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In a recent poll by the Albuquerque Journal, New Mexico voters were asked which candidate they support: 35% said Hillary Clinton, 31% said Donald Trump, 24% said Gary Johnson, and 2% said Jill Stein.
As these numbers suggest, if a significant share of Trump supporters were to vote for Johnson, then this would give Johnson a plurality of New Mexico’s voters, which by New Mexico law, would give Johnson all five of New Mexico’s electoral votes.
If the electoral vote among the other states is sufficiently close, this would cause no candidate to win a majority of the Electoral College, which would mean that the presidential race would be decided by the US House of Representatives. Should this happen, the Constitution requires House members to vote by state delegations, whereby each state only has one vote.
The latter rule severely disadvantages Democrats. It means, for example, that California’s 39 House Democrats are just as influential as South Dakota’s one Republican House member. Consequently, because House Democrats tend to be clumped in large states, if the House were given this power, Hillary Clinton’s chance of becoming president would be essentially nil.
Because of all these factors, as I’ll show in the analysis below, New Mexican voters can help Trump the most by voting against him. In the parlance of political science, I’m suggesting that Trump supporters in New Mexico, rather than voting “sincerely” for Trump, should vote “sophisticatedly” for Johnson.
To see why this is their optimal strategy, first recall that there are a total of 538 votes in the Electoral College. Thus, to win a majority, a candidate must win at least 270 of the votes. If the top candidate wins 269 or fewer, then the House, not the Electoral College, decides the election.
Next, suppose it is election night, and let us consider the electoral votes that have been cast by all the states other than New Mexico. One of four things must be true: A) Those states have cast more than 269 votes for Hillary. B) Those states have cast between 265 and 269 votes for Hillary. C) Those states have cast exactly 264 votes for Hillary. D) Those states have cast fewer than 264 votes for Hillary.
Now suppose you are a Trump supporter who resides in New Mexico. For each of the four possibilities, I want to examine whether your optimal strategy is to vote sincerely (for Trump) or sophisticatedly (for Johnson).
First suppose that A has occurred—that Hillary has won more than 269 electoral votes from the non-New Mexico states. Then Hillary wins the presidency no matter how New Mexico votes. Your decision to vote sophisticatedly or sincerely does not matter.
Similar logic applies if D occurs. In this situation Hillary has won fewer than 264 votes from the non-New Mexico states. Even if she wins New Mexico’s five electoral votes, she will have fewer than 269 and Trump will have at least 270. Thus, in this situation Trump wins the presidency regardless how New Mexico votes. Here again, your decision to vote sophisticatedly or sincerely does not matter.
The following should now be obvious: Your decision to vote sophisticatedly or sincerely is only relevant if B or C has occurred—that is, if the non-New Mexico states have cast between 264 and 269 votes for Hillary. Thus, to determine what is your optimal strategy, you need to condition your decision upon the latter event.
Let us now do that. Thus, for the remaining analysis, let us assume that B or C has occurred—that the non-New Mexico states have cast between 264 and 269 votes for Hillary.
Now, if the latter is true, then the national vote between Donald Trump and Hillary Clinton must have been close. This, in turn, implies that the expected purple states—which I define as Iowa, Ohio, North Carolina, Florida, Nevada, Colorado, Pennsylvania, Wisconsin, Virginia, and New Hampshire—have each voted approximately 50-50 in terms of their support for Trump or Hillary.
In the 2012 presidential election, New Mexico was at least a few points more “blue” than any of these states. That is, of these purple states, Romney received the smallest percentages in Wisconsin (45.9%) and Pennsylvania (46.6%), while his percentage in New Mexico was 42.8%. Because of the large Latino population in New Mexico, it is reasonable to believe that in 2016 New Mexico is even more blue, relative to the above list of purple states, than it was in 2012.
