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Politicians and journalists are two professions that are known to be easily confused by numbers.  The consequences of that confusion are on full display during this election cycle in the U.S.  Real estate people cannot afford to be confused by numbers, either because lenders will not allow them to go over budget or because the personal costs of getting the numbers wrong is scary.

This post uses some examples of the more annoying examples of innumeracy to show that, although a math class does not look like a class in literature, numbers convey meaning.  That meaning is enhanced by making good comparisons.

“Some” vs. “All” vs. “Most” vs “A few”

Clinton got into trouble for saying that about half of Trump’s supporters were deplorables.  The response by Clinton’s opponents was to claim that Clinton implied that all of the people who supported Trump were deplorable, so you should vote against Clinton.  Nobody thinks of themselves as deplorable.  The slippage between “about half”,  “all” and “none” shows the imprecision of words.

The same issue applies to any attempt to enforce “extreme vetting” of potential immigrants for being terrorists.  While we can agree that some people are not good, “some” is not “all”.  Any test is likely to be imperfect.  So, the only solution which eliminates all risk from a few is to exclude all, without a clear definition of “a few”.

The lesson is that numbers matter and words can be slippery.  This conclusion would be obvious in other situations.  Before giving out some of its money, a bank wants to see clear evidence that it will be repaid.  Before hiring somebody, you want clear evidence of performance.  Saying that “I increased sales by some amount” sends a different message than “I increased sales by 15 percent in one year.”

Skittles

Candy companies usually do not intend to get involved in election campaigns.  This year, it was Tic Tacs and Skittles.  Skittles were used by Eric Trump to illustrate the dangers of immigration.

To start, I note that many people are intimidated by numbers.  (As an aside, that has two implications.  First, if you are intimidated, get over it by using any of the many resources which are available.  Second, if talking with an individual or group who may be intimidated, using a colourful example is good advice.  Making an idea personal is often persuasive because it is seen as relevant and memorable.  A lesson conveyed by this moment is that “persuasive” is not always “accurate”.)

A comparison was made between the willingness to allow dangerous immigrants into the US and eating Skittles, when three were known to be poisonous.  It was quickly noted that, to be accurate, the risk implied by 3 needed to be compared to many billions of Skittles.

This is a great example of having a sense of numbers: specifically in terms of relative quantities.  Without knowing if a specific number is right or wrong, having this sense shows if you are close.

The unstated comparison with three has other problems deeply connected to decision making in an uncertain environment.

Suppose that you know that the poisonous Skittles (i.e. dangerous immigrants or whichever market segment you think that want to target) are the red ones.  Then there is no problem; they are easy to identify.  The problem is that some of the green ones and yellow are also poisonous (e.g. gun deaths or car accidents).  These kinds of comparison lead to a question: which is more important?

Finally, as a decision problem, maybe Skittles taste so great that you are willing to risk death.  A more sophisticated solution would be to marry a doctor as a contingency plan: if you do eat one of the poisonous ones then they can revive you.

Number sense features prominently when companies need to manage their risk: admitting the size of the problem is a necessary first step.

Election math

It has been very interesting to observe how the analysis of elections by the media has evolved over the last 10 years or so.  The catalyst for change was the success of Nate Silver of http://fivethirtyeight.com/. He advocates working with numbers carefully and uses statistics in ways which are not too much more sophisticated than is taught in a mid-level stats class.

To start, remember that the President of the United States is chosen not by popular vote but by the Electoral College.  The media like to talk about how the popular vote moves from week to week or in response to a specific event.  It is always relatively close: 48 to 42 or 46 to 43 or ….  When people estimate the vote in the Electoral College, most calculations are much less close.

This example show how small changes can have big effects.  It illustrates the Black Swan effect of Taleb.  That is the scary part of the real estate business, yet that is where the focus should be.

PA

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