF" or "DEF is 3 times more likely than ABC". Is the "3 times less" usage against any sort of math language rules, or just something I'll have to learn to live with?
 A: What does "three times less likely" mean?  The only natural interpretation I can give to it is to interpret it as "three times as unlikely".  That is:  if we can measure how unlikely an event is, it makes sense to compare the two events by using a ratio of unlikeliness.
For example, suppose $A$ is an event with a probability of 80%, so its unlikeliness -- that it, the probability that it doesn't happen -- is 20%.  If $B$ is a second event with a probability of 40%, then its unlikeliness would be measured at 60%.
Notice that in this example, if we focus on likeliness, we would say that $A$ is twice as likely to occur as $B$, or we could say that $B$ is half as likely as $A$.  But if we focus on unlikeliness, we would say that $B$ is three times as unlikely as $A$.
That is to say: "$B$ is three times as unlikely as $A$" and "$A$ is three times as likely as $B$" are both meaningful statements, but they do not mean the same thing.
All of these are meaningful ways of describing reality, and depending on what you are interested in, you might choose one or the other.  If you are trying to measure the risk of contracting an infectious disease, you might say that one population is at twice as much risk as another.  If you are trying to measure how safe you are from an infectious disease, you might say that one population is three times safer than the other.  (Personally I think the second formulation is less clear and more likely to be misunderstood, but it seems to be mathematically coherent, in this specific context.)
What's really wrong is when people use this verbal formulation to describe things that don't even make sense.  "Three times smaller" is the example that grates on me the most.  If building $A$ is 180 feet tall and building $B$ is 60 feet tall, it makes sense to say that $A$ is three times larger than $B$, or that $B$ is one-third the size of $A$, but "$B$ is three times smaller than $A$" doesn't make any sense at all.  How do you measure "smallness" of an object?  What is the reference point for "not at all small"?  "Three times smaller" is not just unclear, it's incoherent.