This leads me to my first assumption, one that I think is nearly certain to be true. This is that, if B or C has occurred (and thus the above purple states have voted near 50-50 for Trump and Hillary), then, in New Mexico, Hillary supporters will outnumber Trump supporters. Let me also assume that, consistent with the poll numbers from the Albuquerque Journal, Hillary supporters will outnumber Johnson supporters, but the sum of Johnson and Trump supporters will be greater than the total number of Hillary supporters. These assumptions imply that: (i) if all New Mexican Trump supporters vote sincerely, then Hillary wins the state, but (ii) if a significant number of New Mexican Trump supporters vote sophisticatedly, then Johnson wins the state.
Finally, let me define two probabilities. For the first, suppose that we know that B or C has occurred—that Hillary’s electoral votes from the non-New Mexico states is between 264 and 269. Given this, what is the probability that C occurs—that, from those states, Hillary’s electoral votes are exactly 264? Define this probability as p. Note that one reasonable way to estimate p is simply to note that, if B or C has occurred, then Hillary’s electoral vote from the non-New Mexico states must be one of six numbers: 264, 265, 266, 267, 268, or 269. If all six numbers are equally likely, then p must be 1/6, i.e. about .17. However, I have run some simulations (where I assume that all “red” states vote for Trump, all “blue” states vote for Hillary, and all purple states vote randomly). These simulations suggest that a more accurate estimate of p is something like .32.
For the second probability, suppose that the House is tasked with deciding the president, and Trump, Hillary, and Johnson have all received at least one vote in the Electoral College. More specific, suppose that Gary Johnson has won the five electoral votes of New Mexico and neither Hillary nor Trump have won more than 269 electoral votes. The Constitution specifies that, if this were to happen, then the House must choose among the top five vote-getters in the Electoral College. According to the scenario I’m painting, only three candidates have received electoral votes. Thus, the House would have to choose among Trump, Hillary, or Johnson. Define q as the probability that the House chooses Trump in such a scenario.
As I’ll show, if q is greater than p, then the optimal strategy for any New Mexican Trump supporter is to vote sophisticatedly for Johnson.
To see why this is true, first suppose that New Mexican Trump supporters vote (sophisticatedly) for Johnson. If the above assumptions are true (including that event B or C has occurred), then this strategy causes Johnson to win New Mexico. It also means that no candidate will have won a majority of electoral votes and thus that the House must decide between Trump, Hillary, and Johnson. According to my definition, this strategy gives Trump a probability of q of winning the presidency.
Now suppose, in contrast, that all New Mexican Trump supporters vote (sincerely) for Trump. Then, according to my assumptions, this causes Hillary to win New Mexico and gain its five electoral votes. If B is true, this gives Hillary a majority of electoral votes and she becomes president. If C is true, then this causes the electoral vote to be 269 for Trump and 269 for Hillary. Since no other candidate receives electoral votes, the House must choose between Trump and Hillary. According to my assumptions, this means that Trump wins for certain. Thus, the probability that Trump wins is the probability that C occurs given that B or C has occurred. According to my definition, this probability is p.
In sum, (assuming that B or C has occurred) if New Mexican Trump supporters choose a sophisticated strategy, then they cause Trump’s probability of winning to be q. But if they choose a sincere strategy, then they cause his probability of winning to be p.
Thus, if q is greater than p, the optimal strategy for Trump supporters (in New Mexico) is to vote sophisticatedly.
Finally, recall that I think .32 is a reasonable estimate for p. What is a reasonable estimate for q? Recall that this is the probability that the House chooses Trump, given that it must choose from Trump, Johnson, or Hillary. Given the Constitutional rules—most important, that the House votes by state delegations—I believe that Hillary’s chances would be essentially nil. But what about Johnson’s chances? I asked a friend who is a senior campaign consultant for several Republican members of the U.S. House. He responded that “Johnson is a clown” and that “zero” Republican House members would vote for him. I suspect that my friend was engaging in hyperbole when he gave that answer, but still I think there is much truth to it. I accordingly think a reasonable estimate for p is something like 95 or 99%, and it’s possibly as high 99.9%.
If so, p is much greater than q. If this is true, it means that Trump supporters in New Mexico would be wise to vote sophisticatedly.
Strangely, the way they can best help their candidate is to vote against him.Published in