A Classic Example of How to Lie With Statistics

The March 3 Republican debate showcased a classic example of how to lie with statistics.  (Note: No partisanship here; it was all Republicans attacking Republicans.  No matter who says it, however, lying with statistics is still lying.)

Senator Rubio kicked off a marathon lesson in how to lie with statistics fairly early in the debate when he attacked Donald Trump by stating: “Two-thirds of the people who have cast a vote in a Republican primary or caucus have voted against you. They do not want you to be our nominee.”

What a classic!  Rubio’s statement starts with an accurate statistical fact and then spins it into deceitful story line that is not supported by the facts he cites.  Let’s look deeper.

The factual statistic at the heart of Marco Rubio’s incredibly dishonest statement is that while Donald Trump has been “winning” (to use the dominant media term) most primaries, he has not won a majority of the votes cast.  Instead, he won a plurality – the largest slice of the vote pie but still less than a majority of all votes cast.  In a multi-candidate field, a 30% to 40% share of the pie is frequently enough to be declared the winner.  Senator Rubio would have been entirely truthful if he had pointed out that Donald Trump only won a plurality of the vote, not a majority.  Senator Rubio even would have been 100% correct had he stated, for example, that “you have received well less than half the votes” or that “taken as a group, the candidates opposing you have won more votes than you in every primary held so far.”  That second version is a bit tortured, but still entirely accurate.

Rather than making statements entirely supported by the statistics he cited, however, Mr. Rubio chose to draw – and attempt to convince viewers to draw – a conclusion that is completely unsupported by the statistics he cited.  To reach his conclusion that “[t]wo thirds of the people who have cast a vote in a Republican primary or caucus have voted against you,” Rubio made the assumption that every person who voted for another candidate specifically voted against Donald Trump.  While it may seem somewhat logical that if you don’t vote “for” someone then you vote “against” him or her, that is not necessarily true in a multi-candidate race.  In a multi-candidate contest, a random voter may have had a very hard time deciding between Mr. Trump and one of the other candidates, but, in the end, wound up voting for the other candidate.  This hypothetical voter did not vote against Mr. Trump but for someone else.  If his or her favorite candidate later drops out, our hypothetical voter may well transfer his/her loyalty to Mr. Trump.

I may be stepping into a mine field here by moving from statistics and logic to religion, but perhaps Mr. Rubio hoped that his comments would remind religious Christian voters of Matthew 12:30, which states “Whoever is not with me is against me…”  Matthew was not referring to politics when we wrote that quote, and he certainly was not talking about a multi-candidate primary race!  Matthew’s observation might have some applicability to a U.S. general election in which only two candidates have a realistic chance of winning.  In early primary voting among a multitude of candidates, however, it is entirely likely that many voters have a 1st choice, 2nd choice, 3rd choice and so on and that those choices are only narrowly separated in their minds.  In such cases, a vote for one candidate is not a vote “against” the others but simply for the person at the top of a list.

Based on my own ‘gut feeling’ (which has no statistical significance) and a look at numerous polls attempting to measure not only which candidates Republican voters support but which candidates they most strongly oppose, there is no doubt that a number – probably even a big number – of Republican voters genuinely “oppose” Mr. Trump and would support any other candidate besides him.  Not one of those polls, however, supports Marco Rubio’s contention that every person, 100% of them, who favored another candidate in a primary or caucus chose that candidate because they oppose Mr. Trump.

Another way to highlight the faulty logic behind Senator Rubio’s claim would be to apply the same logic to Mr. Rubio’s own showing in the primaries and caucuses that have been held to date.  That same false logic that leads to the conclusion that two-thirds of Republicans “voted against” Donald Trump would also lead to the conclusion that over 85% “voted against” Senator Marco Rubio.  Ouch!

Unfortunately for him, the normally quick-witted Donald Trump seemed to fail to zero in on the source of the lie – the disconnect between statistical fact and utterly false assumption that every vote he failed to win as a vote against him – at the heart of Senator Rubio’s charges.  As a result, Trump’s initial rebuttal was so confusing as to be difficult to analyze.  Rather than focusing on the deception at the heart of Rubio’s charge, the exchange devolved into a meaningless exchange of random poll numbers about how each candidate might fare in a hypothetical match-up with Hillary Clinton.  Given how incredibly variable and inaccurate such polls are this far out from the general election, it is entirely unsurprising that each candidate participating in this pointless exchange (Rubio, Cruz, Kasich) was able to cite “polling data” purporting to show that he would do better against former Secretary Clinton in a general election.  I have not bothered to fact check the polls each cited since that type of poll means nothing at this point in the contest.

Much later in the debate, Senator Cruz essentially launched the same attack – based on the same unstated faulty and misleading assumptions that allowed Rubio to go from statistical facts to an outright lie.  By that time, however, Mr. Trump seemed to have zeroed in on the core fallacy at the heart of the argument and used it to turn the tables by noting that, by Mr. Cruz’s own logic, the fact that Cruz polled just 15% in some poll means that 85% of voters are absolutely opposed to him.  Typical for the entire debate, the ensuing exchange was a bit garbled as candidates yelled over each other, but in the melee it seemed clear to me, at least, that Mr. Trump had grasped the fundamental fallacy in the argument presented by both Senator Cruz and Senator Rubio.

Postscript:  Just to be clear:  this is not a political argument.  I am not trying to tell anyone who to support.  Instead, I just found it interesting how such a classic example of “how to lie with statistics” popped up in the March 3 Republican debate.  There were many other lies told that night, but I won’t go into those.  As someone who is a student of statistical reasoning and its abuses, however, I found that particular exchange in the debate highly amusing.

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